A new high-fidelity signal frequency multiplication technology

Abstract

The present invention discloses a new high-fidelity signal frequency multiplication technology. In the present invention, by directly operating the Fourier expansion coefficients, the accurate maintenance of the waveform and phase characteristics during the signal frequency multiplication process is achieved, and the signal distortion problem caused by spectrum leakage and error accumulation is overcome. Frequency multiplication is directly achieved by matrix operation, without the need for frequency domain transformation and inverse transformation processes, which simplifies the implementation steps of frequency multiplication signal generation and significantly improves calculation efficiency. Through the mathematical design of the frequency multiplication diagonal matrix, it is theoretically possible to support the accurate generation of any frequency multiplication signal without the need for additional spectrum interpolation and expansion operations, thereby eliminating the spectrum interference problem in high frequency multiplication scenarios. Through the matrix-based operation method, the present invention reduces the hardware resource requirements and implementation complexity, making it suitable for deployment in embedded devices or resource-constrained application environments, and has higher economy and scalability.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to a new type of high-fidelity signal frequency multiplication technology. Background Art

[0002] Signal processing technology is an important part of modern information science and is widely used in communication systems, electronic equipment, audio processing, industrial control, image processing and other fields. In the analysis and synthesis of periodic signals, Fourier analysis, as a core mathematical tool, can decompose complex signals into a series of frequency components, providing a theoretical basis for the spectrum processing of signals. The frequency adjustment method of periodic signals is widely used in scenarios such as spectrum expansion and compression in wireless communications, pitch conversion in audio processing, and harmonic analysis of power systems, becoming one of the key technologies for various signal processing systems. There are two main ways to implement traditional signal frequency multiplication methods: one is hardware-based circuit design, frequency multiplier; the other is spectrum analysis and synthesis technology based on digital signal processing. In digital signal processing, Fourier transform is one of the core tools for periodic signal analysis. Through Fourier expansion, periodic signals can be fully characterized by frequency domain features.

[0003] However, the existing technology requires the signal to be transformed in the frequency domain, reorganized in the spectrum, and then restored to the time domain signal through inverse transformation. In this process, problems such as spectrum leakage and boundary effects may cause signal waveform distortion, especially in high-frequency and complex signal processing. At the same time, for scenarios where the waveform characteristics and phase characteristics of the signal need to be strictly maintained, the existing technology is difficult to provide sufficient accuracy. In addition, the FFT method relies on frequency domain operations, and the frequency multiplication process requires interpolation or expansion of spectral components. This spectrum reorganization method has a high processing complexity for complex signals, especially in applications with high real-time requirements, and there is a bottleneck in computing efficiency. Summary of the invention

[0004] The purpose of the present invention is to provide a new high-fidelity signal frequency multiplication technology in order to solve the above-mentioned problems.

[0005] The technical solution adopted by the present invention is as follows: a new high-fidelity signal frequency multiplication technology, comprising the following steps:

[0006] S1: Fourier coefficient extraction, using the signal Fourier expansion formula to extract the coefficient u n ;

[0007] S2: Frequency multiplication matrix construction: construct the frequency multiplication diagonal matrix A according to the target frequency multiplication multiple m m ;

[0008] S3: Signal frequency doubling generation, quantizing the signal and adding it to A m Perform matrix multiplication to generate a frequency-multiplied signal;

[0009] S4: Multi-phase signal superposition, construct a diagonal matrix B for the multi-phase signal, and adjust it with A m The proportional relationship is realized to realize the superposition of frequency-doubled signals;

[0010] S5: Using the L2 norm or other signal quality evaluation indicators, evaluate the difference between the frequency-multiplied signal y(t) and the original signal u(t) to ensure the consistency of the signal waveform and phase;

[0011] S6: According to the signal quality evaluation result, adjust the parameters of the frequency multiplication matrix A_m or the phase superposition matrix B to optimize the fidelity of the frequency multiplication signal;

[0012] S7: Implement the above method on a hardware platform such as FPGA or DSP to improve computing efficiency.

