31 results about "Factor matrix" patented technology

The application provides a method and system for offshore wind turbine integrated dynamic feature reservation. The full state time series data of the offshore wind turbine multi-physical field coupling system is obtained, the modal parameters of the system are extracted by using a dynamic modal decomposition method, the participation factor matrix is calculated, the participation degree of each state quantity and the corresponding physical link to each mode is quantified, the dominant state quantity of the extracted mode and the corresponding physical link are located, the dominant state set is constructed, the time scale distribution of each mode is quantified, the time scale distribution characteristic atlas of different physical links of the overall system is formed, the fast time scale, analysis time scale and slow time scale boundaries in the atlas are divided according to different research needs, and the offshore wind turbine integrated reduced order model is constructed based on the singular perturbation theory. The application can effectively reserve the dynamic features of the offshore wind turbine multi-field coupling characteristics, and provides a precondition and quantitative basis for physical-based model reduction modeling.

The application discloses a power system frequency estimation method and system, which comprises the following steps: obtaining a power grid model and remote signaling data, a generator rotating speed and a PMU frequency measurement, forming a node branch model; forming an extended node admittance matrix according to the node branch model, a generator internal reactance parameter and the remote signaling data; performing node reordering on the extended node admittance matrix; forming a factor table of the reordered extended node admittance matrix by using a symbolic decomposition and a numerical decomposition method; calculating a frequency participation factor matrix F by using a multi-thread parallel technology; obtaining a reduced frequency participation factor matrix F' according to the size of element values in the frequency participation factor matrix F and a set threshold value; and calculating a node frequency by using a multi-thread parallel method. The application overcomes the shortcoming that the inertia center frequency of a power grid can only calculate an average frequency of the power grid, and has important reference significance for guiding the selection of a power generator frequency point monitored by a dispatching center.

The invention relates to the technical field of image noisy point removal, and discloses a noisy point suppression method and system for a black light camera, and the method comprises the steps: constructing a response rate factor matrix and an intercept factor matrix, carrying out the collection of a working scene image based on the black light camera, obtaining a working scene image, carrying out the correction of the working scene image, and obtaining a noise point suppression result. Performing stripe noise suppression operation on the corrected working scene image to obtain a stripe noise removed image; performing connected domain analysis operation on the binarized image to obtain an independent connected domain set; performing central point diffusion operation on the independent connected domain set to obtain an expanded independent connected domain set; and performing noisy point distinguishing operation on the extended independent connected domain set to obtain a denoised working scene image, and completing noisy point suppression of the black light camera based on the denoised working scene image. According to the invention, stripe noise can be effectively suppressed, defective pixel noise points can be accurately eliminated, and effective targets can be accurately distinguished.

This invention discloses a campus energy consumption intelligent analysis system based on big data, belonging to the fields of big data analysis and energy management technology. It acquires multi-source energy consumption data from the campus and constructs a dynamic event graph. The system includes: a matrix construction module that builds a Bayesian causal network based on the dynamic event graph and historical energy consumption data, outputting a causal influence factor matrix; a candidate instruction module that generates a candidate instruction set based on the causal influence factor matrix using a genetic algorithm; a priority instruction module that outputs a priority instruction sequence based on the simulated energy consumption curve after executing the candidate instruction set; a collaborative optimization module that distributes the priority instruction sequence to each building node, generating device-level control instructions; and an autonomous strategy module that performs deep reinforcement learning optimization iterations based on the actual energy saving rate and comfort deviation feedback after executing the device-level control instructions. This invention effectively solves the inefficiency problems of IoT systems due to resource heterogeneity, rigid scheduling, and lack of autonomous optimization capabilities.

This invention relates to a localized differential privacy recommendation method and system that balances algorithmic fairness, belonging to the fields of computer recommendation systems and information security technology. The method first divides the dataset into three groups—active, moderate, and inactive—based on user activity. The server initializes and pre-trains the item latent factor matrix, saving the latent factor matrices for each group. Gradient updates and dynamic gradient clipping are performed on each group, adaptively adding noise based on a clipping threshold. In each iteration, the gradient clipping threshold and noise scale are updated. Each group uploads the perturbed item gradients to the server for secure aggregation. Finally, the recommendation server uses the updated item latent factor matrix and distributes it to the local group for further training. After iteration, users generate a top-K recommendation list through local prediction. This invention effectively protects user privacy in scenarios where the server is untrusted, significantly alleviates the performance differences in recommendations between user groups with different activity levels, and achieves a balance between privacy protection and algorithmic fairness.

