Frequency spectrum optimization calculation method based on single-bit frequency measurement technology

Abstract

The invention discloses a frequency spectrum optimization calculation method based on a single-bit frequency measurement technology, which is based on a weighted stacking single-bit DFT (Discrete Fourier Transform) algorithm and is characterized in that sampling signals are cached and then are split bit by bit. Each split single-bit signal is calculated through an optimized Fourier transform module, and windowing operation is executed after twiddle factors are quantized. And frequency information is extracted from a final result through a spectrum analysis module. In combination with a multi-bit data splitting and superposition method, a single-bit frequency measurement technology and a twiddle factor windowing method, efficient and rapid frequency measurement can be realized in a multi-bit sampling system. According to the method, the advantages of multi-bit signals and the simplification characteristic of single-bit frequency measurement are combined, the extremely high frequency measurement speed is guaranteed, and meanwhile the computing resources and the frequency spectrum performance are optimized.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital signal processing, and particularly relates to a spectrum optimization calculation method based on single-bit frequency measurement technology. Background Art

[0002] With the wide application of multi-bit ADC (Analog-to-Digital Converter), especially in high-precision radar systems and communication systems, traditional frequency measurement methods usually rely on the signals output by multi-bit ADC. However, existing multi-bit frequency measurement methods generally have high computational complexity and resource consumption, which is particularly prominent in embedded systems.

[0003] Single-bit frequency measurement technology (i.e., frequency measurement through single-bit quantized signals) has received increasing attention due to its advantages such as simplified hardware requirements and reduced power consumption. However, traditional single-bit frequency measurement methods usually process multi-bit sampled signals after converting them into single-bit signals. Although it can effectively reduce the amount of data, there are still problems of accuracy loss in high-frequency and high-precision applications. Especially in multi-bit sampling systems, how to combine the high precision of multi-bit signals with the simplified characteristics of single-bit frequency measurement for effective optimization is still a challenge faced by current technologies. Summary of the Invention

[0004] The present invention proposes a spectrum optimization calculation method based on single-bit frequency measurement technology to solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above object, the present invention provides a spectrum optimization calculation method based on single-bit frequency measurement technology, including the following steps:

[0006] Input multi-bit digital signals and perform N-point buffering, where N is the number of points of the discrete Fourier transform;

[0007] Split the buffered multi-bit signals bit by bit to obtain several groups of single-bit sampled data;

[0008] Perform transformation on the single-bit sampled data through an optimized Fourier transform algorithm to obtain the single-bit discrete Fourier transform result; where the optimized Fourier transform algorithm simplifies the calculation process of the Fourier transform based on the windowing technology of the rotation factor and the conjugate symmetry of the spectrum;

[0009] Perform weighted superposition on the single-bit discrete Fourier transform result to restore the spectrum information of the multi-bit data;

[0010] Extract the frequency characteristics of the spectrum information through a spectrum peak detection algorithm.

[0011] Preferably, the optimized Fourier transform algorithm includes:

[0012] Quantize the rotation factor matrix, quantize the rotation factors into high-precision integer values, and reduce the requirements for high-precision floating-point calculations;

[0013] Transfer the windowing operation from the input signal level to the rotation factor level, and perform windowing by adjusting the amplitude of the rotation factors.

[0014] Preferably, the optimized Fourier transform algorithm only calculates some of the rotation factors through the symmetry and anti-symmetry of the rotation factors, and the remaining rotation factors are generated through conjugate symmetry, reducing the computational amount and storage requirements.

[0015] Preferably, when splitting the cached multi-bit signal bit by bit, invert the highest-bit data of the split, and convert the sampled multi-bit signal into an unsigned number.

[0016] Preferably, the optimized Fourier transform algorithm is implemented using a pipeline structure in the FPGA, reorder the sampled signals through bit transposition, and calculate the discrete Fourier transform results in segments.

[0017] The present invention also proposes a computer device, including a memory, a processor, and a computer program stored on the memory, and the processor executes the computer program to implement the steps of the method.

[0018] The present invention also proposes a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method are implemented.

[0019] The present invention also proposes a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the method are implemented.

