Signal analysis method and system based on laplace-decay envelope quadratic convolution

Abstract

The application relates to the technical field of one-dimensional time sequence signal analysis, and provides a signal analysis method and system based on Laplacian attenuation envelope quadratic convolution.The signal analysis method based on the Laplacian attenuation envelope quadratic convolution comprises the following steps: segmenting, normalizing and channel aligning a one-dimensional time sequence signal to obtain an input tensor; calling at least one layer of a Laplacian attenuation envelope quadratic convolution layer to perform feature extraction on the input tensor; and obtaining a classification result / abnormality detection result through a classifier / detection head from the features extracted from the input tensor, so that the problems that a conventional convolution kernel has weak interpretability, a structured convolution kernel has insufficient discrete frequency domain control capability, and a lookup table is difficult to efficiently reuse when a low-bit-width deployment is performed can be solved.

Description

Technical Field

[0001] This invention relates to the field of one-dimensional time-series signal analysis technology, and in particular to a signal analysis method and system based on Laplace decay envelope quadratic convolution. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In existing technologies, conventional one-dimensional convolutional layers typically extract features by learning weights at discrete locations within the convolution kernel. The parameter size increases with the number of input channels, output channels, and the kernel length. When processing long-range or multi-channel signals, conventional convolutional layers usually directly learn weights of a fixed length. The number of parameters in a convolutional kernel increases linearly with the number of input channels, output channels, and kernel length, which easily leads to problems such as parameter redundancy and overfitting. Furthermore, due to the lack of explicit priors, the phase characteristics, center band preference, and bandwidth variations of the convolutional kernel are often difficult to explain directly from the parameters themselves. To improve these situations, existing technologies have proposed various structured convolutional kernels, such as those based on the Sinc function, Gabor function, cosine function, or learnable time-frequency transform. While these schemes can constrain the shape of the convolutional kernel with fewer parameters, most still employ a technique of first generating discrete convolutional kernels in the time domain and then performing ordinary convolution or numerical FFT on them. In other words, there is usually a lack of a direct, stable, and precisely controlled analytical mapping relationship between the convolutional kernel parameters and the discrete frequency domain response. Additionally, in long sequence scenarios, if FFT acceleration is used, it is often necessary to repeatedly perform frequency domain transform calculations on each instantiated convolutional kernel to obtain the corresponding frequency domain response, resulting in high training and inference costs and impacting the internal performance of the computer.

[0004] On the other hand, with the increasing demand for deploying one-dimensional time-series signal analysis models on edge devices, low-bit-width quantization has become an important technical means to reduce model storage overhead, memory access pressure, and computational power consumption. Existing low-bit-width deployment schemes typically quantize discrete convolution kernel weights directly, which leads to a significant performance degradation at low quantization bit widths (such as 4 bits). Especially in edge deployment scenarios for signals such as EEG and ECG, the accumulation of inter-layer errors, memory access pressure, and power consumption constraints further amplify these shortcomings. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a signal analysis method and system based on Laplace decay envelope quadratic convolution. While ensuring high fidelity of signal morphology, it significantly reduces the storage overhead of edge computing terminals and is suitable for efficient classification and early warning of one-dimensional time-series signals.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of the present invention provides a signal analysis method based on Laplace decay envelope quadratic convolution.

[0007] A signal analysis method based on Laplace decay envelope quadratic convolution includes: The one-dimensional time-series signal is segmented, normalized, and channel-aligned to obtain the input tensor; At least one Laplacian decaying envelope quadratic convolutional layer is invoked to extract features from the input tensor; The features extracted from the input tensor are processed by a classifier / detection head to obtain classification results / anomaly detection results; Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used as the scaling parameter. Based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points using the amplitude parameter, scale parameter, and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantization inference mode, the scale parameter is quantized into an index. The unit amplitude half-wave template corresponding to the index is read from the template lookup table. Then, the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

[0008] As one implementation method, the Laplace decay envelope quadratic convolutional layers are grouped according to odd kernel lengths, and layers with the same odd kernel length are grouped together. The layers share the same template lookup table, where the first... Group lookup table contains only One template item, This decouples template storage from the number of channels; This represents the number of bits used for the unsigned quantization of the scale parameter.

[0009] As one implementation method, the template lookup table is constructed as follows: The scale parameter is applied... Bit-unsigned quantization, quantization scaling factor is ,in Represents the maximum value of the scale parameter of all Laplacian decay envelope quadratic convolutional layers; for each quantization index and each center offset Establish unit amplitude template ,in , To prevent positive numbers from being divided by zero; and only store The half-wave template is used to obtain a complete symmetrical convolution kernel by mirroring.

[0010] As one implementation method, the batch normalized parameters after the Laplacian decay envelope quadratic convolutional layer are first fused into the convolutional parameters before quantization inference, satisfying... ,in and They represent the first The amplitude and bias parameters after layer fusion These are the smallest positive constants used to ensure numerical stability. , , and These correspond to the scaling factor, bias, running mean, and running variance of the batch normalization layer, respectively. Obtained by layer-by-layer symmetric quantization .

[0011] As one implementation method, the pre-activation quantization scaling factor for each layer is determined using the Kullback-Leibler divergence minimization approach. Block output quantization scaling factor and according to as well as Perform fixed-point recalibration. The relevant parameters are defined as follows: and The first Layer-specific recalibration multipliers and recalibration biases; For the first Floating-point bias of the layer, This is the shift bit width; , as well as Corresponding to the first Layer amplitude quantization scaling factor, template lookup table quantization scaling factor, and input quantization scaling factor.

[0012] As one implementation method, the first The first Laplacian decay envelope quadratic convolutional layer The pre-activation values ​​for each output channel satisfy: ,in, , Indicates the previous level. The output sequence of each input channel Indicates the first Number of layer input channels Indicates the first Layer output sequence length; the convolution kernel satisfies Thus, the corresponding discrete frequency domain response satisfy ,in This is the zero-phase real even amplitude term.

[0013] As one implementation method, the zero-phase real even amplitude term Determine using the following formula: , , , , ; in, Indicates the first Layer The input channel to the first The envelope scale parameter of the convolution kernel for each output channel. This represents the envelope attenuation factor corresponding to the scale parameter; Indicates the first The length of the single-sided support interval of the convolutional kernel; The order of the space moments is represented by . Indicates the corresponding The complex frequency domain response term of the first-order space moment; This represents the magnitude normalization coefficient of the convolution kernel; Indicates the first Layer length is Discrete angular frequencies of discrete Fourier sampling points. This represents a complex exponential base with radial decay. This indicates taking the real part of a complex number.

[0014] As one implementation method, calculation A two-branch stable evaluation mechanism is used: when At that time, a rational expression based on truncated geometric power sums is used to calculate... and ;when When using cosine series Evaluate, where This is a preset stability threshold.

[0015] A second aspect of the present invention provides a signal analysis system based on Laplace decay envelope quadratic convolution.