This invention discloses an intelligent configuration method for graphics card workstations based on big data analysis, comprising: S1, collecting data and features to generate an original holographic runtime dataset; S2, constructing a three-dimensional heterogeneous tensor matrix, extracting the kernel tensor and factor matrix using HOSVD decomposition, and generating a deep computing power feature vector; S3, constructing a computing power feature profile library, calculating similarity to identify task load pressure patterns, and outputting a target task feature profile; S4, generating a preliminary configuration scheme using an improved WGAN-GP model, and introducing a manifold regularization projection mechanism to filter candidate configuration subsets; S5, parsing and obtaining hard constraints, and matching the final configuration parameters; S6, issuing configuration parameters and collecting real-time load data for dynamic correction; S7, constructing incremental samples to feed back into the original dataset, and performing continuous iterative self-optimization. This invention achieves accurate matching of graphics card resources and task load, effectively improving the computing power utilization efficiency of the workstation.

The present disclosure belongs to the field of geomagnetic station earthquake anomaly extraction, and is an earthquake magnetic field anomaly extraction method, system and electronic equipment, comprising: constructing a three-dimensional non-negative tensor data body; adopting a spatial weighted non-negative tensor decomposition method to decompose the three-dimensional non-negative tensor data body, extracting R characteristic components, each characteristic component containing a frequency factor matrix, a time factor matrix and a station contribution factor matrix; calculating the proportion of the total energy of a target frequency band in the frequency factor matrix of each characteristic component in the total energy in the entire frequency range, and selecting the characteristic component with the largest proportion as the earthquake-related characteristic component; and based on the time factor matrix of the earthquake-related characteristic component, adopting an over-limit threshold method to extract an earthquake anomaly point. The present disclosure can retain and utilize all measured data to study earthquakes, and effectively detect earthquake anomalies by obtaining more relevant components of earthquake activity.

The application relates to the technical field of industrial control, and provides an industrial production parameter intelligent matching method and system based on a knowledge graph. Process data in a production process is preprocessed to generate standardized process tensors and constraint vectors; a convolutional neural network is used to extract an equipment feature vector from the process tensors, the equipment feature vector is projected in hyperbolic space and spherical space to generate a splicing vector; a factor matrix is decomposed from the splicing vector, a linear combination vector of the constraint vectors is generated based on preset constraint weights, and a first tensor core is generated based on the linear combination vector and the factor matrix; the constraint vectors are mapped to a tensor space and fused with the first tensor core to generate a second tensor core; the second tensor core is input into a preset target optimization module to obtain an adaptive parameter combination, and the parameter combination is sent to a control terminal. The application realizes intelligent matching and dynamic adjustment of production parameters, and improves the accuracy and efficiency of parameter matching in a production process.

The present application relates to a kind of photovoltaic output data recovery method and device based on latent feature analysis, which is based on Fourier enhanced adaptive latent feature analysis framework, by constructing the space adjacent graph between photovoltaic station and time embedding matrix, photovoltaic output matrix is low rank modeling and optimization recovery.The method first extracts the multi-frequency Fourier feature of photovoltaic time series, forms time dynamic regular term;While according to site geographical location or output correlation, construct graph laplace matrix to enhance the ability of spatial structure modeling.Introduce Huber robust loss function, to improve the stability of recovery under abnormal value interference.Using segmented random gradient optimization strategy, latent factor matrix is updated efficiently, realize the high quality reconstruction of photovoltaic data.The method still has good robustness and recovery accuracy in the face of large proportion missing and complex interference scene, is suitable for distributed photovoltaic system data repair, load forecasting and dispatching optimization etc.scene.

The application discloses a physical information neural network optimized soil carbon storage precise evaluation system, relates to the cross field of artificial intelligence and geoscience, and comprises a multi-source heterogeneous data intelligent fusion module which is used for realizing multi-source heterogeneous data fusion from satellite hyperspectral images, unmanned aerial vehicle laser radar point clouds, microwave remote sensing, ground sensors, electromagnetic and thermal sensing, optical and acoustic monitoring, metagenomic sequencing, XRD mineralogy, hydrology and DEM through multi-modal space-time alignment, multi-physical field coupling perception, biological-mineral map construction and dynamic hydrological topology construction, and outputting consistency feature matrix, hydrological driving factor matrix and carbon stability biological index. In the application, key physical, chemical and biological kinetic equations of soil carbon cycle are embedded in a deep learning framework, so that the interpretability, generalization ability and prediction precision of the model in a complex environment are improved, and unified modeling and layered consistency prediction of surface and deep soil carbon cycle processes are realized.