[0020] Compared with the prior art, the present invention has the following advantages and technical effects:

[0021] The present invention discloses a spectrum optimization calculation method based on single-bit frequency measurement technology, which includes the following steps: input a multi-bit digital signal and perform N-point buffering, where N is the number of points of the discrete Fourier transform; split the buffered multi-bit signal bit by bit to obtain several groups of single-bit sampling data; perform transformation on the single-bit sampling data through an optimized Fourier transform algorithm to obtain the single-bit discrete Fourier transform result; wherein the optimized Fourier transform algorithm simplifies the calculation process of the Fourier transform based on the windowing technology of the rotation factor and the conjugate symmetry of the spectrum; perform weighted superposition on the single-bit discrete Fourier transform result to restore the spectrum information of the multi-bit data; extract the frequency characteristics of the spectrum information through a spectrum peak detection algorithm. The present invention combines the multi-bit data splitting and superposition method, the single-bit frequency measurement technology, and the rotation factor windowing method, and can achieve efficient and fast frequency measurement in a multi-bit sampling system. This method combines the advantages of multi-bit signals and the simplified characteristics of single-bit frequency measurement, and while ensuring an extremely high frequency measurement speed, optimizes the computing resources and spectrum performance. Brief Description of the Drawings

[0022] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0023] Figure 1 It is a flowchart of the method of the embodiment of the present invention. Detailed Embodiments

[0024] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

[0025] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0026] The following explains some terms:

[0027] A multi-bit digital signal is a signal form in which each sampling point is represented by multiple bits, which can provide high precision and high dynamic range, and is widely used in complex signal processing fields such as high-quality audio, image processing, communication systems, and radar. Compared with single-bit signals, although multi-bit signals have a large amount of data, high processing complexity, and require more storage and transmission resources, they can represent the details and changes of signals more accurately and are suitable for application scenarios with high requirements for accuracy and dynamic range.

[0028] The twiddle factor is a key element in the Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) algorithms, which is used to achieve the conversion of signals from the time domain to the frequency domain. It is essentially a complex rotation operation that can map each sample of the input signal to a specific position in the frequency domain. The twiddle factor has periodicity and symmetry, and these properties enable the FFT algorithm to significantly reduce the computational complexity through a divide-and-conquer strategy, thereby improving the computational efficiency. In practical applications, the efficient implementation of the twiddle factor is crucial for reducing the complexity of the FFT algorithm, decreasing the storage requirements, and enhancing the computational speed. Especially in embedded systems with limited hardware resources, its optimized design can significantly improve the performance of signal processing.

[0029] Embodiment 1

[0030] In this embodiment, a spectrum optimization calculation method based on single-bit frequency measurement technology is provided, including the following steps:

[0031] Input a multi-bit digital signal and perform N-point buffering, where N is the number of points of the discrete Fourier transform;

[0032] Split the buffered multi-bit signal bit by bit to obtain several groups of single-bit sampling data;

[0033] Transform the single-bit sampling data through an optimized Fourier transform algorithm to obtain the single-bit discrete Fourier transform result; wherein the optimized Fourier transform algorithm simplifies the calculation process of the Fourier transform based on the windowing technique of the twiddle factor and the conjugate symmetry of the spectrum;

[0034] Perform weighted superposition on the single-bit discrete Fourier transform result to restore the spectrum information of the multi-bit data;

[0035] Extract the frequency characteristics of the spectrum information through a spectrum peak detection algorithm.

[0036] Specifically, it is divided into the following steps:

[0037] Input signal sampling and processing:

[0038] The input signal is a multi-bit digital signal, and the sampling bit number is m;

[0039] Perform N-point buffering on the sampled multi-bit signal, where N is the number of points for the discrete Fourier transform.

[0040] Splitting and conversion of single-bit signals:

[0041] Split the buffered multi-bit signal bit by bit to obtain m groups of N-point single-bit sampling data;

[0042] Invert the highest bit data of the split, and convert the sampled multi-bit signal into an unsigned number.

[0043] Optimized Fourier Transform Algorithm:

[0044] Apply the optimized Fourier transform algorithm to each bit of the split N - point single - bit data. This optimized algorithm is based on the windowing technique of the twiddle factor and mirror symmetry, simplifies the calculation of the Fourier transform, reduces the storage requirements and computational complexity, and effectively reduces the computational delay and power consumption.