[0016] A signal analysis system based on Laplace decay envelope quadratic convolution includes: The input tensor calculation module is used to segment, normalize, and channel-align a one-dimensional time-series signal to obtain the input tensor. The feature extraction module is used to call at least one Laplacian decaying envelope quadratic convolutional layer to extract features from the input tensor. The feature mapping module is used to extract features from the input tensor and pass them through a classifier / detection head to obtain classification results / anomaly detection results; Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used as the scaling parameter. Based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points using the amplitude parameter, scale parameter, and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantization inference mode, the scale parameter is quantized into an index. The unit amplitude half-wave template corresponding to the index is read from the template lookup table. Then, the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

[0017] A third aspect of the present invention provides a signal analysis device based on Laplace decay envelope quadratic convolution.

[0018] In one or more embodiments, a signal analysis device based on Laplacian decay envelope quadratic convolution includes: a signal acquisition module, a storage module, a processing module, and a result output module; the storage module is used to store network parameters and at least one Laplacian decay envelope quadratic convolution template lookup table; the processing module is connected to the signal acquisition module, storage module, and result output module; The signal acquisition module is used to acquire one-dimensional time-series signals; The processing module is configured to perform the steps in the signal analysis method based on Laplace decay envelope quadratic convolution as described above. The result output module is used to output classification results / anomaly detection results.

[0019] In other embodiments, a signal analysis apparatus based on Laplace decay envelope quadratic convolution includes: The signal analysis device based on Laplace decay envelope quadratic convolution includes: a signal acquisition module, a preprocessing module, a processing module, a quantization module, and a deployment module; The signal acquisition module is used to acquire one-dimensional time-series signals; The preprocessing module is connected to the signal acquisition module and is used to perform segmentation, normalization and alignment operations on the one-dimensional time series signal in sequence to obtain the input tensor. The processing module is connected to the preprocessing module and is used to construct and train at least one Laplacian decaying envelope quadratic convolutional layer and a classifier / detector head based on the input tensor, and to determine the network parameters therein. The quantization module is connected to the processing module and is used to perform fixed-point quantization conversion on the trained network parameters to generate a fixed-point model. The deployment module is connected to the quantization module and is used to solidify and deploy the fixed-point model to the target processor or accelerator chip to perform online inference using the signal analysis method based on Laplace decay envelope quadratic convolution as described above.

[0020] Compared with the prior art, the beneficial effects of the present invention are: (1) This invention constructs a centrally symmetric LEQ convolution kernel by combining a Laplace decay envelope and a quadratic curvature, achieving a balance between high-resolution local feature extraction and distortion-free waveform morphology. This structure only requires configuration of amplitude and scale parameters to accurately characterize local temporal features. At the same time, its central symmetry ensures the linear phase characteristics of the filter at the physical level. This feature completely eliminates the group delay distortion caused by traditional nonlinear phase, providing a high-fidelity, distortion-free feature extraction method for physiological time-series signals such as EEG and ECG that are highly sensitive to waveform morphology.

[0021] (2) This invention does not simply stop at the time-domain parameterization level, but further provides an explicit construction of the discrete frequency domain response, so that a directly controllable analytical mapping relationship is formed between the convolution kernel parameters and the discrete spectrum shape. As a result, when the system performs frequency domain training or long sequence inference, it can directly analyze and obtain the frequency domain response, effectively avoiding the computational redundancy of repeatedly performing numerical FFT on the instantiated time-domain convolution kernel, and greatly reducing the underlying computational burden of the computing platform.

[0022] (3) This invention innovatively changes the underlying weight storage method, completely breaking the storage wall bottleneck of low-bit-width deployment. For LEQ convolution kernels, this invention proposes a joint quantization scheme based on scale index, half-wave lookup table and amplitude separation. The core of this scheme is to establish a lookup table for scale index and center offset, which only needs to store the waveform template of half a symmetrical period, and the complete convolution kernel can be restored without loss through time domain mirroring. This storage method avoids the memory redundancy of directly storing full-length fixed-point weights in conventional schemes, and also surpasses the simple lookup table logic of single function values, showing extremely high on-chip space utilization, providing an excellent decoupled storage scheme for 4-bit and other mixed precision inference, and effectively alleviating the static storage bottleneck of computing platforms when deployed in low-bit-width environments. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0024] Figure 1 This is a flowchart illustrating the signal analysis device and LEQ inference main process based on Laplace decay envelope quadratic convolution, as described in an embodiment of the present invention. Figure 2 This is a Laplacian decaying envelope convolution with residual connections, as described in this embodiment of the invention. Figure 3 This invention includes a channel attention mechanism and a Laplacian decaying envelope convolution with residual connections. Figure 4 This is a flowchart illustrating the construction of the LEQ low-bit-width quantized lookup table and integer inference in an embodiment of the present invention. Figure 5 This is a time-frequency image of the trained LEQ convolution operator according to an embodiment of the present invention. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0027] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0028] With the development of signal processing and artificial intelligence technologies, signal analysis methods based on deep learning and Laplace decaying envelope quadratic convolution have been widely applied in scenarios such as EEG seizure detection, ECG abnormality recognition, EMG pattern discrimination, and industrial vibration monitoring. Because one-dimensional convolutional neural networks can directly extract hierarchical features from raw signals or signals after simple preprocessing, balancing feature learning ability and application flexibility, they have become one of the mainstream technical solutions in one-dimensional time-series signal analysis.

[0029] There is an urgent need for a one-dimensional time-series signal analysis technology that simultaneously takes into account the following capabilities: First, the convolution kernel should have clear local morphological constraints and stable physical meaning, and be able to directly express its zero-phase amplitude response in the discrete frequency domain; Second, the convolution kernel should be easy to deploy with low bit width quantization, and in particular, should support cross-layer reuse of lookup tables, symmetric template compression, and low-bit mixed-precision inference.

[0030] The signal analysis method and system based on Laplace decay envelope quadratic convolution provided by this invention is based on a collaborative design architecture that integrates time-domain morphological constraints, frequency-domain feature controllability, and efficient hardware deployment. This architecture is specifically implemented through the following technical means: From the time domain perspective, a centrally symmetric convolutional kernel structure is used to eliminate phase distortion, ensuring that the system generates only a deterministic linear group delay, thereby avoiding phase distortion and guaranteeing that the waveform structure of the input signal remains undistorted in the time domain analysis. This enhances the ability to distinguish local transients, oscillation bursts, and waveform inflection points. Based on this, a quadratic factor is introduced to precisely control the curvature distribution and zero-crossing point position of the convolutional kernel center, enabling multi-scale feature capture of local transient signals, oscillation bursts, and waveform inflection points.

[0031] From the frequency domain perspective, the exponential noise reduction characteristics of the Laplace attenuation envelope enable it to effectively suppress interference from far-end noise samples while transforming the direct evaluation of the convolution kernel in the discrete frequency domain into a mathematical structure with geometric power sum characteristics. This structure supports the direct execution of zero-phase spectrum construction in the discrete frequency domain, avoiding the computational redundancy caused by the traditional process of "constructing in the time domain first and then performing numerical FFT", and realizing the analytical controllability of frequency domain filtering characteristics.