[0013] In a preferred embodiment, in step S1, for a periodic signal u(t) with an angular frequency of ω0, its Fourier expansion series is:

[0014]

[0015] Defining vectors The m-fold frequency-doubling diagonal matrix is ​​defined as A m , A m The off-diagonal elements of are all 0, and A m The diagonal element of

[0016]

[0017] If u h =0, then

[0018] (A m ) h,h ≡0.

[0019] Now A u Act on (left multiplication) Get a new periodic signal f(t):

[0020]

[0021] Among them, ω1 = mω0. Since the Fourier series coefficients of f(t) are exactly the same as those of u(t), and the angular frequency ω1 of f(t) is m times that of ω0, f(t) is a periodic signal with the same properties (such as waveform and phase) as u(t) and a frequency m times that of u(t).

[0022] Suppose the superposition signal of a series of signals u1(t), u2(t), u3(t), ... with the same frequency, waveform and different phase as u(t) is g(t).

[0023] g(t)=∑ k u k (t),

[0024] in,

[0025] u k (t) = u(t + φ k ).

[0026] will u k (t) is Fourier expanded, then

[0027]

[0028] Where B is a diagonal matrix with off-diagonal elements equal to 0 and diagonal elements equal to

[0029]

[0030] If we choose an appropriate k (k=1,2,…), so that B∝A m , then g(t)∝f(t), that is, g(t) is a periodic signal with the same properties (such as waveform, phase) as u(t) and a frequency m times that of u(t).

[0031] The frequency of the signal to be amplified is accompanied by noise.

[0032] u R,k (t) = u(t + φ k )+u err,k (t),

[0033] Among them, u(t) is the target signal (i.e. the signal whose frequency needs to be amplified), and u err,k (t) is the noise. At this time,

[0034] g(t)=∑ k [u(t+φ k )+u err,k (t)].

[0035] It is considered that g(t) is obtained by multiplying the frequency of the noisy signal, and f(t) is obtained by multiplying the frequency of the target signal. At the same time, the L of g(t)-f(t) can be used 2 The norm is used to illustrate the difference between two signals and to measure the degree of distortion after the signal frequency is multiplied.

[0036] In a preferred embodiment, in the process of measuring the distortion of the signal after frequency multiplication, the signal period is assumed to be 2π.

[0037] By Parseval equation

[0038]

[0039] where u n with u err,n are u(t) and u err,k (t) is the Fourier coefficient of g(t). After considering the noise, the design goal of matrix B is to make the L2 norm of g(t)-f(t) as small as possible, so that the distortion of the signal after the signal frequency is doubled is as small as possible. In fact, without distinguishing between the target signal and the noise signal, at least the distortion of the signal after the frequency is doubled can be guaranteed.

[0040] In a preferred embodiment, in step S2, the off-diagonal elements of the matrix A_m are all 0, and the diagonal elements are:

[0041] (A_m)_{h,h}=0, when mod(h,m)≠0;

[0042] (A_m){h,h}=u{h / m}, when mod(h,m)=0 and h≠0;

[0043] (A_m)_{h,h}=u_h,when h=0.

[0044] In a preferred embodiment, in step S3, if the signal length is long, the signal can be divided into multiple blocks, and matrix multiplication operations can be performed in parallel on multiple processors or threads, which can significantly reduce the calculation time, especially on multi-core processors.

[0045] If there are a large number of zero or near-zero Fourier coefficients in the signal, the frequency matrix A_m can be converted into a sparse matrix format, which can reduce the storage space requirements and improve the efficiency of matrix multiplication operations.

[0046] In a preferred embodiment, in step S4, if a multi-phase frequency-multiplied signal needs to be generated, a diagonal matrix B is constructed, whose diagonal elements are B_{n,n}=e^{iφ_k}, where φ_k is the phase offset of the kth signal. Matrix B is multiplied by A_m to obtain a new frequency-multiplied matrix C=B*A_m. After the signal u(t) is vectorized, a matrix multiplication operation is performed with the matrix C to generate a multi-phase frequency-multiplied signal g(t).

