A method and device for estimating a noise distortion signal of a windowed FFT algorithm

Abstract

The application discloses a noise distortion signal estimation method and device of a windowed FFT algorithm. The application comprises sampling and windowing a noise distortion signal, performing a discrete Fourier transform to obtain a discrete frequency spectrum X(l); finding a maximum spectral line position index l1 and a second maximum spectral line position index l2 in |X(l)|; determining a search interval [a, b] according to l1 and l2; using a loss function of a normalized frequency value error value based on a minimum fundamental wave constructed through the relationship between positive and negative spectral components to calculate the accurate position index of the fundamental wave frequency in the search interval [a, b] by using a Fibonacci iteration; and calculating the fundamental wave frequency in the noise distortion signal v(n) according to the accurate position index of the fundamental wave frequency. The application aims to solve the technical problem that the effect of windowed interpolation discrete Fourier transform sharply decreases in a short period, and existing frequency estimation methods cannot efficiently and accurately measure the frequency of a noise distortion signal.

Description

Technical Field

[0001] This invention belongs to the field of noise signal testing and analysis, specifically relating to a method and apparatus for estimating noise distortion signals using a windowed FFT algorithm. Background Technology

[0002] Frequency estimation of noisy signals is a crucial aspect of spectrum analysis, with significant applications in various social and economic fields such as military, power, medicine, and communications, attracting widespread attention. The frequency estimation problem in noisy signals refers to the process of estimating the signal frequency within the noise by calculating and transforming the sampled signal values. In practical power systems, power signals are inevitably subject to noise interference, resulting in random errors. When the signal-to-noise ratio (SNR) is sufficiently high, the impact of noise on frequency estimation is negligible; however, when noise interference is significant, it increases the random error in the frequency measurement algorithm. In power systems, both low-voltage distribution networks and high-voltage transmission networks contain background noise. Although analog filters are used before sampling, the signal noise level can still affect the accuracy of frequency measurements.

[0003] Therefore, to accurately estimate the power grid frequency, frequency estimation algorithms such as Fast Fourier Transform (FFT), Prony method, wavelet transform, least squares method, and artificial neural networks have been proposed. Among these, the traditional FFT algorithm has advantages such as low computational cost and fast computation speed, but it suffers from disadvantages such as spectral leakage and picket-fence effect, resulting in large frequency estimation errors under noise interference. Other algorithms have excessive computational cost and low real-time performance, failing to meet the requirements of real-time measurement in power systems. Windowed interpolation can suppress spectral leakage and eliminate the picket-fence effect to some extent, thereby reducing noise interference. However, when using a short time window, the analytical accuracy of the windowed interpolation discrete Fourier transform method, which simultaneously considers negative frequency and harmonic spectral leakage, is significantly reduced. To date, there is still no ideal and mature solution to this problem. In existing technologies, window functions are generally used to suppress noise interference and to compensate for errors in the two-point interpolation discrete Fourier transform method. However, when the observation period is less than 2, the compensation effect for spectral leakage under noise interference decreases. For short-range spectral leakage, compensation is typically achieved through interpolation based on several maximum spectral lines, or by using the maximum spectral values ​​at different time stamps for spectral correction. However, the measurement error in frequency estimation within a short time window mainly stems from short-range spectral leakage at negative frequencies, the presence of which can significantly impact the accuracy of frequency measurements. Summary of the Invention

[0004] The technical problem to be solved by the present invention: In view of the above problems in the prior art, the present invention provides a noise-distorted signal estimation method and apparatus based on the windowed FFT algorithm, aiming at solving the technical problem that the effect of the windowed interpolation discrete Fourier transform drops sharply in a short period, and the existing frequency estimation methods cannot realize efficient and accurate measurement of the frequency of the noise-distorted signal.