This invention proposes a method and system for ECG clustering based on multi-lead semantic consistency, belonging to the field of ECG signal processing technology. The method includes: constructing a similarity correlation matrix for an ECG signal set using adaptive graph learning; learning the spectral representation of each lead of the ECG signal using spectral clustering on the similarity correlation matrix, whereby spectral clustering utilizes multi-lead shared spectral embedding to measure the correlation between ECG signals, obtained through an optimized minimum edge weight objective function; wherein the optimized minimum edge weight objective function includes the multi-lead shared semantic similarity matrix; after obtaining the spectral embedding matrix, constructing a spectral rotation objective function by introducing an orthogonal rotation factor matrix; merging the minimum edge weight objective function and the spectral rotation objective function into a total objective function, and optimizing the total objective function using the alternating direction multiplier method to obtain the ECG clustering result. This invention significantly improves the clustering quality through the learning of semantically consistent graphs.

Embodiments of the present application provide a linear regression method based on privacy protection. The method comprises: a current participant receives an inverse decomposition factor matrix of a regularized symmetric matrix, or a transformed form thereof, wherein the regularized symmetric matrix comprises, as a submatrix, a column-encryption data transformation encryption matrix corresponding to private raw data of a preceding participant; the current participant cooperates with the preceding participant to determine respective product matrixes or transformed forms thereof of the current participant and the preceding participant; the current participant sends the inverse decomposition factor matrix or the transformed form thereof to a subsequent participant; or, the current participant obtains and utilizes the respective product matrixes or the transformed forms thereof of the preceding participant and the current participant, and cooperates with the preceding participant and a label data owner to determine a multiplicatively encrypted linear regression coefficient vector, wherein the multiplicatively encrypted linear regression coefficient vector is equal to the product of the respective inverse decomposition factor matrix of the preceding participant and the current participant and a first product vector. The method provided in the present application can reduce implementation complexity, satisfying practical application requirements.

This disclosure proposes a signal processing method and apparatus based on integrated communication and sensing. In response to acquiring an echo signal, the method denoises the echo signal using a pre-constructed sensing model to obtain a target-denoised echo signal, thus removing noise to a certain extent and solving the problem of poor echo signal quality. Further, the target-denoised echo signal is subjected to multilinear decomposition to obtain a subcarrier factor matrix, a symbol factor matrix, and an antenna factor matrix. Based on these matrices, the elevation angle, azimuth angle, range, and velocity of multiple targets included in the echo signal are estimated. By utilizing structured prior knowledge of the signal, stable and high-precision extraction of target parameters from low-quality echo signals is achieved.

The application provides a CTMU-based adaptive variable current source ultrasonic flow measurement method, and belongs to the technical field of downhole pipeline flow measurement. The method comprises the following steps: adopting a least square method to establish a flow rate influencing factor matrix, a measured flow rate matrix, a residual variable matrix and an unmeasured flow rate matrix; based on the flow rate influencing factor matrix, the measured flow rate matrix, the residual variable matrix and the unmeasured flow rate matrix, a multiple regression equation is established; based on the multiple regression equation, the unmeasured flow rate of fluid in a downhole pipeline is predicted; or, according to the measured flow rate and the flow rate influencing factor, a sum of squared deviations of the measured flow rate is calculated; and based on the sum of squared deviations of the measured flow rate, the unmeasured flow rate is predicted. The application can improve the accuracy of ultrasonic flow measurement and has strong ease of use and practicality.

The application discloses a kind of multi-dimensional self-adaptive streaming reconstruction methods of spectrum situation tensor for space-based dynamic incomplete observation, comprising: based on spectrum measurement data, construct dynamic tensor and determine dimension evolution mode by the spatial coverage dimension variation of dynamic tensor;When dimension evolution mode is expansion or invariable, using historical factor matrix as prior constraint to process current observation tensor, obtain the factor matrix of current time slot;When dimension evolution mode is short, using time series prediction method to pre-fill blind area, obtain the factor matrix of current time slot;Based on factor matrix, reconstruct spectrum situation tensor, and separate abnormal interference from reconstruction residual using soft threshold operator;Based on the reconstruction residual after separating abnormal interference, calculate relative change rate, update tensor rank in combination with sliding window regression trend;Based on the tensor rank after updating, adjust factor matrix structure, use the adjusted factor matrix for the processing of next time slot, iterate until the reconstruction result converges.

