CN117493769A - Noise distortion signal estimation method and device of windowed FFT algorithm - Google Patents
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Abstract
The invention discloses a noise distortion signal estimation method and device of a windowed FFT algorithm, the invention comprises the steps of sampling and windowing the noise distortion signal, and performing discrete Fourier transform to obtain a discrete frequency spectrum X (l); find the maximum line position index l in |X (l) | 1 Second largest line position index l 2 The method comprises the steps of carrying out a first treatment on the surface of the According to l 1 L 2 Determining search intervals [ a, b ]]In the search interval [ a, b ] using a loss function based on the normalized frequency value error value of the minimum fundamental wave constructed by the relation between the positive and negative spectral components]The fibonacci iteration is adopted to calculate the accurate position index of the fundamental frequency; the fundamental frequency in the noise distortion signal v (n) is calculated from the exact position index of the fundamental frequency. The invention aims to solve the problem that the discrete Fourier transform effect of windowing interpolation is suddenly reduced in a short periodThe existing frequency estimation method cannot realize the technical problem of efficiently and accurately measuring the frequency of the noise distortion signal.
Description
Technical Field
The invention belongs to the field of noise signal testing and analysis, and particularly relates to a noise distortion signal estimation method and device of a windowed FFT algorithm.
Background
The frequency estimation of noise signals is an important content of spectrum analysis, has important application value in a plurality of social and economic fields such as military, electric power, medicine, communication and the like, and is widely focused. The problem of frequency estimation in noise signals refers to the process of estimating the frequency of signals in noise by calculating and transforming the sampled values of the signals. In an actual power system, a power signal is inevitably interfered by noise to generate random errors. When the signal-to-noise ratio of the signal is high enough, the effect of noise on the frequency estimate is negligible; and when noise interference in the signal is obvious, random errors in the frequency measurement algorithm are increased. In an electrical power system, both the low voltage distribution network and the high voltage transmission network contain background noise. Although it is processed through an analog filter before sampling, the signal noise level can still affect the accuracy of the frequency measurement.
Thus, to accurately estimate grid frequencies, frequency estimation algorithms such as Fast Fourier Transform (FFT), prony method, wavelet transform, least squares method, and artificial neural network have been proposed. The traditional FFT algorithm has the advantages of small calculated amount, high calculation speed and the like, but has the defects of spectrum leakage, fence effect and the like, so that the frequency estimation error of the signal is larger under noise interference. The calculation amount of other algorithms is too large, the real-time performance is low, and the requirement of real-time measurement of a power system cannot be met. The windowing interpolation method can inhibit spectrum leakage and eliminate fence effect to a certain extent, so that interference of noise signals is reduced. However, when a short time window is adopted, the analysis accuracy of the windowed interpolation discrete fourier transform method which simultaneously considers negative frequency and harmonic spectrum leakage is greatly reduced, and an ideal mature solution for the problem is not yet available. In the prior art, a window function is generally selected to suppress noise interference and perform error compensation on a discrete fourier transform method of two-point interpolation. However, when the observation period is less than 2, the compensation effect of the spectrum leakage under the noise interference is reduced. For short range spectral leakage, spectral correction is typically done by interpolation based on several maximum spectral lines, or using spectral maxima of different time labels. However, the measurement error of the frequency estimation in a short time window is mainly due to short-range spectrum leakage of negative frequencies, where the presence of negative frequencies has a considerable influence on the accuracy level of the frequency measurement.
Disclosure of Invention
The invention aims to solve the technical problems: aiming at the problems in the prior art, the invention provides a noise distortion signal estimation method and device of a windowed FFT algorithm, which aim to solve the technical problem that the effect of windowing interpolation discrete Fourier transform is rapidly reduced in a short period, and the existing frequency estimation method cannot realize efficient and accurate measurement of the frequency of the noise distortion signal.
In order to solve the technical problems, the invention adopts the following technical scheme:
a noise distortion signal estimation method of a windowed FFT algorithm comprises the following steps:
s101, sampling a noise distortion signal v (n) at a specified sampling frequency and windowing a window function;
s102, performing discrete Fourier transform on the windowed noise distortion signal X (n) to obtain a discrete frequency spectrum X (l);
s103, searching the maximum spectral line position index l in the |X (l) | for the discrete spectrum X (l) 1 Second largest line position index l 2 ；
S104, indexing according to the maximum spectral line position 1 Second largest line position index l 2 Determining search intervals [ a, b ]]In the search interval [ a, b ] using a loss function based on the normalized frequency value error value of the minimum fundamental wave constructed by the relation between the positive and negative spectral components]The fibonacci iteration is adopted to calculate the accurate position index of the fundamental frequency;
s105, calculating the fundamental wave frequency in the noise distortion signal v (n) according to the accurate position index of the fundamental wave frequency.