[0032] From a deployment perspective, the traditional quantization of full-length convolution kernel weights is transformed into index lookup of unit amplitude LEQ lookup tables through the scale index quantization mechanism. This transforms the convolution kernel reconstruction method from high-bandwidth memory read and write to lightweight template mirror mapping, greatly reducing the storage burden of the model on edge devices and achieving a deep integration of computing performance and deployment cost.

[0033] The following symbols are used uniformly in this invention: Indicates the network layer index; Indicates the input channel index; Indicates the output channel index; Indicates the convolution tap index; Indicates the first The length of the convolutional kernel, and Take an odd number; Indicates the first Layer convolution kernel center index; Indicates the first The first in the layer The output channel and the first Each input channel corresponds to the magnitude parameter of the convolution kernel; This represents the scale parameter of the corresponding convolution kernel; Represents discrete frequency sampling points; Represents the zero-phase real even amplitude term; Indicates the index in the quantized lookup table Offset The corresponding value; and These represent the quantized amplitude parameter and scale index, respectively. Unless otherwise stated, the convolutions in this invention employ a correlation operation form consistent with deep learning frameworks in their network implementation.

[0034] The signal analysis method based on Laplace decay envelope quadratic convolution according to embodiments of the present invention may include the following steps: Step 1: Segment, normalize, and channel-align the one-dimensional time-series signal to obtain the input tensor; One-dimensional time-series signals are acquired by a signal acquisition block, which includes at least one of a sensor, an electrode, an analog front-end, and an analog-to-digital converter. The one-dimensional time-series signals are electroencephalograms (EEG), electrocardiograms (ECG), electromyograms (EMG), pulse waves, vibration signals, and other one-dimensional time-series signals with local transient characteristics.

[0035] Step 2: Call at least one Laplacian decay envelope quadratic convolutional layer to extract features from the input tensor.

[0036] Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used as the scaling parameter. Based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points using the amplitude parameter, scale parameter, and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantization inference mode, the scale parameter is quantized into an index. The unit amplitude half-wave template corresponding to the index is read from the template lookup table. Then, the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

[0037] In the temporal tap expression of the LEQ convolution kernel in this embodiment of the invention, Controlling the polarity of the convolution kernel and the overall gain; The rate of envelope decay and the scale of expansion of the central quadratic curvature are determined; This represents the center of symmetry of the convolution kernel. The convolution kernel is about... Its centrosymmetric property essentially makes it a finite-length filter with a linear phase frequency response. From a physical perspective, the quadratic term... It characterizes the curvature distribution and the location of zero-crossing points in the central region of the convolution kernel, which directly determines the filter's resolution for signal spikes, abrupt edge changes, and local oscillations; while the exponential decay term... The attenuation rate of the response is determined when it is far from the center. Its physical significance lies in suppressing far-end noise through spatial weighting and improving the robustness of local discrimination.

[0038] In this embodiment of the invention, the first The first Laplacian decay envelope quadratic convolutional layer The pre-activation values ​​for each output channel satisfy: ,in, , Indicates the previous level. The output sequence of each input channel Indicates the first Number of layer input channels Indicates the first Layer output sequence length; the convolution kernel satisfies Thus, the corresponding discrete frequency domain response satisfy ,in This is the zero-phase real even amplitude term.

[0039] No. The first Laplacian decay envelope quadratic convolutional layer The pre-activation values ​​of each output channel are convolutional outputs in a time-dependent form. Since the LEQ convolutional layer in this embodiment can directly replace the standard one-dimensional convolutional layer in a deep learning framework, its forward output can be seamlessly integrated into residual modules, attention mechanism units, and various task classification heads. From an implementation perspective, the time-dependent convolutional output clarifies that this invention is not an abstract mathematical model detached from hardware and network systems. The double accumulation operator in the formula (for the input channel)... With nuclear chief It can be configured to be directly mapped to the execution unit of a general-purpose processor (CPU / GPU) or a dedicated accelerator (DSP / FPGA), and the multiply-accumulate operation sequence contained therein can be directly converted into an arithmetic logic unit pipeline in a hardware description language, thus having clear industrial applicability.

[0040] The decomposition of the discrete frequency domain response: linear phase factor introduced by centrosymmetry. By generating a uniform group delay proportional to frequency, the physical execution layer ensures that all frequency components of the input signal experience completely consistent time shifts in the time domain. This achieves a global translation of the signal envelope and fine structure, fundamentally eliminating phase distortion caused by nonlinear phase. The real even amplitude term... This constitutes the zero-phase response of the filter, a core physical quantity that determines the system's passband gain, stopband rejection, and cutoff bandwidth. By directly constructing this term analytically in the frequency domain, the processing module can achieve filtering of specific physiological frequency bands (such as EEG) with zero-phase delay as a prerequisite. This invention enables refined extraction of rhythmic or electrocardiogram (ECG) characteristic waveforms. It is designed for physiological signal analysis tasks such as EEG and ECG, which are highly sensitive to waveform morphology. Utilizing this linear phase characteristic, the invention effectively avoids waveform distortion, signal broadening, or false spikes caused by phase distortion, thus providing reliable support for the accurate detection of subsequent pathological feature points.

[0041] Zero-phase real even amplitude term Determine using the following formula: , , , , ; in, Indicates the first Layer The input channel to the first The envelope scale parameter of the convolution kernel for each output channel. This represents the envelope attenuation factor corresponding to the scale parameter; Indicates the first The length of the single-sided support interval of the convolutional kernel; The order of the space moments is represented by . Indicates the corresponding The complex frequency domain response term of the first-order space moment; This represents the magnitude normalization coefficient of the convolution kernel; Indicates the first Layer length is Discrete angular frequencies of discrete Fourier sampling points. This represents a complex exponential base with radial decay. This indicates taking the real part of a complex number.

[0042] calculate A two-branch stable evaluation mechanism is used: when At that time, a rational expression based on truncated geometric power sums is used to calculate... and ;when When using cosine series Evaluate, where This is a preset stability threshold.

[0043]

[0044]

[0045] make , The processing module utilizes truncated geometric powers and sums. , and By analytically evaluating the frequency response, the discrete frequency domain response can be obtained directly without explicitly generating a complete time-domain convolution kernel or performing a numerical FFT. Compared to the traditional computational path of "first constructing a time-domain convolution kernel and then performing a numerical FFT on the kernel," this invention reduces the kernel FFT overhead proportional to the number of kernels, significantly improving computational efficiency in long sequence scenarios. Furthermore, to avoid... The system can pre-set a stability threshold to address the numerical singularity problem caused by this. ,when The time processing module automatically switches from the geometric power and evaluation branch to the cosine series evaluation branch. Through the above branch switching mechanism, this invention ensures the numerical accuracy and robustness of feature extraction across the entire frequency band (especially in the low-frequency region) while maintaining high-efficiency analytical computation, laying a numerical foundation for the stable training and high-precision inference of subsequent deep neural networks.