[0045] Twiddle Factor Windowing and Quantization Processing:

[0046] Twiddle Factor Pre - processing: The twiddle factor matrix is simplified through a quantization algorithm, and the twiddle factors are quantized into high - precision integer values, thereby reducing the need for high - precision floating - point calculations, and reducing the complexity and power consumption of hardware implementation;

[0047] Windowing Operation: Transfer the windowing operation from the input signal level to the twiddle factor level. By adjusting the amplitude of the twiddle factor to achieve windowing, optimize the spectral characteristics, reduce spectral leakage, and improve the measurement accuracy.

[0048] Utilization of Spectral Conjugate Symmetry and Anti - symmetry

[0049] Utilize the conjugate symmetry of the spectrum to calculate only half of the spectrum, reducing the computational amount of twiddle factors and storage;

[0050] The symmetry of the twiddle factor further optimizes the calculation process of the Fourier transform. By conjugate symmetry, redundant calculations are reduced, and the hardware resource requirements are lowered.

[0051] Parallel Computing and Data Storage:

[0052] The present invention adopts a high - parallelism design. The Fourier transform results of each bit of single - bit data are weighted and superimposed to restore the spectral information of multi - bit data;

[0053] To achieve efficient calculation, each group of data is temporarily stored in registers before transformation, and parallel calculation is performed through combinational logic, thereby reducing the delay and increasing the throughput.

[0054] Data Weighting and Spectrum Extraction:

[0055] Superimpose the weighted single - bit discrete Fourier transform results of each group to restore the frequency characteristics of multi - bit data;

[0056] Finally, extract the frequency characteristics of the signal through the spectrum peak detection algorithm.

[0057] Embodiment 2

[0058] The embodiment of the present invention provides a spectrum optimization calculation method based on single - bit frequency measurement technology. This method includes the following steps:

[0059] Step S1: The input signal is a multi-bit digital signal with a sampling bit number of m. The sampled multi-bit signal is cached at N points, where N is the number of points for discrete Fourier transform.

[0060] Step S2: The cached multi-bit signal is split bit by bit to obtain m groups of N-point single-bit sampling data. Among them, the highest-bit data after splitting is inverted, and the sampled multi-bit signal is converted into an unsigned number.

[0061] Step S3: Apply the optimized Fourier transform algorithm to each bit of the split N-point single-bit data. This optimized algorithm utilizes the symmetry and anti-symmetry inside the rotation factor and the special requirements of the single-bit signal, avoiding the multi-segment complex multiplication of the traditional FFT algorithm, simplifying the calculation of the Fourier transform, reducing the storage requirements and computational complexity, and effectively reducing the computational delay and power consumption.

[0062] Specifically, the optimized single-bit Fourier transform algorithm used in the present invention utilizes the symmetry and degenerate properties of the rotation factor under specific conditions, as shown in the following table:

[0063]

[0064] According to the symmetry and anti-symmetry characteristics inside the rotation factor, the rotation factor matrix can be disassembled in parts.

[0065] When n = 2^q·r, only calculate the rotation factors of the first k = N / (2^(q + 1)), and the rest are generated through conjugate symmetry, where r = 0, 1..., N / (2^(q + 1)); q = 0, 1..., log2(N) - 1.

[0066] When n = 2^q·(2r + 1), only calculate the rotation factors of the first k = N / (2^(q + 2)), and the rest are generated through conjugate anti-symmetry, where r = 0, 1..., N / (2^(q + 2)); q = 0, 1,..., log2(N) - 2.

[0067] The index of the input signal is reversed in binary to achieve bit transposition, so that the rotation factors of n = 2^q·r or n = 2^q·(2r + 1) become adjacent data after sequence rearrangement for subsequent segmented calculation.

[0068] Specifically, special integer approximation and windowing processing are required for the rotation factors used in this algorithm:

[0069] For the rotation factor The approximate kernel quantization formula is:

[0070]

[0071] b is the bit width of integer quantization. In this embodiment, b is taken as 4. For any rotation factor with N points (N≥16), it will be approximately rounded to a rotation factor with a maximum bit width of 4 bits for 16 points to simplify the operation.

[0072] Transfer the windowing operation from the input signal level to the rotation factor level, and realize windowing by adjusting the amplitude of the approximated rotation factor. Without affecting the internal symmetry and anti-symmetry characteristics of the above rotation factor, eliminate multiplication operations and reduce resource overhead.

[0073] Specifically, a spectrum optimization calculation method based on single-bit frequency measurement technology is shown in the figure, and the method flow chart is as Figure 1 shown.