The invention provides a power grid data restoration method and system based on Huber norm tensor decomposition, and belongs to the technical field of intelligent power grids and high-dimensional data processing. The method comprises the following steps: constructing multi-source and multi-dimensional power grid load data into a high-dimensional tensor structure; a Huber norm-based tensor decomposition model is adopted as a core reconstruction engine, through differential punishment of different residual errors, random noise is effectively suppressed, key abnormal modes such as electricity stealing are reserved, and excessive smoothing of abnormal features by a traditional method is avoided; efficiently solving the low-rank factor matrix of the tensor by using a stochastic optimization algorithm; and finally, realizing accurate filling of massive missing values in the original data through the reconstructed factor matrix. According to the method, the restoration precision and robustness of the power grid data containing noise and abnormal values can be remarkably improved, a high-quality data basis is provided for subsequent advanced analysis tasks such as electricity larceny detection and load prediction, and the method has important practical application value.

This invention discloses a recommendation method based on personalized differential privacy and gradient perturbation, belonging to the interdisciplinary field of computer recommendation systems and information security. The method uses an implicit feedback matrix to represent user-item interaction data, randomly initializes user and item latent factor matrices, and constructs and optimizes the objective function through Bayesian personalized ranking matrix decomposition to obtain the user latent factor matrix. In privacy-preserving training, the dataset is divided into groups for sampling, and the sampling rate is calculated by combining the privacy budget, failure probability, and iteration count of each group, and a training subset is extracted. An objective function is constructed separately for the matrix, the gradient is clipped using the L2 norm and the threshold is adaptively adjusted, and Gaussian noise is added to achieve gradient perturbation, thus iteratively updating the matrix. Finally, the matrix is ​​shared, and users calculate predicted ratings locally, rank uninterrupted items, and select items to complete the recommendation. This invention effectively improves the accuracy of the recommendation model while achieving privacy protection.

This invention discloses an image reconstruction method, apparatus, device, and medium based on cooperative block term tensor decomposition, relating to the field of signal processing technology. The method includes: decomposing the original tensor into a sum of multiple low-rank terms; decomposing each low-rank term based on a cooperative block term tensor to obtain a low-rank decomposition model of the original tensor, wherein the N mode factor matrices of each low-rank term are represented by shared factor matrices and independent factor matrices; constructing a reconstruction task model based on the low-rank decomposition model, and solving the reconstruction task model using an optimization algorithm to obtain solutions for each factor matrix; substituting the solutions of each factor matrix into the low-rank decomposition model to obtain the reconstructed image. This invention improves the reconstruction effect by enabling different low-dimensional terms to interact through a shared factor mechanism, while significantly reducing computational resources.

This invention relates to the field of mineral resource exploration technology and discloses a three-dimensional mineralization prediction method, apparatus, equipment, and medium. The method includes: fusing and standardizing multi-source mineralization control information to construct a mineralization control factor matrix; processing the mineralization control factor matrix using an SE-DNN model to obtain mineralization reference values ​​for voxels, and constructing a correlation potential function based on these reference values; calculating the spatial weights, feature similarity weights, and kriging coupling coefficients of voxels using a 3D ellipsoidal kriging model to construct an interaction potential function that integrates multi-dimensional weights; constructing a COPF global energy function based on the correlation potential function and the interaction potential function, and using a mean field approximation for posterior distribution inference to obtain the initial mean and variance of the voxel mineralization variables; optimizing the learnable parameters by performing recurrent convolution and end-to-end training on the voxel mineralization variables to obtain a three-dimensional mineralization regression prediction result. Through the above scheme, this invention improves the accuracy of mineralization prediction.