[0046] In this embodiment of the invention, before quantization inference, the batch normalized parameters after the Laplacian decay envelope quadratic convolutional layer are first fused into the convolutional parameters to satisfy... ,in and They represent the first The amplitude and bias parameters after layer fusion These are the smallest positive constants used to ensure numerical stability. , , and These correspond to the scaling factor, bias, running mean, and running variance of the batch normalization layer, respectively. Obtained by layer-by-layer symmetric quantization .

[0047] The above describes the operator parameter fusion mechanism during the inference deployment phase. Since the LEQ convolutional layer of this invention does not require pre-setting independent bias terms during feature extraction, this provides high structural flexibility for subsequent batch normalization (BN) fusion. Before deployment, the processing module pre-fuses the affine parameters of the batch normalization layer into the convolutional parameters to obtain the fused amplitude parameters. With bias parameters This operation further reduces the execution overhead of independent BN operators during the inference phase, significantly reduces the number of operator switching and independent memory accesses during inference, and achieves more efficient hardware resource utilization, making it particularly suitable for embedded timing signal monitoring terminals with limited computing power.

[0048] In this embodiment of the invention, the template lookup table is constructed as follows: The scale parameter is applied... Bit-unsigned quantization, quantization scaling factor is ,in Represents the maximum value of the scale parameter of all Laplacian decay envelope quadratic convolutional layers; for each quantization index and each center offset Establish unit amplitude template ,in , To prevent positive numbers from being divided by zero; and only store The half-wave template is used to obtain a complete symmetrical convolution kernel by mirroring.

[0049] The above describes a core construction method for a scale-indexed quantization lookup table (LUT), achieving deep decoupling between convolutional kernel weight storage and channel size. Unlike traditional methods that directly perform full quantization storage on the complete convolutional kernel weights, the processing module first stores the scale parameters... Quantization Scale Index Then, a template table is constructed only for the unit amplitude LEQ shape function. Therefore, the lookup table does not need to store the full-length fixed-point weights of each convolutional kernel, nor is it limited to a single function value sample. Leveraging the symmetrical distribution of the convolutional kernels, the corresponding half-wave lookup table can be uniquely determined solely by the scale index. At runtime, it only requires reading the template, mirroring it, and multiplying by the quantization amplitude. This allows for the reconstruction of LEQ convolutional kernels, thereby significantly compressing the underlying storage. Since the lookup table is only related to scale quantization accuracy and kernel half-length, this invention achieves complete decoupling of storage requirements from the number of network channels. In multi-channel, deep network deployment scenarios, this mechanism can support large-scale feature extraction operations with minimal on-chip storage cost, effectively solving the storage wall bottleneck problem of embedded AI chips when processing high-dimensional signals.

[0050] The pre-activation quantization scaling factor for each layer was determined using the Kullback-Leibler divergence minimization method. Block output quantization scaling factor and according to as well as Perform fixed-point recalibration. The relevant parameters are defined as follows: and The first Layer-specific recalibration multipliers and recalibration biases; For the first Floating-point bias of the layer, This is the shift bit width; , as well as Corresponding to the first Layer amplitude quantization scaling factor, template lookup table quantization scaling factor, and input quantization scaling factor.

[0051] In this embodiment of the invention, the Laplace decay envelope quadratic convolutional layers are grouped according to odd kernel lengths, and layers with the same odd kernel length are... The layers share the same template lookup table, where the first... Group lookup table contains only One template item, This decouples template storage from the number of channels; This represents the number of bits used for the unsigned quantization of the scale parameter.

[0052] The above describes the specific transformation mechanism for fixed-point recalibration parameters after integer convolution. Specifically, Indicates the first The target quantization scaling factor of the convolutional layer output. This represents the quantization scaling factor of the amplitude parameter after fusion. This represents the quantization scaling factor of the template table. This represents the quantization scaling factor for the input activation of this layer. This indicates the fixed-point shift width. The processing module is configured to utilize recalibration parameters. Displacement width with preset fixed point A linear mapping is performed on the accumulated INT32 result of the convolution. This process replaces complex division operations with shift operations, remapping the high-bit-width intermediate values ​​to the target activation quantization domain. This significantly reduces hardware resource overhead while preserving the dynamic range of feature information to the greatest extent. This mechanism effectively suppresses rounding errors and overflow risks introduced by fixed-point quantization, ensuring that the signal features maintain a very high signal-to-noise ratio even after the model has multiple deep stacked convolutional layers. This supports the high-precision performance of low-bit-width quantization networks in complex time-series signal classification tasks.

[0053] During the training phase, the processing module provides a time-frequency dual-domain collaborative deep learning model training method, which can directly perform relevant operations in the time domain based on equation (2), or perform analytical spectral convolution in the frequency domain. For the first... If the input is zero-padded and cyclically shifted, the resulting layer is... Then it can be used for Performing FFT yields And the analytical spectrum directly constructed using equation (4) By performing point-by-point multiplication and finally applying IFFT and truncating the valid interval, an output equivalent to equation (2) can be obtained. Since Directly by , and This design allows for direct control of the frequency domain response and analytical gradient calculation during network training, avoiding the lack of interpretability in weight updates common in traditional convolutional kernels. It also enables direct constraints on frequency domain characteristics such as filter passband bandwidth and center curvature. This dual-domain equivalent transformation mechanism ensures that the model can fully utilize the analytical properties of the frequency domain for rapid convergence during training, while seamlessly switching to efficient time-domain impulse response execution during deployment. This design guarantees the numerical stability and robustness of the feature extraction operator across different computing platforms and processing scenarios.

[0054] During the training phase, the parameter gradient is directly calculated based on the analytical frequency domain response, and the parameter gradient is obtained through the frequency domain sensitivity. and , The product is obtained by multiplying and summing, thus avoiding repeated numerical FFTs on the instantiated convolution kernel.

[0055] During the deployment phase, when multiple one-dimensional convolutional neural network architectures have the same odd-numbered kernel length... When using LEQ convolutional layers, the same unit amplitude quantization lookup table can be jointly invoked and shared, leveraging the structural consistency of LEQ operator parameterization and eliminating redundant storage requirements between layers. For the first layer with a specific kernel length... The group convolution operator has a corresponding lookup table parameter size of 1. Controlled by the quantization bit width With nuclear half-length ,in In other words, the total template storage of the system described in this invention is configured to be related only to the preset quantization precision and kernel half-length. Compared to the traditional architecture that directly stores the full-length fixed-point weights of each convolutional layer (whose storage capacity varies with...), this provides a more efficient and efficient storage solution. (Rapidly increasing), this invention achieves a deployment effect that decouples template storage from the number of channels. This feature makes it possible to deploy complex timing signal analysis operators in large-scale deep networks, significantly reducing the system's capacity requirements for on-chip static random access memory (SRAM) or non-volatile memory, and effectively improving the deployment feasibility on resource-constrained edge computing terminals.