[0074] In step S3, the optimized grouped single-bit Fourier transform algorithm used is implemented in a three-stage pipeline structure in the FPGA. The following is an example using the 64-point spectrum optimization calculation method:

[0075] Reorder the sampled signal by bit transposition. In the first stage, perform DFT calculations with index value k from 0 to 2 on the sampled data at positions 0 - 3 after bit transposition, perform DFT calculations with index value k from 0 to 2 on the sampled data at positions 4 - 7 after bit transposition, perform DFT calculations with index value k from 0 to 4 on the sampled data at positions 8 - 15 after bit transposition, perform DFT calculations with index value k from 0 to 8 on the sampled data at positions 16 - 31 after bit transposition, and perform DFT calculations with index value k from 0 to 16 on the sampled data at positions 32 - 64 after bit transposition.

[0076] In the second stage, according to the internal symmetry and anti-symmetry characteristics of the rotation factor, for the sampled data at positions 0 - 31 after bit transposition, the complete result with index value k from 0 to 16 can be restored through simple assignment and inversion.

[0077] In the third stage, according to the internal symmetry and anti-symmetry characteristics of the rotation factor, for the sampled data at positions 0 - 63 after bit transposition, the complete result with index value k from 0 to 32 can be restored through simple assignment and inversion.

[0078] Step S4, reuse the algorithm structure used in step S3, repeat step S3 time-divisionally, and shift and superimpose the single-bit discrete Fourier transform results of each group to restore the frequency characteristics of multi-bit data.

[0079] Step S5, calculate the modulus value of the result obtained in step S4 to perform spectral peak search to obtain the spectral peak of the radar signal.

[0080] This embodiment also proposes a computer device, including a memory, a processor, and a computer program stored on the memory. The processor executes the computer program to implement the steps of the method.

[0081] This embodiment also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method are implemented.

[0082] This embodiment also provides a computer program product, including a computer program. When the computer program is executed by a processor, the steps of the method are implemented.

[0083] The present invention is based on the weighted superposition single-bit DFT algorithm. The sampled signal is split bit by bit after being cached. Each split single-bit signal is calculated by an optimized Fourier transform module, and the rotation factor is windowed after quantization processing. The final result extracts frequency information through a spectrum analysis module. Combining the multi-bit data splitting and superposition method, the single-bit frequency measurement technology, and the rotation factor windowing method can achieve efficient and fast frequency measurement in a multi-bit sampling system. This method combines the advantages of multi-bit signals and the simplified characteristics of single-bit frequency measurement, optimizing the computing resources and spectrum performance while ensuring an extremely high frequency measurement speed.

[0084] The above are only the preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the technical field of the present application within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A spectrum optimization calculation method based on single-bit frequency measurement technology, characterized in that: The following steps are involved: Input a multi-bit digital signal and perform N-point buffering, where N is the number of discrete Fourier transform points; Splitting the cached multi-bit signal bit by bit to obtain several groups of single-bit sampling data; The single-bit sampled data is transformed by optimizing the Fourier transform algorithm to obtain a single-bit discrete Fourier transform result; wherein the optimized Fourier transform algorithm simplifies the calculation process of the Fourier transform based on the windowing technology of the rotation factor and the conjugate symmetry of the spectrum; Perform weighted superposition on the single-bit discrete Fourier transform results to restore the spectrum information of multi-bit data; The frequency characteristics of the spectrum information are extracted through the spectrum peak detection algorithm.

2. The method according to claim 1, characterized in that The optimized Fourier transform algorithm comprises: Quantize the rotation factor matrix and convert the rotation factor into high-precision integer values ​​to reduce the need for high-precision floating-point calculations. The windowing operation is transferred from the input signal level to the rotation factor level, and windowing is performed by adjusting the amplitude of the rotation factor.

3. The method according to claim 2, characterized in that The optimized Fourier transform algorithm calculates only part of the rotation factors through the symmetry and antisymmetry of the rotation factors, and the remaining rotation factors are generated through conjugate symmetry, thereby reducing the amount of calculation and storage requirements.

4. The method according to claim 1, characterized in that When the buffered multi-bit signal is split bit by bit, the highest bit data of the split is inverted, and the sampled multi-bit signal is converted into an unsigned number.

5. The method according to claim 1, characterized in that The optimized Fourier transform algorithm is implemented in FPGA using a pipeline structure, reorders the sampled signals by bit transposition, and calculates discrete Fourier transform results in segments.

6. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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