[0047] In a preferred embodiment, in step S5, the waveform similarity between the frequency-doubled signal y(t) and the original signal u(t) is calculated using a cross-correlation function or waveform matching technology. The waveform similarity can reflect the consistency of the signal waveform and help identify signal distortion, specifically including:

[0048] S1: Signal preprocessing: perform necessary preprocessing on the original signal u(t) and the frequency-doubled signal y(t), such as denoising and normalization, to ensure signal quality and eliminate the influence of amplitude differences on similarity calculation.

[0049] S2: Calculate the cross-correlation function, calculate the cross-correlation function R uy(τ) of u(t) and y(t), which reflects the similarity between the two signals at different time delays.

[0050] The cross-correlation function is defined as: R uy(τ) = ∫ [u(t)*y(t+τ)] dt, where τ is the time delay. By finding the maximum value of the cross-correlation function and its corresponding time delay, the best alignment and similarity of the two signals can be determined.

[0051] S3: Use waveform matching techniques, such as dynamic time warping (DTW) or waveform similarity analysis (WSA), to measure the waveform similarity of u(t) and y(t). DTW minimizes the cumulative difference between two signals through nonlinear time alignment and is suitable for signals of different lengths or asynchronous signals. WSA calculates similarity based on the matching degree of waveform feature points and focuses more on the similarity of waveform structure.

[0052] S4: Similarity index calculation, based on the results of the cross-correlation function or waveform matching technology, calculate specific similarity indicators, such as correlation coefficient, matching score, etc. The correlation coefficient is a commonly used similarity index with a value range of -1 to 1. The closer the value is to 1, the more similar the two signals are.

[0053] S5: Result analysis and optimization, analyze the results of the similarity index and evaluate the waveform consistency between the doubled signal y(t) and the original signal u(t). If the similarity is low, it may be necessary to adjust the doubled method or parameters to optimize the quality and similarity of the doubled signal.

[0054] S6: Visual comparison: Visually compare the original signal u(t) and the frequency-doubled signal y(t) to intuitively show the waveform differences and similarities between the two signals. Visualization tools can be waveform graphs, correlation graphs, etc., which help to further understand the results of similarity calculation.

[0055] In a preferred embodiment, in step S6, multiple objectives are considered simultaneously, such as waveform similarity, phase error, and spectrum distortion, etc. Through multi-objective optimization, a better parameter combination can be found, thereby improving the fidelity of the frequency-multiplied signal.

[0056] In a preferred embodiment, in step S7, on an FPGA or DSP, parallel processing capabilities are used to accelerate matrix multiplication operations. Matrix multiplication can be decomposed into multiple parallel tasks and executed simultaneously on different processing units to improve computational efficiency. In hardware design, resource reuse technology can be used to implement matrix multiplication operations using a multiplication accumulator (MAC) unit of a digital signal processor. This can reduce the use of hardware resources and improve computational efficiency.

[0057] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0058] 1. In the present invention, by directly operating the Fourier expansion coefficients, the waveform and phase characteristics are accurately maintained during the signal frequency doubling process, thereby overcoming the signal distortion problem caused by spectrum leakage and error accumulation. Frequency doubling is directly achieved using matrix operations without the need for frequency domain transformation and inverse transformation processes, which simplifies the implementation steps of frequency doubling signal generation and significantly improves computational efficiency. Through the mathematical design of the frequency doubling diagonal matrix, it is theoretically possible to support the accurate generation of any frequency doubling signal without the need for additional spectrum interpolation and expansion operations, thereby eliminating the spectrum interference problem in high frequency doubling scenarios.