[0056] The quantization inference mode of this embodiment of the invention adopts a mixed precision configuration, wherein the scale index, amplitude parameter and template lookup table adopt 2 to 8-bit quantization, and activation adopts 4 to 8-bit quantization; preferably, the scale index, amplitude parameter and template lookup table adopt 4-bit quantization, and activation adopts 8-bit quantization.

[0057] Step 3: The features extracted from the input tensor are processed by a classifier / detection head to obtain the classification result / anomaly detection result.

[0058] In one or more embodiments, a signal analysis system based on Laplace decaying envelope quadratic convolution is also provided, which can be implemented in software. The signal analysis system based on Laplace decaying envelope quadratic convolution includes the following software modules: The input tensor calculation module is used to segment, normalize, and channel-align a one-dimensional time-series signal to obtain the input tensor. The feature extraction module is used to call at least one Laplacian decaying envelope quadratic convolutional layer to extract features from the input tensor. The feature mapping module is used to extract features from the input tensor and pass them through a classifier / detection head to obtain classification results / anomaly detection results; Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used as the scaling parameter. Based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points using the amplitude parameter, scale parameter, and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantization inference mode, the scale parameter is quantized into an index. The unit amplitude half-wave template corresponding to the index is read from the template lookup table. Then, the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

[0059] It should be noted that each module in the signal analysis system based on Laplace decay envelope quadratic convolution in this embodiment corresponds one-to-one with each step in the signal analysis method based on Laplace decay envelope quadratic convolution in the above embodiment, and their specific implementation processes are the same, so they will not be repeated here.

[0060] In other embodiments, a one-dimensional time-series signal analysis device includes: a signal acquisition module, a preprocessing module, a storage module, a processing module, and a result output module; the storage module is used to store network parameters and at least one Laplacian decay envelope quadratic convolution template lookup table; the processing module is connected to the signal acquisition module, the preprocessing module, the storage module, and the result output module; The signal acquisition module is used to acquire one-dimensional time-series signals; The processing module is configured to perform the steps in the signal analysis method based on Laplace decay envelope quadratic convolution as described above. The result output module is used to output classification results / anomaly detection results.

[0061] The signal analysis method based on Laplace decay envelope quadratic convolution of the present invention will be described in detail below with reference to specific embodiments.

[0062] Example 1: One-dimensional time-series signals are electroencephalogram (EEG) signals used to detect whether an epileptic seizure is occurring.

[0063] The signal analysis method based on Laplace decay envelope quadratic convolution is described below in conjunction with the appendix. Figure 1 The present invention provides a detailed description of the one-dimensional time-series signal detection system based on a Laplacian decaying envelope convolutional neural network and its parameter configuration, along with specific embodiments.

[0064] like Figure 1 As shown in the figure, the signal analysis device based on Laplace decay envelope quadratic convolution provided by the embodiment of the present invention includes the following overall working chain from the macro system level to the underlying micro architecture: including: signal acquisition module, preprocessing module, processing module, quantization module and deployment module; The signal acquisition module is used to acquire one-dimensional time-series signals. The signal acquisition module acquires the original physiological signals of the object through sensors or electrode arrays. In this embodiment, the original physiological signals are specifically multi-channel electroencephalogram (EEG) signals used to detect physiological states.

[0065] The preprocessing module is connected to the signal acquisition module and is used to perform segmentation, normalization and alignment operations on the one-dimensional time series signal in sequence to obtain the input tensor. This can eliminate baseline drift and unify the data scale, thereby constructing a standardized data sequence that meets the requirements of subsequent network input.

[0066] The processing module is connected to the preprocessing module and is used to construct and train at least one Laplacian decaying envelope quadratic convolutional layer and a classifier / detector head based on the input tensor, and to determine the network parameters therein. The quantization module is connected to the processing module and is used to perform fixed-point quantization conversion on the trained network parameters to generate a fixed-point model to adapt to the fixed-point computing characteristics of the underlying hardware.

[0067] The deployment module is connected to the quantization module and is used to solidify and deploy the fixed-point model to the target processor or accelerator chip (such as a field-programmable gate array FPGA) to perform online inference using the signal analysis method based on Laplace decay envelope quadratic convolution as described above.

[0068] like Figure 1 As shown in the lower half, after the deployment module is solidified, the specific software or firmware data flow and processing levels within the target processor or accelerator during online inference include: The input receiving layer is used to receive the standardized EEG signal sequence output by the preprocessing module as network input.

[0069] The basic feature extraction layer, connected to the input receiving layer, consists of two cascaded Laplacian decay envelope convolutional modules (ResBlock×2) with residual connections. It utilizes the physical properties of the Laplacian decay envelope to extract local transient change features of the standardized EEG signal sequence in the spatiotemporal domain and suppresses gradient vanishing through residual connections.

[0070] The deep feature enhancement layer, connected to the basic feature extraction layer, consists of four cascaded Laplacian decay envelope convolutional modules (SE-ResBlock×4) with channel attention mechanisms and residual connections. The channel attention mechanism adaptively learns and assigns weight coefficients to each feature channel based on the global context information of the feature map, guiding the network to focus on core frequency bands and spatial features that are highly correlated with specific physiological events.

[0071] The feature aggregation layer, connected to the deep feature enhancement layer, is composed of a global average pooling layer (GAP). It compresses the one-dimensional feature sequence of each channel into a single value by calculating the average value of the time dimension, thereby combining the outputs of all channels into a global one-dimensional feature vector. This significantly reduces the number of model parameters while enhancing the network's robustness to temporal shifts of the input signal.

[0072] The classification output layer, connected to the feature aggregation layer, is a classifier composed of a two-layer perceptron and a Softmax activation function. It calculates the probability distribution of target features in each preset category through fully connected mapping and outputs the final physiological state classification prediction result.

[0073] As a core implementation method of the present invention, the processing module shapes the convolution kernel by defining a specific discrete frequency domain response when constructing the core LEQ convolutional neural network.

[0074] In the neural network, the output sequence of the c-th input channel of the previous layer is processed by the convolutional kernel of the l-th layer and then mapped to the output sequence of the o-th output channel. Satisfy the following formula:

[0075] in, , This represents the output sequence of the c-th input channel of the previous layer. This represents the number of input channels in the l-th layer. This represents the length of the output sequence of the l-th layer; the convolution kernel satisfies temporal symmetry. Thus, the corresponding discrete frequency domain response satisfy: ; in, This is a zero-phase real even amplitude term. Specifically, the zero-phase real even amplitude term... Determine using the following set of formulas: ; ; ; ; In the above set of formulas: Represents discrete angular frequency. This represents a complex exponential base with radial decay. This represents the operation of extracting the real part of a complex number; Indicates the first Layer The input channel to the first The envelope scale parameter of the convolution kernel for each output channel. This represents the envelope decay factor corresponding to the envelope scale parameter, which physically controls the receptive field expansion and energy decay rate of the convolution kernel in the temporal space. Indicates the first The length of the single-sided support interval of the convolutional kernel; The order of the space moments is represented by . Indicates the corresponding The complex frequency domain response term of the first-order space moment is obtained through the zeroth-order space moment response. With second-order space moment response A linear combination of these elements shapes a specific bandpass feature extraction response in the frequency domain; The magnitude normalization coefficient of the convolution kernel is used to ensure the stability of the energy gain of the operator at different scales.