[0005] To solve the above technical problem, the technical solution adopted by the present invention is:

[0006] A noise-distorted signal estimation method based on the windowed FFT algorithm, comprising the following steps:

[0007] S101, sampling the noise-distorted signal v(n) at a specified sampling frequency and applying windowing with a window function;

[0008] S102, performing discrete Fourier transform on the windowed noise-distorted signal x(n) to obtain a discrete frequency spectrum X(l);

[0009] S103, searching for the maximum spectral line position index l1 and the second maximum spectral line position index l2 in |X(l)| for the discrete frequency spectrum X(l);

[0010] S104, determining a search interval [a, b] according to the maximum spectral line position index l1 and the second maximum spectral line position index l2, and using a loss function of the normalized frequency value error based on the fundamental wave constructed by the relationship between the positive and negative frequency spectrum components, adopting Fibonacci iteration in the search interval [a, b] to calculate the accurate position index of the fundamental frequency;

[0011] S105, calculating the fundamental frequency in the noise-distorted signal v(n) according to the accurate position index of the fundamental frequency.

[0012] Optionally, when determining the search interval [a, b] according to the maximum spectral line position index l1 and the second maximum spectral line position index l2 in step S104, determining the search interval [a, b] includes: comparing the maximum spectral line position index l1 with the second maximum spectral line position index l2, if l1>l2, then a=l1-a1, b=l2+a2; if l1<l2, then a=l1-a2, b=l2+a1, where a1 and a2 are parameters less than 1 and a1 is greater than a2.

[0013] Optionally, adopting Fibonacci iteration in the search interval [a, b] to calculate the accurate position index of the fundamental frequency in step S104 includes:

[0014] S201, initializing the iteration variable i to 1, as well as the test points z1 and y1 for the first Fibonacci iteration:

[0015]

[0016] In the above formula, a and b are the lower and upper boundaries of the search interval [a, b], respectively, ρ1 is the compression ratio of the first Fibonacci iteration, and we have:

[0017]

[0018] In the above formula, ρ i Let F(i+2-i) be the compression ratio of the i-th Fibonacci iteration, F(i+2-i) be the (i+2-i)-th element of the Fibonacci sequence F, and F(i+3-i) be the (i+3-i)-th element of the Fibonacci sequence F, and we have:

[0019]

[0020] In the above formula, F(m), F(m-1), and F(m-2) are the m-th, m-1-th, and m-2-th elements of the Fibonacci sequence F, respectively; the number of elements r of the Fibonacci sequence F ranges from [3, +∞).

[0021] S202, using a loss function based on the normalized frequency error value of the minimum fundamental wave, constructed through the relationship between positive and negative spectral components, compares the pilot z of the i-th Fibonacci iteration. i and y i The loss function value, if the pilot z i The loss function value is greater than the pilot y i The loss function value is then updated according to the following formula: i The loss function value and the lower boundary 'a' of the search interval [a, b]:

[0022] a = z i ,

[0023] z i =y i ,

[0024] y i =a+(1-ρ i+1 )*(ba),

[0025] Otherwise, update z according to the following formula. i The loss function value and the upper boundary b of the search interval [a, b]:

[0026] b = z i ,

[0027] y i =z i ,

[0028] z i =a+ρ i+1 *(ba),

[0029] Where, ρi+1 is the compression ratio of the i+1-th Fibonacci iteration;

[0030] S203: Increment the iteration variable i by 1, if the incremented iteration variable i is less than or equal to the preset maximum number of iterations I, jump to step S202; otherwise, jump to step S204;

[0031] S204: Calculate the accurate position index of the fundamental frequency according to the updated search interval [a, b].

[0032] Optionally, the rule for setting the value of the preset maximum number of iterations I is: when the value of m satisfies the following formula, the value of m is taken as the maximum number of iterations I:

[0033]

[0034] In the above formula, F(m+3) is the m+3-th element of the Fibonacci sequence F, a and b are respectively the lower boundary and the upper boundary of the search interval [a, b], and L is the preset final interval length.