[0059] 2. In the present invention, through the matrix-based operation method, the present invention reduces the hardware resource requirements and implementation complexity, making it suitable for deployment in embedded devices or resource-constrained application environments, with higher economy and scalability. It can flexibly process a variety of signal forms, including multi-phase and multi-frequency signals, and is suitable for a variety of signal processing scenarios, multi-signal synthesis, periodic signal analysis and modulation, and other fields, with strong versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic diagram of the structure of the present invention. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0062] Reference Figure 1 ,

[0063] Example:

[0064] A new high-fidelity signal frequency multiplication technology includes the following steps:

[0065] S1: Fourier coefficient extraction, using the signal Fourier expansion formula to extract the coefficient u n ;

[0066] S2: Frequency multiplication matrix construction: construct the frequency multiplication diagonal matrix A according to the target frequency multiplication multiple m m ;

[0067] S3: Signal frequency doubling generation, quantizing the signal and adding it to A m Perform matrix multiplication to generate a frequency-multiplied signal;

[0068] S4: Multi-phase signal superposition, construct a diagonal matrix B for the multi-phase signal, and adjust it with A m The proportional relationship is realized to realize the superposition of frequency-doubled signals;

[0069] S5: Using the L2 norm or other signal quality evaluation indicators, evaluate the difference between the frequency-multiplied signal y(t) and the original signal u(t) to ensure the consistency of the signal waveform and phase;

[0070] S6: According to the signal quality evaluation result, adjust the parameters of the frequency multiplication matrix A_m or the phase superposition matrix B to optimize the fidelity of the frequency multiplication signal;

[0071] S7: Implement the above method on a hardware platform such as FPGA or DSP to improve computing efficiency.

[0072] In step S1, for a periodic signal u(t) with an angular frequency of ω0, its Fourier expansion series is:

[0073]

[0074] Defining vectors The m-fold frequency-doubling diagonal matrix is ​​defined as A m , A m The off-diagonal elements of are all 0, and A m The diagonal element of

[0075]

[0076] If u h =0, then

[0077] (A m ) h,h ≡0.

[0078] Now A u Act on (left multiplication) Get a new periodic signal f(t):

[0079]

[0080] Among them, ω1 = mω0. Since the Fourier series coefficients of f(t) are exactly the same as those of u(t), and the angular frequency ω1 of f(t) is m times that of ω0, f(t) is a periodic signal with the same properties (such as waveform and phase) as u(t) and a frequency m times that of u(t).

[0081] Suppose the superposition signal of a series of signals u1(t), u2(t), u3(t), ... with the same frequency, waveform and different phase as u(t) is g(t).

[0082] g(t)=∑ k u k (t),

[0083] in,

[0084] u k (t) = u(t + φ k ).

[0085] will u k (t) is Fourier expanded, then

[0086]

[0087]

[0088] Where B is a diagonal matrix with off-diagonal elements equal to 0 and diagonal elements equal to

[0089]

[0090] If we choose an appropriate k (k=1,2,…), so that B∝A m , then g(t)∝f(t), that is, g(t) is a periodic signal with the same properties (such as waveform, phase) as u(t) and a frequency m times that of u(t).

[0091] The frequency of the signal to be amplified is accompanied by noise.

[0092] u R,k (t) = u(t + φ k )+u err,k (t),

[0093] Among them, u(t) is the target signal (i.e. the signal whose frequency needs to be amplified), and u err,k (t) is the noise. At this time,

[0094] g(t)=∑ k [u(t+φ k )+u err,k (t)].

[0095] It is considered that g(t) is obtained by multiplying the frequency of the noisy signal, and f(t) is obtained by multiplying the frequency of the target signal. At the same time, the L of g(t)-f(t) can be used 2 The norm is used to illustrate the difference between two signals and to measure the degree of distortion after the signal frequency is multiplied.

[0096] 3. A high-fidelity new signal frequency multiplication technology as claimed in claim 2, characterized in that: in the process of measuring the distortion of the signal after frequency multiplication, the signal period is set to 2π.

[0097] By Parseval equation

[0098]

[0099] where u n with u err,n are u(t) and u err,k (t) is the Fourier coefficient of g(t). After considering the noise, the design goal of matrix B is to make the L2 norm of g(t)-f(t) as small as possible, so that the distortion of the signal after the signal frequency is doubled is as small as possible. In fact, without distinguishing between the target signal and the noise signal, at least the distortion of the signal after the frequency is doubled can be guaranteed.

[0100] In step S2, the off-diagonal elements of the matrix A_m are all 0, and the diagonal elements are:

[0101] (A_m)_{h,h}=0, when mod(h,m)≠0;

[0102] (A_m){h,h}=u{h / m}, when mod(h,m)=0 and h≠0;

[0103] (A_m)_{h,h}=u_h,when h=0.