[0076] To optimize the computational efficiency of the deployment module on the underlying hardware, the quantization module first performs batch normalization (BN) folding on the trained model output by the processing module before performing fixed-point normalization. Batch normalization folding integrates the parameters of the BN layer into the original weights of the previous convolutional layer. And in the original bias, thus converting to the folded floating-point weights. and floating-point bias The calculation formula is as follows:

[0077]

[0078] in, and The first Scaling and translation factors for batch normalization operations. and These are the characteristic mean and characteristic variance, respectively. It is a numerical stability constant, specifically a very small positive constant, used to prevent the denominator from being zero in order to ensure the computational stability of digital logic circuits under extreme data flow conditions.

[0079] Finally, after completing the batch normalization folding, the quantization module adjusts the floating-point weights. and floating-point bias Perform fixed-point recalibration mapping to generate the final fixed-point recalibration multipliers burned into the accelerator. and fixed-point recalibration bias The specific calculation formula is as follows:

[0080]

[0081] in, This indicates the rounding operation; For the calculated first The layer's fixed-point recalibration multiplier, For the first Layer-specific recalibration offset; This refers to the floating-point bias after the aforementioned folding. This refers to the shift bit width of the underlying hardware shift circuit. For the first The pre-activation quantization scaling factor of the layer, For the first The amplitude quantization scaling factor of the layer, Quantify the scaling factor for the template lookup table. Input quantization scaling factor.

[0082] Based on the above recalibration relationship, the hardware accelerator can fully realize the complete inference process of the entire network through low-bit-width fixed-point shift and multiply-accumulate logic.

[0083] Step a1 involves acquiring multi-channel time-series signals and forming a continuous digital sequence. In practice, one-dimensional time-series EEG signals are acquired using 18 EEG acquisition electrodes. These signals are then converted from analog to digital signals using an analog-to-digital converter (ADC) to obtain the corresponding digital signals, which are then transmitted to the processor. The ADC sampling rate is set to 256Hz. The 18 bipolar leads acquired are, in order: FP1-F7, F7-T7, T7-P7, P7-O1, FP1-F3, F3-C3, C3-P3, P3-O1, FP2-F4, F4-C4, C4-P4, P4-O2, FP2-F8, F8-T8, T8-P8, P8-O2, FZ-CZ, and CZ-PZ.

[0084] Steps a2 and a3 are executed within the processor; the processor segments the input signal using a 4-second sliding time window, with the time window overlap rate set to 50%. Therefore, the input tensor for a single sample is... .

[0085] Step a2: Invoke at least one Laplacian decay envelope quadratic convolutional layer to extract features from the input tensor; Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used as the scaling parameter. Based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points using the amplitude parameter, scale parameter, and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantization inference mode, the scale parameter is quantized into an index. The unit amplitude half-wave template corresponding to the index is read from the template lookup table. Then, the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

[0086] like Figure 2 As shown, this embodiment uses six Laplacian decaying envelope convolutional blocks with residual connections as the feature extraction backbone network. The number of output channels for each residual block is set to 32, 32, 64, 64, 128, and 128 respectively. All convolutional main branches use LEQ convolutional layers, and the kernel length is uniformly set to... ,thus Simultaneously, a 1x1 convolutional residual connection branch is responsible for dimension alignment. Each residual block includes, in sequence, LEQ convolution, batch normalization (BN), ELU activation, and... Max pooling and Dropout, where the Dropout rate is set to 0.5; for example... Figure 3 As shown, the 3rd to 6th residual blocks are followed by an SE channel attention module, with the SE reduction ratio set to 8. After global average pooling, the feature vector is obtained, and then a two-layer perceptron is used to complete the seizure / non-seizure binary classification.

[0087] To facilitate the understanding of the physical meaning of each variable, this embodiment uses a representative convolutional kernel in the first layer as an example. , , At this point, the center tap... It mainly determines the intensity of the local central response; when As it gradually increases, the quadratic term The kernel gradually decreases and zero-crossing occurs at certain points, while the Laplace decay envelope causes taps far from the center to decay exponentially. Therefore, this convolutional kernel can simultaneously characterize EEG morphologies such as local bursts, spike-slow wave combinations, and short-term oscillations.

[0088] Step a3: The features extracted from the input tensor are processed by a classifier / detector head to obtain classification results / anomaly detection results, in order to detect whether an epileptic seizure has occurred.

[0089] During the training phase, this embodiment employs cross-entropy loss and... and Apply Regularity constraint, regularity coefficient set to The optimizer chosen is AdamW, and the initial learning rate is set to... The batch size is set to 64. For longer EEG sequences, the processor preferably uses the analytical spectrum convolution path: first, zero-padding and cyclic shifting are performed on the input, and then the sequence is directly generated according to formula (4). Finally, FFT / IFFT is combined to obtain an output equivalent to time-domain related operations.

[0090] This embodiment achieved an average AUC of 98.49% on the CHB-MIT dataset, an event-level sensitivity of 99.13%, and an FDR of 0.66 / h. To highlight the accuracy-efficiency advantages of this invention, Table 1 provides representative comparison results of the standard convolutional residual SE system, the full-precision LEQ system, and the 4-bit / 8-bit mixed-precision LEQ system.

[0091] Table 1. Representative Precision-Efficiency Comparison in Epilepsy EEG Detection Tasks

[0092] Example 2: An example of LEQ low-bit-width quantization deployment based on scale-indexed half-wave templates.

[0093] The following is in conjunction with the appendix Figure 4 The following is a description of a specific embodiment. This embodiment performs post-training quantization based on the EEG detection network of Embodiment 1. To highlight the advantages of this invention in ultra-low bitwidth deployment, the kernel length of all LEQ layers is uniformly set to... ,therefore The quantization configuration is set as follows: , , , Fixed point displacement width The activation distribution was statistically analyzed using 512 calibration samples, and KL divergence calibration was performed.

[0094] Let the maximum value of the scale parameter in the model before deployment be... ,but Therefore, 4-bit scale index There are only 16 possible values, each corresponding to a unit amplitude half-wave template. Because... Each template only needs to be stored to There are 11 items in total, so the entire template table only contains The template table contains 21 fixed-point weights for each convolutional kernel. If stored as 4-bit signed integers, the theoretical storage size of the template table is only 704 bits, or 88 bytes. Compared to directly storing the full 21-point fixed-point weights for each convolutional kernel, this template table can be reused across all LEQ layers of the same kernel length, significantly reducing on-chip storage requirements.