[0035] Optionally, the function expression for calculating the accurate position index of the fundamental frequency according to the updated search interval [a, b] in step S204 is:

[0036]

[0037] In the above formula, is the accurate position index of the fundamental frequency, and a and b are respectively the lower boundary and the upper boundary of the updated search interval [a, b].

[0038] Optionally, in step S104, the function expression of the loss function based on the error value of the normalized frequency value of the minimum fundamental wave constructed through the relationship between the positive and negative spectral components is:

[0039] g(ξ)=(Im[Q - (ξ)]-Im[Q + (ξ)]) 2 +(Re[Q - (ξ)]+Re[Q - (ξ)]) 2 ,

[0040] In the above formula, g(ξ) is the loss function, ξ represents the estimated value of the normalized frequency value k1 of the fundamental wave; when l1>l2, the range of ξ is (l2,l1); when l1<l2, the range of ξ is (l1,l2); Im is the imaginary part, Re is the real part, Q - (ξ) and Q + (ξ) are a pair of symmetric conjugate cancellation factors.

[0041] Optionally, the functional expression of the pair of symmetric conjugate elimination factors is:

[0042]

[0043] In the above formula, X(l1) is the discrete spectrum at the maximum spectral line position index l1, and X(l2) is the discrete spectrum at the second largest spectral line position index l2.

[0044] Optionally, the functional expression for calculating the fundamental frequency of the noise distortion signal in step S105 is:

[0045]

[0046] In the above formula, f1 is the fundamental frequency of the noise-distorted signal v(n), and f s Let N be the sampling frequency of the noise-distorted signal v(n), and N be the number of sampling points of the noise-distorted signal v(n). This is the precise location index for the fundamental frequency.

[0047] Furthermore, the present invention also provides a noise distortion signal estimation device for a windowed FFT algorithm, comprising a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the noise distortion signal estimation method of the windowed FFT algorithm.

[0048] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program for being programmed or configured by a microprocessor to perform the noise distortion signal estimation method of the windowed FFT algorithm.

[0049] Compared with existing technologies, the present invention has the following main advantages: The traditional method for determining the normalized frequency value k1 of the fundamental wave is to perform peak search on the discrete spectrum, using the position index of the maximum peak spectral line as the normalized frequency value k1 of the fundamental wave. The present invention uses Fibonacci iteration to calculate the precise position index of the fundamental wave frequency. Since the ratio between values ​​in the Fibonacci sequence approaches the golden ratio (approximately 0.618), the method of the present invention can quickly and efficiently approximate the optimal solution. It can effectively solve the technical problem that the effect of windowed interpolation discrete Fourier transform drops sharply within short periods, and existing frequency estimation methods cannot achieve efficient and accurate measurement of the frequency of noise-distorted signals. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0051] Figure 2 This is a detailed flowchart illustrating the method of an embodiment of the present invention. Detailed Implementation

[0052] like Figure 1 As shown, the noise distortion signal estimation method of the windowed FFT algorithm in this embodiment includes the following steps:

[0053] S101, sample the noise-distorted signal v(n) at the specified sampling frequency and use the Hanning window function for windowing; it should be noted that the window function can be selected as needed. In addition to the Hanning window function, other window functions can also be selected as needed, such as rectangular window, triangular window, Hamming window and Gaussian window, etc.

[0054] S102, Perform a discrete Fourier transform on the windowed noise distortion signal x(n) to obtain the discrete spectrum X(l);

[0055] S103, for the discrete spectrum X(l), find the maximum spectral line position index l1 and the second largest spectral line position index l2 in |X(l)|;

[0056] S104. The search interval [a,b] is determined based on the maximum spectral line position index l1 and the second largest spectral line position index l2. The loss function based on the normalized frequency value error value of the minimum fundamental wave is constructed by the relationship between positive and negative spectral components. The precise position index of the fundamental wave frequency is calculated in the search interval [a,b] using Fibonacci iteration.

[0057] S105, calculate the fundamental frequency in the noise distortion signal v(n) based on the precise location index of the fundamental frequency.