[0104] In step S3, if the signal length is long, the signal can be divided into multiple blocks and matrix multiplication operations can be performed in parallel on multiple processors or threads. This can significantly reduce the calculation time, especially on multi-core processors.

[0105] If there are a large number of zero or near-zero Fourier coefficients in the signal, the frequency matrix A_m can be converted into a sparse matrix format, which can reduce the storage space requirements and improve the efficiency of matrix multiplication operations.

[0106] In step S4, if a multi-phase frequency-multiplied signal needs to be generated, a diagonal matrix B is constructed, whose diagonal elements are B_{n,n}=e^{iφ_k}, where φ_k is the phase offset of the kth signal. Matrix B is multiplied by A_m to obtain a new frequency-multiplied matrix C=B*A_m. After the signal u(t) is vectorized, a matrix multiplication operation is performed with matrix C to generate a multi-phase frequency-multiplied signal g(t).

[0107] In step S5, the waveform similarity between the frequency-multiplied signal y(t) and the original signal u(t) is calculated using a cross-correlation function or waveform matching technology. The waveform similarity can reflect the consistency of the signal waveform and help identify signal distortion, including:

[0108] S1: Signal preprocessing: perform necessary preprocessing on the original signal u(t) and the frequency-doubled signal y(t), such as denoising and normalization, to ensure signal quality and eliminate the influence of amplitude differences on similarity calculation.

[0109] S2: Calculate the cross-correlation function, calculate the cross-correlation function R uy(τ) of u(t) and y(t), which reflects the similarity between the two signals at different time delays.

[0110] The cross-correlation function is defined as: R uy(τ) = ∫ [u(t)*y(t+τ)] dt, where τ is the time delay. By finding the maximum value of the cross-correlation function and its corresponding time delay, the best alignment and similarity of the two signals can be determined.

[0111] S3: Use waveform matching techniques, such as dynamic time warping (DTW) or waveform similarity analysis (WSA), to measure the waveform similarity of u(t) and y(t). DTW minimizes the cumulative difference between two signals through nonlinear time alignment and is suitable for signals of different lengths or asynchronous signals. WSA calculates similarity based on the matching degree of waveform feature points and focuses more on the similarity of waveform structure.

[0112] S4: Similarity index calculation, based on the results of the cross-correlation function or waveform matching technology, calculate specific similarity indicators, such as correlation coefficient, matching score, etc. The correlation coefficient is a commonly used similarity index with a value range of -1 to 1. The closer the value is to 1, the more similar the two signals are.

[0113] S5: Result analysis and optimization, analyze the results of the similarity index and evaluate the waveform consistency between the doubled signal y(t) and the original signal u(t). If the similarity is low, it may be necessary to adjust the doubled method or parameters to optimize the quality and similarity of the doubled signal.

[0114] S6: Visual comparison: Visually compare the original signal u(t) and the frequency-doubled signal y(t) to intuitively show the waveform differences and similarities between the two signals. Visualization tools can be waveform graphs, correlation graphs, etc., which help to further understand the results of similarity calculation.

[0115] In step S6, multiple objectives are considered simultaneously, such as waveform similarity, phase error, and spectrum distortion. Through multi-objective optimization, a better parameter combination can be found, thereby improving the fidelity of the frequency-multiplied signal.

[0116] In step S7, on the FPGA or DSP, the parallel processing capability is used to accelerate the matrix multiplication operation. The matrix multiplication can be decomposed into multiple parallel tasks and executed simultaneously on different processing units to improve the computational efficiency. In the hardware design, resource reuse technology can be used to implement the matrix multiplication operation using the multiplication accumulator (MAC) unit of the digital signal processor. This can reduce the use of hardware resources and improve the computational efficiency.