This invention provides a deep denoising-based multi-RIS indoor positioning method. For indoor scenarios with multipath interference and noise, this invention first constructs a fourth-order tensor model from the channel state information reflected from multiple indoor RIS points and scattering points to the receiver. Second, it uses antenna rearrangement technology to rearrange the tensor model to satisfy the decomposition uniqueness condition. Then, it utilizes the denoising capabilities of a deep learning architecture to suppress noise in the received signal. Further, it employs an optimized quadlinear alternating least squares algorithm to estimate the factor matrix and extract channel parameters. Finally, it uses a geometrically based search-free spatial positioning method to estimate the user's location and azimuth angle, and map the indoor environment. Therefore, the deep denoising-based multi-RIS indoor positioning method proposed in this invention has higher accuracy and robustness compared to comparative algorithms, and is more in line with the needs of practical communication scenarios.

The application discloses a robust multi-modal system direction finding method in a multipath environment, deduces a multi-modal system multipath channel impulse response, models a multi-modal system multipath channel tensor, performs parallel factor decomposition on the tensor model of the multi-modal system multipath channel, and performs parameter estimation on the factor matrix obtained through the decomposition. Compared with a parameter estimation method based on subcarrier smoothing, the application has more advantages in estimation performance, can distinguish more multipath signal quantities, and improves direction finding stability, and is more efficient in engineering implementation, specifically represented as significant reduction of calculation complexity and more simplified system structure.

Provided in the embodiments of the present application are a data processing method and a related apparatus. In the present application, a matrix multiplication operation is performed on a rotation factor matrix and an input signal by means of cube units, so as to accelerate in combination with the cube units a fast Fourier transform (FFT) operation performed on the input signal. The method comprises: on the basis of the length of a first input signal, generating a rotation factor matrix, wherein the rotation factor matrix comprises a plurality of rotation factors, which are used for performing an FFT operation on the first input signal; and performing a matrix multiplication operation on the rotation factor matrix and the first input signal, so as to obtain a first matrix-product matrix, wherein the first matrix-product matrix comprises a result of performing the FFT operation on the first input signal.

The application provides a kind of early warning prevention and control method and device based on dust big data tensor decomposition and learning, it is related to intelligent control technical field, the method includes: collecting the field data of crushing and transportation site;Based on the modal information of field data, the feature alignment and mapping of each modal data of field data are carried out, and a multi-modal feature set is generated;Based on the multi-modal feature set and the core tensor, factor matrix pre-constructed, construct coupling tensor model;Based on the processing of multi-modal feature set, the corresponding high-order fusion feature vector is generated based on coupling tensor model;Combine high-order fusion feature vector and the physical layout of crushing and transportation site to construct heterogeneous graph;Call pre-constructed heterogeneous graph contrast learning model to process heterogeneous graph, and in the case of fault node, generate compensation strategy;Call pre-constructed strategy decoder to generate control instruction based on compensation strategy, and the control parameter of all nodes except fault node is included in control instruction.

The invention belongs to the field of geomagnetic station seismic anomaly extraction, and relates to a seismic magnetic field anomaly extraction method and system and electronic equipment, and the method comprises the steps: constructing a three-dimensional non-negative tensor data body; decomposing the three-dimensional non-negative tensor data volume by using a spatial weighted non-negative tensor decomposition method, extracting R feature components, each feature component including a frequency factor matrix, a time factor matrix and a station contribution factor matrix; calculating the proportion of the energy sum of the target frequency band in the frequency factor matrix of each characteristic component in the whole frequency range, and selecting the characteristic component with the maximum proportion as an earthquake related characteristic component; and on the basis of the time factor matrix of the seismic related characteristic component, extracting a seismic abnormal point by adopting an over-limit threshold method. According to the invention, all data obtained by measurement can be reserved and utilized to research the earthquake, and meanwhile, components more related to the earthquake activity are obtained to effectively carry out earthquake anomaly detection.

The application relates to the technical field of deep learning and artificial intelligence model optimization, and discloses a model merging method and device, an electronic device and a storage medium, the method comprising the following steps: constructing a preset dimension task tensor based on task vectors of a plurality of preset expert models and a pre-training base model; performing Tucker decomposition on the task tensor to obtain a core tensor and a factor matrix; constructing a static correction matrix based on a residual tensor of the Tucker decomposition and a task mask; the task mask is generated by analyzing neuron activation patterns in each preset expert model; in a model inference stage, a dynamic update matrix is reconstructed based on real-time input data, the factor matrix and the core tensor, and the dynamic update matrix and the static correction matrix are merged with the pre-training base model to obtain a fused model parameter, the application realizes efficient merging of multiple expert models without accessing original training data, reduces deployment cost, and improves multi-task processing performance.