[0058] In step S101 of this embodiment, the sampling frequency f is specified. s By sampling the noise-distorted signal v(n) to obtain an N-point discrete sequence, the discrete signal model of the noise-distorted signal v(n) is obtained as follows:

[0059]

[0060] In the above formula, p(n) represents the noise interference signal, and A h f is the amplitude of the h-th harmonic; h θ is the frequency of the h-th harmonic; h Let H be the phase of the h-th harmonic; H is the total number of harmonics in the noise-distorted signal. h f h θ h H and p(n) are all unknown parameters. Specifically, in this embodiment, the time-domain expression of the noise distortion signal is:

[0061]

[0062] In the above formula, p(t) is the noise interference component at time t.

[0063] Discrete sampling of the noise-distorted signal yields a discrete voltage sequence with a signal length N = 1024:

[0064]

[0065] In the above formula, n = 0, 1, 2, ..., N-1; the first part is the fundamental component with a frequency of 50 Hz, the second part is the harmonic component with a frequency of 150 Hz, and p(n) is the discrete noise interference component.

[0066] In step S101, the Hanning window is applied, which includes applying a Hanning window w(n) of length N to the discrete noise distortion signal v(n) to obtain the windowed noise distortion signal x(n):

[0067] x(n) = v(n)·w(n),

[0068] In the above formula, · represents the dot product of the noise-distorted signal v(n) and the Hanning window w(n).

[0069] The function expression for the Hanning window w(n) is as follows:

[0070] w(n)=0.5(1-cos(2πn / N)),n=0,1,...,N-1,

[0071] Specifically, in this embodiment, a Hanning window w(n) of length 1024 is used to window the discretized noise distortion signal v(n) to obtain the weighted noise distortion signal x(n).

[0072] In step S102, the discrete Fourier transform of the windowed noise-distorted signal x(n) is performed to obtain the discrete spectrum X(l), whose functional expression is as follows:

[0073]

[0074] Where W(·) represents the result of the discrete Fourier transform of the Hanning window w(n), and l is the spectral line index, l = 0, 1, 2, ..., N-1. h Let be the normalized frequency value of the h-th harmonic frequency. When h = 1, k1 is the normalized frequency value of the fundamental wave. That is, k1 = f1 / Δf represents the normalized frequency value of the fundamental wave frequency f1, where A1 is the amplitude parameter of the fundamental wave of the estimated signal, and θ1 is the phase parameter of the fundamental wave of the estimated signal.

[0075] In step S104 of this embodiment, when determining the search interval [a, b] according to the maximum spectral line position index l1 and the second maximum spectral line position index l2, determining the search interval [a, b] includes: comparing the maximum spectral line position index l1 and the second maximum spectral line position index l2; if l1>l2, then a=l1-a1, b=l2+a2; if l1<l2, then a=l1-a2, b=l2+a1, where a1 and a2 are parameters less than 1, and a1 is greater than a2. For example, in this embodiment, a1=0.7, a2=0.3, specifically: if l1>l2, then a=l1-0.7, b=l2+0.3; if l1<l2, then a=l1-0.3, b=l2+0.7.

[0076] In step S104 of this embodiment, using Fibonacci iteration in the search interval [a, b] to calculate the precise position index of the fundamental frequency includes:

[0077] S201, initialize the iteration variable i to 1, as well as the test points z1 and y1 of the first Fibonacci iteration:

[0078]

[0079] In the above formula, a and b are the lower boundary and upper boundary of the search interval [a, b] respectively, ρ1 is the compression ratio of the first Fibonacci iteration, and:

[0080]

[0081] In the above formula, ρ i is the compression ratio of the i-th Fibonacci iteration, F(I+2-i) is the (I+2-i)-th element of the Fibonacci sequence F, F(I+3-i) is the (I+3-i)-th element of the Fibonacci sequence F, and:

[0082] And:

[0083]