[0117] In the present invention, by directly operating the Fourier expansion coefficients, the waveform and phase characteristics are accurately maintained during the signal frequency doubling process, thereby overcoming the signal distortion problem caused by spectrum leakage and error accumulation. Frequency doubling is directly achieved by matrix operation without the need for frequency domain transformation and inverse transformation processes, which simplifies the implementation steps of frequency doubling signal generation and significantly improves computational efficiency. Through the mathematical design of the frequency doubling diagonal matrix, it is theoretically possible to support the accurate generation of any frequency doubling signal without the need for additional spectrum interpolation and expansion operations, thereby eliminating the spectrum interference problem in high frequency doubling scenarios.

[0118] In the present invention, through the matrix-based operation method, the present invention reduces the hardware resource requirements and implementation complexity, making it suitable for deployment in embedded devices or resource-constrained application environments, with higher economy and scalability. It can flexibly process a variety of signal forms, including multi-phase and multi-frequency signals, and is suitable for a variety of signal processing scenarios, multi-signal synthesis, periodic signal analysis and modulation, and other fields, with strong versatility.

[0119] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0120] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A new high-fidelity signal frequency multiplication technology, characterized by: The following steps are involved: S1: Fourier coefficient extraction, using the signal Fourier expansion formula to extract the coefficient u n ; S2: Frequency multiplication matrix construction: construct the frequency multiplication diagonal matrix A according to the target frequency multiplication multiple m m ; S3: Signal frequency doubling generation, quantizing the signal and adding it to A m Perform matrix multiplication to generate a frequency-multiplied signal; S4: Multi-phase signal superposition, construct a diagonal matrix B for the multi-phase signal, and adjust it with A m The proportional relationship is realized to realize the superposition of frequency-doubled signals; S5: using the L2 norm or other signal quality evaluation indicators to evaluate the difference between the frequency-multiplied signal y(t) and the original signal u(t) to ensure the consistency of the signal waveform and phase; S6: According to the signal quality evaluation result, adjust the parameters of the frequency multiplication matrix A_m or the phase superposition matrix B to optimize the fidelity of the frequency multiplication signal; S7: Implement the above method on an FPGA or DSP hardware platform to improve computing efficiency.

2. A high-fidelity new signal frequency multiplication technology as claimed in claim 1, characterized in that: In step S1, for a periodic signal u(t) with an angular frequency of ω0, its Fourier expansion series is: Defining vectors The m-fold frequency-doubling diagonal matrix is ​​defined as A m , A m The off-diagonal elements of are all 0, and A m The diagonal element of If u h =0, then (A m ) h,h ≡0. Now A u Act on (left multiplication) Get a new periodic signal f(t): Where ω1=mω0; since the Fourier series coefficients of f(t) are exactly the same as those of u(t), and the angular frequency ω1 of f(t) is m times that of ω0, f(t) is a periodic signal with the same properties as u(t) and a frequency m times that of u(t); Assume a series of signals u1(t) with the same frequency, waveform and different phase as u(t), The superposition signal of u2(t),u3(t),… is g(t), g(t)=∑ k u k (t), in, u k (t)=u(t+φ k ). will u k (t) is Fourier expanded, then Where B is a diagonal matrix with off-diagonal elements equal to 0 and diagonal elements equal to If we choose an appropriate k (k=1,2,…), so that B∝A m , then g(t)∝f(t), that is, g(t) is a periodic signal with the same properties as u(t) and a frequency m times that of u(t); The signal whose frequency needs to be amplified is accompanied by noise; u R,k (t)=u(t+φ k )+u err,k (t), Among them, u(t) is the target signal (i.e. the signal whose frequency needs to be amplified), and u err,k (t) is the noise; at this time, g(t)=∑ k [u(t+φ k )+u err,k (t)]. It is considered that g(t) is obtained by multiplying the frequency of the noisy signal, while f(t) is obtained by multiplying the frequency of the target signal. At the same time, using the L of g(t)-f(t) 2 The norm is used to illustrate the difference between two signals and to measure the degree of distortion after the signal frequency is multiplied.

3. A high-fidelity new signal frequency multiplication technology as claimed in claim 2, characterized in that: In the process of measuring the distortion after the signal frequency is doubled, the signal period is assumed to be 2π; By Parseval where u n with u err,n are u(t) and u err,k (t); after considering the noise, the design goal of the matrix B is to make the L2 norm of g(t)-f(t) as small as possible, so that the distortion of the signal after the signal frequency is doubled is as small as possible.