[0095] like Figure 4 As shown, this embodiment presents a fixed-point inference process based on a scale-indexed half-wave template. During the deployment preparation phase, the FP32 scale parameters obtained during network training... and FP32 amplitude parameters They are respectively mapped to quantized scale indices and quantized amplitude parameters Indexed by a certain scale For example, its inverse quantization scale is The processor pre-calculates the half-wave template according to equation (8), performs 4-bit quantization, and writes it to the on-chip SRAM or BRAM. During the actual inference execution phase, if the quantization scale index of a certain channel pair... Quantization amplitude The processor first utilizes The half-wave template with index 9 is retrieved from the half-wave lookup table, then mirrored to restore it as a temporal symmetric convolution kernel (i.e., the complete 21-point template). Finally, it is combined with... Combined integer convolutions. For example... Figure 4 As shown at the end, after the convolution output is recalibrated at the fixed point corresponding to Equation (9) (combining multiplier M and offset B), the final output is an 8-bit activation value, which is then fed into the subsequent ELU, pooling, SE and residual addition modules.

[0096] The lookup table organization method used in this embodiment has the following characteristics: the index object of the lookup table is a scale parameter. The lookup table stores unit amplitude half-wave shape templates, which are accessed via an index retrieval-mirror restoration-amplitude combination-integer convolution. This decouples the lookup table from the number of channels and maintains good shape consistency of the LEQ convolution kernel under 4-bit quantization.

[0097] Figure 5 This is a time-frequency image of the trained LEQ convolution operator according to an embodiment of the present invention. With the above configuration, this embodiment achieves an average AUC of 98.52%, an event-level sensitivity of 99.13%, and an FDR of 0.57 / h on the CHB-MIT dataset, demonstrating that the scale-indexed half-wave template quantization scheme proposed in this invention can maintain high detection performance under 4-bit / 8-bit mixed precision.

[0098] Example 3: One-dimensional time-series signals are used as electrocardiogram (ECG) signals to achieve ECG multi-label classification.

[0099] This embodiment applies the present invention to the PTB-XL ECG database. The system hardware can be a hospital server, a portable analysis terminal, or a cloud-edge collaborative device; the signal input is a 12-lead ECG. The sampling frequency is set to 100 Hz, and during the training phase, it is randomly pruned every 2.5 seconds. Therefore, the input tensor can be represented as... The network backbone uses xresnet1d101, except for the shortcut branches. In addition to convolution, the other suitable one-dimensional convolutional layers are replaced with LEQ convolutional layers.

[0100] In this embodiment, to illustrate the parameter setting method, the first replaceable convolutional layer is used as an example, and its kernel length is set to be... ,but The amplitude parameter initialization range is set to... The initial value of the scale parameter after positive value mapping is set to During training, binary cross-entropy loss and the AdamW optimizer are used, along with a 1-cycle learning rate scheduling strategy. For other layers, their respective odd kernel lengths can be set according to the receptive field requirements of the original backbone network, and they can all be replaced with LEQ convolutional layers.

[0101] Under full precision conditions, the xresnet1d101 (LEQ) model corresponding to this embodiment achieves a macro-average AUC of 93.2% on all tasks of PTB-XL; under mixed precision deployment conditions, after using 4-bit quantization of LEQ-related quantities and retaining 8-bit activation, the macro-average AUC of all tasks reaches 93.4%. These results indicate that the present invention is not limited to EEG detection, but can also be extended to other one-dimensional physiological temporal tasks such as ECG multi-label classification.

[0102] This invention achieves extreme compression of model size and memory access bandwidth, balancing extreme lightweight design with high diagnostic accuracy. When multiple LEQ convolutional layers have the same odd kernel length, this invention allows these layers to share the same lookup table, thereby significantly reducing redundant template storage and bandwidth occupied by parameter reading. Experimental and test data show that applying the system of this invention to epilepsy EEG detection tasks can drastically compress the number of model parameters from 709.5k to 95.4k; simultaneously, in a 4-bit / 8-bit mixed precision deployment mode, the overall model size is further compressed to only 0.11 MB, while still maintaining an average AUC (area under the curve) as high as 98.52%. This fully demonstrates that this invention can provide excellent clinical-grade diagnostic accuracy with extremely low hardware resource consumption.

[0103] In one or more embodiments, a signal analysis system based on Laplace decay envelope quadratic convolution is provided, comprising: The input tensor calculation module is used to segment, normalize, and channel-align a one-dimensional time-series signal to obtain the input tensor. The feature extraction module is used to call at least one Laplacian decaying envelope quadratic convolutional layer to extract features from the input tensor. The feature mapping module is used to extract features from the input tensor and pass them through a classifier / detection head to obtain classification results / anomaly detection results; Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used as the scaling parameter. Based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points using the amplitude parameter, scale parameter, and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantization inference mode, the scale parameter is quantized into an index. The unit amplitude half-wave template corresponding to the index is read from the template lookup table. Then, the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

[0104] In one or more embodiments, a signal analysis device based on Laplacian decay envelope quadratic convolution is provided, comprising: a signal acquisition module, a storage module, a processing module, and a result output module; the storage module is used to store network parameters and at least one Laplacian decay envelope quadratic convolution template lookup table; the processing module is connected to the signal acquisition module, the storage module, and the result output module; The signal acquisition module is used to acquire one-dimensional time-series signals; The processing module is configured to perform the steps in the signal analysis method based on Laplace decay envelope quadratic convolution as described above. The result output module is used to output classification results / anomaly detection results.

[0105] In some embodiments, the signal analysis system based on Laplace's decaying envelope quadratic convolution provided in this invention can be implemented using a combination of hardware and software. For example, the signal analysis system based on Laplace's decaying envelope quadratic convolution provided in this invention can be a processor in the form of a hardware decoding processor, programmed to execute the signal analysis method based on Laplace's decaying envelope quadratic convolution provided in this invention. For instance, the processor in the form of a hardware decoding processor can employ one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0106] As an example, a processor can be an integrated circuit chip with signal processing capabilities, such as a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., where a general-purpose processor can be a microprocessor or any conventional processor, etc.

[0107] As an example of the hardware implementation of the signal analysis system based on Laplace decaying envelope quadratic convolution provided in this embodiment of the invention, the device provided in this embodiment of the invention can be directly executed by a processor in the form of a hardware decoding processor. For example, it can be implemented by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components to implement the signal analysis method based on Laplace decaying envelope quadratic convolution provided in this embodiment of the invention.

[0108] In this embodiment of the invention, the memory is used to store various types of data to support the operation of a signal analysis system based on Laplace's decaying envelope quadratic convolution, or to store program code for executing the aforementioned signal analysis method based on Laplace's decaying envelope quadratic convolution. Examples of such data include: any executable instructions for operating on the signal analysis system based on Laplace's decaying envelope quadratic convolution, such as executable instructions; the program implementing the signal analysis method based on Laplace's decaying envelope quadratic convolution of this embodiment of the invention may be included in the executable instructions.

[0109] Specifically, according to embodiments of this application, the processes described in the above-referenced flowcharts can be implemented as computer software programs. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the signal analysis method based on Laplace decay envelope quadratic convolution described above. In such embodiments, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by a central processing unit, it performs the various functions defined in the apparatus of this application.