[0084] In the above formula, F(m), F(m-1) and F(m-2) are the m-th, (m-1)-th and (m-2)-th elements of the Fibonacci sequence F respectively; the number r of elements in the Fibonacci sequence F ranges from [3, +∞);

[0085] S202, using the loss function of the normalized frequency value error based on the minimum fundamental wave constructed by the relationship between the positive and negative frequency spectrum components, compare the loss function values of the test point z of the i-th Fibonacci iteration i and y i , if the loss function value of test point z i is greater than the loss function value of test point y i , then update y according to the following formula iThe loss function value and the lower boundary 'a' of the search interval [a, b]:

[0086] a = z i ,

[0087] z i =y i ,

[0088] y i =a+(1-ρ i+1 )*(ba),

[0089] Otherwise, update z according to the following formula. i The loss function value and the upper boundary b of the search interval [a, b]:

[0090] b = z i ,

[0091] y i =z i ,

[0092] z i =a+ρ i+1 *(ba),

[0093] Where, ρ i+1 The compression ratio is the (i+1)th Fibonacci iteration.

[0094] S203, increment the iteration variable i by 1. If the iteration variable i after incrementing by 1 is less than or equal to the preset maximum number of iterations I, then jump to step S202; otherwise, jump to step S204.

[0095] S204, calculate the precise location index of the fundamental frequency based on the updated search interval [a,b].

[0096] In this embodiment, the preset rule for the maximum number of iterations I is that the value of m is the maximum number of iterations I when the value of m satisfies the following formula:

[0097]

[0098] In the above formula, F(m+3) is the (m+3)th element of the Fibonacci sequence F, a and b are the lower and upper boundaries of the search interval [a,b], respectively, and L is the preset length of the last interval (1e-3≤L≤1e-10). For example, in this embodiment, the length of the last interval is specifically defined as L=1e-3. It should be noted that the Fibonacci sequence F is a well-known sequence, and its expression is:

[0099] F={0,1,1,2,3,5,8,13,21,34,...}.

[0100] In step S204 of this embodiment, the function expression for calculating the accurate position index of the fundamental frequency according to the updated search interval [a, b] is:

[0101]

[0102] In the above formula, is the accurate position index of the fundamental frequency, and a and b are the lower boundary and the upper boundary of the updated search interval [a, b], respectively.

[0103] In this embodiment, the loss function based on the minimum normalized frequency value error of the fundamental wave is used to solve the normalized frequency value k1 of the fundamental wave. In an ideal case, the real part and the imaginary part of the positive frequency part and the negative frequency part of the discrete frequency spectrum of the signal are symmetrical; but in practice, due to various noise interferences on the power system signal, the aforementioned symmetry cannot be satisfied. This loss function obtains the square values of the real part and the imaginary part of the positive and negative frequency parts in the discrete frequency spectrum of the signal, that is, it considers the error influence caused by the asymmetry of the positive and negative frequency parts, and improves the estimation accuracy of the normalized frequency value of the fundamental wave. Specifically, in step S104 of this embodiment, the function expression of the loss function based on the minimum normalized frequency value error of the fundamental wave, which is constructed through the relationship between the positive and negative spectrum components, is:

[0104] g(ξ)=(Im[Q - (ξ)]-Im[Q + (ξ)]) 2 +(Re[Q - (ξ)]+Re[Q - (ξ)]) 2 ,

[0105] In the above formula, g(ξ) is the loss function, ξ represents the estimated value of the normalized frequency value k1 of the fundamental wave; when l1>l2, the range of ξ is (l2, l1); when l1<l2, the range of ξ is (l1, l2); Im is the imaginary part, Re is the real part, Q - (ξ) and Q + (ξ) are a pair of symmetric conjugate cancellation factors. The function expression of the pair of symmetric conjugate cancellation factors is:

[0106]

[0107] In the above formula, X(l1) is the discrete frequency spectrum at the maximum spectral line position index l1, and X(l2) is the discrete frequency spectrum at the second-largest spectral line position index l2.