The application discloses a multi-factor space-time power load prediction method and system based on deep learning, which comprises the following steps: collecting and cleaning multi-source heterogeneous data, constructing a space-time load data matrix and an external factor matrix; performing variational mode decomposition on the load sequence of each power grid spatial distribution area in the space-time load data matrix, and dividing the load sequence into a trend sequence, a seasonal sequence and a residual sequence; constructing a trend component model, a seasonal component model and a residual component model; using a physical perception gate unit downstream of each component model to dynamically adjust the contribution degree of each component model, and outputting a fused total power load prediction value; training each component model, fixing the parameters of each component model after the training is completed, optimizing and training a fusion model composed of each component model and the physical perception gate unit, and using the trained fusion model to perform power load prediction; and the application has the advantages of strong robustness and feasibility in engineering application.

This application relates to a method for improving the accuracy of smart meter data completion, comprising: sampling multiple first meter data sequences to generate a meter sequence matrix and a mask matrix; performing a multipath delay embedding transformation on the meter sequence matrix and the mask matrix, dividing the obtained first tensor and mask tensor into multiple time-block first sub-tensors and mask sub-tensors, and decomposing each first sub-tensor into a first core sub-tensor and a factor matrix based on the mask sub-tensors; inputting the first target sequence generated based on the multiple first core sub-tensors and the corresponding position encoding results into a Transformer model to obtain multiple second core sub-tensors; performing inverse tensor decomposition based on the multiple second core sub-tensors and the factor matrix, performing an inverse multipath delay embedding transformation on the obtained second tensors, and adjusting parameters based on the numerical differences between the inversely transformed second meter data sequences and the first meter data sequences at the same missing position, thereby iteratively training the completion model. This method can improve the accuracy of data completion.

The application relates to the technical field of intelligent driving and specifically discloses an edge deployment and federal mask learning method for a vehicle-mounted large model, which is applied to a distributed vehicle-mounted intelligent driving system and comprises the following steps: a four-order parameter tensor is constructed, a low-rank core tensor and a factor matrix are extracted through Tucker decomposition, a holographic base is formed and broadcast to each vehicle-mounted intelligent terminal, a binary mask is introduced into each vehicle-mounted intelligent terminal to selectively activate the core tensor, a straight-through estimator and a composite regularization strategy are adopted to optimize mask scores on the basis of a local driving perception dataset, only the activation index set of a sparse mask is uploaded by each vehicle-mounted intelligent terminal to realize sub-linear communication, the cloud server aggregates masks of each node through logical superposition and screens based on an activation frequency threshold, knowledge is solidified to the holographic base through limited optimization to realize the persistence and propagation of cross-vehicle perception knowledge, the model compression efficiency is improved, the federal communication overhead is reduced, and cross-vehicle perception knowledge sharing is realized.

This invention discloses a target parameter estimation method for an L-shaped array OFDM integrated sensing system based on Coupled Tensor Decomposition (CPD). The method includes: constructing an OFDM integrated sensing system model using an L-shaped receiving array, which consists of two sets of mutually orthogonal uniform linear arrays; establishing corresponding third-order tensor signal models based on the received echo signals along the horizontal and vertical axes, and constructing a coupled tensor that satisfies typical multilinear decomposition; transforming the multi-target parameter estimation problem into a coupled CPD solution problem, designing a two-stage coupled CPD parameter estimation algorithm, and sequentially extracting target azimuth, elevation, Doppler frequency shift, time delay, and complex reflection coefficient information from the estimated coupling factor matrix; and finally completing the joint estimation of multi-target parameters. This invention has stronger target parameter estimation capabilities and can improve the reliability and accuracy of target parameter estimation while reducing array hardware complexity.

Embodiments of the present application provide a data processing method and related device, which performs matrix multiplication operation on a twiddle factor matrix and an input signal by a cube unit to realize fast Fourier operation on the input signal combined with the cube unit acceleration. The method comprises: generating a twiddle factor matrix according to the length of a first input signal, the twiddle factor matrix comprising a plurality of twiddle factors used for fast Fourier transform (FFT) operation on the first input signal; performing matrix multiplication operation on the twiddle factor matrix and the first input signal to obtain a first matrix multiplication matrix, the first matrix multiplication matrix comprising the result of FFT operation on the first input signal.