[0110] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0111] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A signal analysis method based on Laplace decay envelope quadratic convolution, characterized in that, include: The one-dimensional time-series signal is segmented, normalized, and channel-aligned to obtain the input tensor; At least one Laplacian decaying envelope quadratic convolutional layer is invoked to extract features from the input tensor; The features extracted from the input tensor are processed by a classifier / detection head to obtain classification results / anomaly detection results; Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used; based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points by the amplitude parameter, scale parameter and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantized inference mode, the scale parameter is quantized into an index, the unit amplitude half-wave template corresponding to the index is read from the template lookup table, and then the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

2. The signal analysis method based on Laplace decay envelope quadratic convolution as described in claim 1, characterized in that, Group the Laplace decay envelope quadratic convolutional layers according to odd kernel lengths, and group the layers with the same odd kernel length... The layers share the same template lookup table, where the first... Group lookup table contains only One template item, This decouples template storage from the number of channels; This represents the number of bits used for the unsigned quantization of the scale parameter.

3. The signal analysis method based on Laplace decay envelope quadratic convolution as described in claim 1, characterized in that, The template lookup table is constructed as follows: The scale parameters are applied using... Bit-unsigned quantization, quantization scaling factor is ,in Represents the maximum value of the scale parameter of all Laplacian decay envelope quadratic convolutional layers; for each quantization index and each center offset Establish unit amplitude template ,in , To prevent positive numbers from being divided by zero; and only store The half-wave template is used to obtain a complete symmetrical convolution kernel by mirroring.

4. The signal analysis method based on Laplace decay envelope quadratic convolution as described in claim 1, characterized in that, Before quantization inference, the batch normalized parameters after the Laplacian decay envelope quadratic convolutional layer are first fused into the convolution parameters, where... and They represent the first The amplitude and bias parameters after layer fusion These are the smallest positive constants used to ensure numerical stability. , , and These correspond to the scaling factor, bias, running mean, and running variance of the batch normalization layer, respectively. Obtained by layer-by-layer symmetric quantization .

5. The signal analysis method based on Laplace decay envelope quadratic convolution as described in claim 4, characterized in that, The pre-activation quantization scaling factor for each layer was determined using the Kullback-Leibler divergence minimization method. Block output quantization scaling factor and according to as well as Perform fixed-point recalibration; and The first Layer-specific recalibration multipliers and recalibration biases; For the first Floating-point bias of the layer; This is the shift bit width; , and Corresponding to the first Layer amplitude quantization scaling factor, template lookup table quantization scaling factor, and input quantization scaling factor.

6. The signal analysis method based on Laplace decay envelope quadratic convolution as described in claim 1, characterized in that, No. The first Laplacian decay envelope quadratic convolutional layer The pre-activation values ​​for each output channel satisfy: ,in, , Indicates the previous level. The output sequence of each input channel Indicates the first Number of layer input channels Indicates the first Layer output sequence length; the convolution kernel satisfies Thus, the corresponding discrete frequency domain response satisfy ,in This is the zero-phase real even amplitude term.

7. The signal analysis method based on Laplace decay envelope quadratic convolution as described in claim 1, characterized in that, Zero-phase real even amplitude term Determine by the following formula: ， ， ， ， ； in, Indicates the first Layer The input channel to the first The envelope scale parameter of the convolution kernel for each output channel. This represents the envelope attenuation factor corresponding to the scale parameter; Indicates the first The length of the single-sided support interval of the convolutional kernel; The order of the space moments is represented by . Indicates the corresponding The complex frequency domain response term of the first-order space moment; This represents the magnitude normalization coefficient of the convolution kernel; Indicates the first Layer length is Discrete angular frequencies of discrete Fourier sampling points. This represents a complex exponential base with radial decay. This indicates taking the real part of a complex number.

8. The signal analysis method based on Laplace decay envelope quadratic convolution as described in claim 7, characterized in that, calculate A two-branch stable evaluation mechanism is used: when At that time, a rational expression based on truncated geometric power sums is used to calculate... and ;when When using cosine series Evaluate, where This is a preset stability threshold.

9. A signal analysis system based on Laplace decaying envelope quadratic convolution, characterized in that, The signal analysis method based on Laplace decay envelope quadratic convolution as described in any one of claims 1-8 includes: The input tensor calculation module is used to segment, normalize, and channel-align a one-dimensional time-series signal to obtain the input tensor. The feature extraction module is used to call at least one Laplacian decaying envelope quadratic convolutional layer to extract features from the input tensor. The feature mapping module is used to extract features from the input tensor and pass them through a classifier / detection head to obtain classification results / anomaly detection results; Among them, the In a Laplacian decay envelope quadratic convolutional layer, the kernel length between the output and input channels is an odd number. The central index is Corresponding to the convolution kernel tap satisfy ; ; For amplitude parameters; The scale parameter is used as the scaling parameter. Based on the symmetry of the convolution kernel about the center index, the discrete frequency domain response is decomposed into a pure delay term and a zero-phase real even amplitude term. The zero-phase real even amplitude term is directly constructed on the discrete Fourier sampling points using the amplitude parameter, scale parameter, and convolution kernel length to perform frequency domain convolution or frequency domain training. In quantization inference mode, the scale parameter is quantized into an index. The unit amplitude half-wave template corresponding to the index is read from the template lookup table. Then, the complete symmetric convolution kernel is obtained through mirror restoration. Finally, it is combined with the quantized amplitude parameter to complete integer convolution and recalibration.

10. A signal analysis device based on Laplace decay envelope quadratic convolution, characterized in that, include: Signal acquisition module, storage module, processing module, and result output module; The storage module is used to store network parameters and at least one Laplacian decay envelope quadratic convolution template lookup table; the processing module is connected to the signal acquisition module, the storage module, and the result output module. The signal acquisition module is used to acquire one-dimensional time-series signals; The processing module is configured to perform the steps in the signal analysis method based on Laplace decay envelope quadratic convolution as described in any one of claims 1-8; The result output module is used to output classification results / anomaly detection results; The signal analysis device based on Laplace decay envelope quadratic convolution may include: a signal acquisition module, a preprocessing module, a processing module, a quantization module, and a deployment module; The signal acquisition module is used to acquire one-dimensional time-series signals; The preprocessing module is connected to the signal acquisition module and is used to perform segmentation, normalization and alignment operations on the one-dimensional time series signal in sequence to obtain the input tensor. The processing module is connected to the preprocessing module and is used to construct and train at least one Laplacian decaying envelope quadratic convolutional layer and a classifier / detector head based on the input tensor, and to determine the network parameters therein. The quantization module is connected to the processing module and is used to perform fixed-point quantization conversion on the trained network parameters to generate a fixed-point model. The deployment module is connected to the quantization module and is used to solidify and deploy the fixed-point model to the target processor or accelerator chip to perform online inference using the signal analysis method based on Laplace decay envelope quadratic convolution as described in any one of claims 1-8.

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