[0108] In step S105 of this embodiment, the function expression for calculating the fundamental frequency of the noise-distorted signal is:

[0109]

[0110] In the above formula, f1 is the fundamental frequency of the noise-distorted signal v(n), and f s Let N be the sampling frequency of the noise-distorted signal v(n), and N be the number of sampling points of the noise-distorted signal v(n). This is the precise location index for the fundamental frequency.

[0111] Finally, the spectrum analysis results obtained in this embodiment are shown in Table 1.

[0112] Table 1: Spectrum Analysis Results.

[0113]

[0114] As shown in Table 1, the noise distortion signal estimation method of the windowed FFT algorithm in this embodiment can accurately estimate the fundamental frequency of the noise distortion signal. Moreover, compared with the traditional three-point iterative interpolation method, the noise distortion signal estimation method of the windowed FFT algorithm in this embodiment has a shorter iteration time and can estimate the fundamental frequency of the noise distortion signal in the power system more quickly.

[0115] Accurately detecting fundamental parameters from power system signals is of significant engineering value for the stable operation of power systems and forms the basis for research on harmonic and interharmonic detection. By accurately estimating the fundamental frequency of noise-distorted signals in a power system, we can better grasp the basic periodicity of the signal, accurately determine the frequency and amplitude of harmonics, and thus better analyze and handle harmonic problems, accurately identifying the main frequency components in the spectrum. Understanding and analyzing the periodicity, harmonic components, and spectral characteristics of noise-distorted signals helps in the analysis of power system fault diagnosis, providing a more accurate foundation for applications such as signal processing, feature extraction, and pattern recognition.

[0116] In summary, the method of this embodiment uses Fibonacci iteration to calculate the precise location index of the fundamental frequency. Since the ratio between the values ​​in the Fibonacci sequence approaches the golden ratio (approximately 0.618), the method of this invention can quickly and efficiently approximate the optimal solution. It can effectively solve the technical problem that the effect of windowed interpolation discrete Fourier transform drops sharply in short periods, and existing frequency estimation methods cannot achieve efficient and accurate measurement of the frequency of noise-distorted signals.

[0117] Furthermore, this embodiment also provides a noise distortion signal estimation device for a windowed FFT algorithm, including a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to execute the noise distortion signal estimation method of the windowed FFT algorithm. This embodiment also provides a computer-readable storage medium storing a computer program for being programmed or configured by a microprocessor to execute the noise distortion signal estimation method of the windowed FFT algorithm.