4. A high-fidelity new signal frequency multiplication technology as claimed in claim 1, characterized in that: In step S2, the off-diagonal elements of the matrix A_m are all 0, and the diagonal elements are: (A_m)_{h,h}=0, when mod(h,m)≠0; (A_m){h,h}=u{h / m}, when mod(h,m)=0 and h≠0; (A_m)_{h,h}=u_h,when h=0.

5. A high-fidelity new signal frequency multiplication technology as claimed in claim 1, characterized in that: In step S3, if the signal length is long, the signal is divided into multiple blocks, and matrix multiplication operations are performed in parallel on multiple processors or threads; this significantly reduces the calculation time, especially on multi-core processors; If there are a large number of zero-valued or near-zero-valued Fourier coefficients in the signal, the frequency matrix A_m is converted into a sparse matrix format.

6. A high-fidelity new signal frequency multiplication technology as claimed in claim 1, characterized in that: In step S4, a multi-phase frequency-doubled signal is first generated, and a diagonal matrix B is constructed, whose diagonal elements are B_{n,n}=∑ k b_k e^{inφ_k}, where φ_k is the phase offset of the kth signal; multiply the matrix B by the vector Perform matrix multiplication operation to generate the frequency-doubled signal g(t).

7. A high-fidelity new signal frequency multiplication technology as claimed in claim 1, characterized in that: In the step S5, the waveform similarity between the frequency-doubled signal y(t) and the original signal u(t) is calculated using a cross-correlation function or a waveform matching technique; Waveform similarity reflects the consistency of signal waveforms and helps identify signal distortion, including: S1: Signal preprocessing: perform necessary preprocessing on the original signal u(t) and the frequency-doubled signal y(t) to ensure signal quality and eliminate the influence of amplitude difference on similarity calculation; S2: Calculate the cross-correlation function, calculate the cross-correlation function Ruy(τ) of u(t) and y(t), which reflects the similarity of two signals at different time delays; The cross-correlation function is defined as: R uy(τ) = ∫ [u(t) * y(t + τ)] dt, where τ is the time delay; by finding the maximum value of the cross-correlation function and its corresponding time delay, the best alignment and similarity of the two signals are determined; S3: Use waveform matching technology, dynamic time warping (DTW) or waveform similarity analysis (WSA), to measure the waveform similarity of u(t) and y(t); DTW minimizes the cumulative difference between two signals through nonlinear time alignment and is suitable for signals of different lengths or asynchronous signals; WSA calculates similarity based on the matching degree of waveform feature points and pays more attention to the similarity of waveform structure; S4: similarity index calculation, based on the results of the cross-correlation function or waveform matching technology, calculate specific similarity indicators, including correlation coefficient and matching score; the correlation coefficient is a commonly used similarity index, with a value range of -1 to 1, and the closer the value is to 1, the more similar the two signals are; S5: Result analysis and optimization, analyzing the results of the similarity index and evaluating the waveform consistency between the doubled signal y(t) and the original signal u(t); If the similarity is low, the frequency doubling method or parameters may need to be adjusted to optimize the quality and similarity of the frequency doubling signals; S6: Visual comparison: Visually compare the original signal u(t) and the frequency-doubled signal y(t) to intuitively show the waveform differences and similarities between the two signals.

8. A high-fidelity new signal frequency multiplication technology as claimed in claim 1, characterized in that: In step S6, multiple objectives, waveform similarity, phase error and spectrum distortion are considered simultaneously; a better parameter combination is found through multi-objective optimization, thereby improving the fidelity of the frequency-multiplied signal.

9. A high-fidelity new signal frequency multiplication technology as claimed in claim 1, characterized in that: In step S7, on the FPGA or DSP, the parallel processing capability is used to accelerate the matrix multiplication operation; the matrix multiplication is decomposed into multiple parallel tasks and executed simultaneously on different processing units to improve the calculation efficiency.

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