[0118] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0119] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for estimating noise-distorted signals using a windowed FFT algorithm, characterized in that, Includes the following steps: S101, sampling the voltage noise distortion signal at a specified sampling frequency. v ( n Sampling is performed and windowing is applied using a window function; S102, for the windowed noise distortion signal x ( n Perform a discrete Fourier transform to obtain the discrete spectrum. X ( l ); S103, for discrete spectrum X ( l Searching for | X ( l The index of the maximum spectral line position in )| l 1 and index of the second largest spectral line position l 2; S104, Indexed by the position of the maximum spectral line l 1 and index of the second largest spectral line position l 2. Determine the search interval [ a , b ], utilizing a loss function based on the normalized frequency error value of the minimum fundamental wave, constructed through the relationship between positive and negative spectral components, within the search interval [ a , b The precise location index of the fundamental frequency is calculated using Fibonacci iteration. S105, calculates the noise distortion signal based on the precise location index of the fundamental frequency. v ( n The fundamental frequency in ) In step S104, within the search interval [ a , b The precise location index for calculating the fundamental frequency using Fibonacci iteration includes: S201, initialize the iteration variable i to 1, and set the pilot for the first Fibonacci iteration. z 1 and y 1: ， In the above formula, a and b The search ranges are respectively [ a , b The lower and upper boundaries of ] Let be the compression ratio of the first Fibonacci iteration, and we have: ， In the above formula, Let be the compression ratio of the i-th Fibonacci iteration. For Fibonacci sequence F The One element, For Fibonacci sequence F The There are n elements, and they have: ， In the above formula, , and These are the Fibonacci sequences. F The m-th, m-1, and m-2-th elements; Fibonacci sequence F number of elements r The range is [3, +∞); S202, using a loss function based on the normalized frequency error value of the minimum fundamental wave, constructed through the relationship between positive and negative spectral components, compares the pilot values ​​of the i-th Fibonacci iteration. z i and y i The loss function value, if the pilot z i The loss function value is greater than the pilot value. y i The loss function value is then updated according to the following formula. y i The loss function value and search interval [ a , b The lower boundary of ] a : ， ， ， Otherwise, update according to the following formula z i The loss function value and search interval [ a , b The upper boundary of ] b : ， ， ， in, For the first i+ Compression ratio of one Fibonacci iteration; S203, increment the iteration variable i by 1. If the incremented iteration variable i is less than or equal to the preset maximum number of iterations... I If yes, proceed to step S202; otherwise, proceed to step S204. S204, based on the updated search range [ a , b Calculate the precise location index of the fundamental frequency; The preset maximum number of iterations I The rule for determining the value of m is that when the value of m satisfies the following formula, the value of m is the maximum number of iterations I: ， In the above formula, For Fibonacci sequence F The m +3 elements, a and b The search ranges are respectively [ a , b The lower and upper boundaries of ] L The preset length of the last interval; The function expression for the loss function based on the normalized frequency value error value of the minimum fundamental wave, constructed in step S104 through the relationship between positive and negative spectral components, is as follows: ， In the above formula, For loss function, Represents the normalized frequency value of the fundamental wave. k The estimated value of 1, when hour, The range is ;when hour, The range is Im is the imaginary part, and Re is the real part. and They are a pair of symmetric conjugate elimination factors.

2. The noise distortion signal estimation method of the windowed FFT algorithm according to claim 1, characterized in that, In step S104, the index is based on the position of the maximum spectral line. l 1 and index of the second largest spectral line position l 2. Determine the search interval [ a , b When [the search interval is determined], the search range is determined. a , b Includes: indexing the position of the maximum spectral line l 1 and second largest spectral line position index l 2. Compare, if l 1> l 2, then a = l 1- a 1, b = l 2+ a 2; if l 1< l 2, then a = l 1- a 2, b = l 2+ a 1, of which a 1 and a 2 is a parameter less than 1 and has a 1 greater than a 2.

3. The noise distortion signal estimation method of the windowed FFT algorithm according to claim 1, characterized in that, In step S204, based on the updated search interval [ a , b The function expression for calculating the precise location index of the fundamental frequency is: ， In the above formula, This provides a precise location index for the fundamental frequency. a and b The updated search ranges are [ a , b The lower and upper boundaries of ].

4. The noise distortion signal estimation method of the windowed FFT algorithm according to claim 1, characterized in that, The functional expression of the pair of symmetric conjugate elimination factors is: ， In the above formula, Index of the position of the maximum spectral line l Discrete spectrum at position 1 Index of the second largest spectral line position l Discrete spectrum at point 2.

5. The method for estimating noise-distorted signals using the windowed FFT algorithm according to claim 1, characterized in that, The functional expression for calculating the fundamental frequency of the noise distortion signal in step S105 is as follows: ， In the above formula, Noise distortion signal v ( n The fundamental frequency of ) Noise distortion signal v ( n The sampling frequency of ) Noise distortion signal v ( n The number of sampling points, This is the precise location index for the fundamental frequency.

6. A noise distortion signal estimation device based on a windowed FFT algorithm, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to perform a noise distortion signal estimation method using the windowed FFT algorithm described in any one of claims 1 to 5.

7. A computer-readable storage medium storing a computer program, characterized in that, The computer program is used to be programmed or configured by a microprocessor to perform the noise distortion signal estimation method of the windowed FFT algorithm according to any one of claims 1 to 5.

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