Optionally, indexing l in step S104 according to the maximum line position 1 Second largest line position index l 2 Determining search intervals [ a, b ]]When determining the search interval [ a, b]Comprising the following steps: index the maximum spectral line position l 1 And the next largest spectral line position index l 2 Comparing if l 1 >l 2 A=l 1 -a 1 ，b＝l 2 +a 2 The method comprises the steps of carrying out a first treatment on the surface of the If l 1 <l 2 A=l 1 -a 2 ，b＝l 2 +a 1 Wherein a is 1 And a 2 Is a parameter less than 1 and has a 1 Greater than a 2 。
Optionally, iteratively calculating the exact location index of the fundamental frequency in the search interval [ a, b ] using fibonacci in step S104 includes:
s201, initializing an iteration variable i to be 1, and a trial point z of the 1 st fibonacci iteration 1 And y 1 ：
In the above formula, a and b are search intervals [ a, b, respectively]Lower and upper boundaries of ρ 1 Compression ratio for fibonacci iteration 1, and has:
in the above, ρ i For the compression ratio of the ith fibonacci iteration, F (i+2-I) is the i+2-I element of fibonacci sequence F, F (i+3-I) is the i+3-I element of fibonacci sequence F, and there are:
in the above formula, F (m), F (m-1) and F (m-2) are respectively the m < th >, m-1 and m-2 > elements of the fibonacci sequence F; the range of the number r of elements of the fibonacci sequence F is [3, + -infinity);
s202, comparing test points z of ith fibonacci iteration by using a loss function based on a normalized frequency value error value of a minimum fundamental wave constructed by a relation between positive and negative frequency spectrum components i And y i If the loss function value of (1) is at test point z i The loss function value is greater than the test point y i Then update y according to the following i Loss function value of (a) and search interval [ a, b ]]Is defined by the lower boundary a:
a＝z i ，
z i ＝y i ，
y i ＝a+(1-ρ i+1 )*(b-a)，
otherwise, z is updated according to i Loss function value of (a) and search interval [ a, b ]]Upper boundary b of (b):
b＝z i ，
y i ＝z i ，
z i ＝a+ρ i+1 *(b-a)，
wherein ρ is i+1 Compression ratio for the i+1th fibonacci iteration;
s203, adding 1 to the iteration variable I, and if the iteration variable I after adding 1 is smaller than or equal to the preset maximum iteration number I, jumping to the step S202; otherwise, jump to step S204;
s204, calculating the accurate position index of the fundamental wave frequency according to the updated search interval [ a, b ].
Optionally, the preset maximum iteration number I takes the value rule that when the value of m satisfies the following formula, the value of m is the maximum iteration number I:
in the above formula, F (m+3) is the m+3 element of fibonacci sequence F, a and b are the lower boundary and the upper boundary of the search interval [ a, b ], respectively, and L is the preset last interval length.
Optionally, the function expression for calculating the exact position index of the fundamental frequency from the updated search interval [ a, b ] in step S204 is:
in the above-mentioned method, the step of,for the exact position index of the fundamental frequency, a and b are updated search intervals [ a, b, respectively]Lower and upper boundaries of (2).
Optionally, the function expression of the loss function based on the normalized frequency value error value of the minimum fundamental wave constructed by the relation between the positive and negative spectral components in step S104 is:
g(ξ)＝(Im[Q - (ξ)]-Im[Q + (ξ)]) 2 +(Re[Q - (ξ)]+Re[Q - (ξ)]) 2 ，
in the above formula, g (ζ) is a loss function, and ζ represents a normalized frequency value k of the fundamental wave 1 When l is 1 >l 2 When xi is in the range of (l) 2 ,l 1 ) The method comprises the steps of carrying out a first treatment on the surface of the When l 1 <l 2 When xi is in the range of (l) 1 ,l 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Im is the imaginary part, re is the real part, Q - (ζ) and Q + (ζ) is a pair of symmetrical conjugated eliminating factors.
Optionally, the functional expression of the pair of symmetrical conjugate cancellation factors is:
in the above, X (l) 1 ) Index l for maximum spectral line position 1 Discrete spectrum at, X (l 2 ) Index l for the next largest spectral line position 2 Discrete frequency spectrum at.
Alternatively, the functional expression for calculating the fundamental frequency of the noise distortion signal in step S105 is:
in the above, f 1 Is the fundamental frequency of the noise distortion signal v (n), f s Is the sampling frequency of the noise distortion signal v (N), N is the number of sampling points of the noise distortion signal v (N),indexing the exact location of the fundamental frequency.
In addition, the invention also provides a noise distortion signal estimation device of the windowed FFT algorithm, which comprises a microprocessor and a memory which are connected with each other, wherein the microprocessor is programmed or configured to execute the noise distortion signal estimation method of the windowed FFT algorithm.
Furthermore, the present invention provides a computer readable storage medium having stored therein a computer program for being programmed or configured by a microprocessor to perform the noise distortion signal estimation method of the windowed FFT algorithm.
Compared with the prior art, the invention has the following advantages: conventional determination of normalized frequency value k of fundamental wave 1 The method is to search the discrete spectrum for peak value, and take the position index of the maximum peak spectral line as the normalized frequency value k of fundamental wave 1 . According to the method, the accurate position index of the fundamental wave frequency is calculated by using fibonacci iteration, and the ratio between numerical values in fibonacci sequences is approximate to the golden section proportion (about 0.618), so that the method can quickly and efficiently approach to the optimal solution, and the technical problem that the windowing interpolation discrete Fourier transform effect is rapidly reduced in a short period and the frequency of a noise distortion signal cannot be efficiently and accurately measured by the existing frequency estimation method can be effectively solved.
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FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.
FIG. 2 is a detailed flow chart of the method according to the embodiment of the invention.
Detailed Description
As shown in fig. 1, the noise distortion signal estimation method of the windowed FFT algorithm of the present embodiment includes the steps of:
s101, sampling a noise distortion signal v (n) at a specified sampling frequency, and windowing by using a Hanning window function; it should be noted that, the windowed window function may be selected according to needs, and other window functions may be selected according to needs besides the Hanning window function, for example, rectangular window, triangular window, hamming window, gaussian window, and the like;
s102, performing discrete Fourier transform on the windowed noise distortion signal X (n) to obtain a discrete frequency spectrum X (l);
s103, searching the maximum spectral line position index l in the |X (l) | for the discrete spectrum X (l) 1 Second largest line position index l 2 ；
S104, indexing according to the maximum spectral line position 1 Second largest line position index l 2 Determining search intervals [ a, b ]]In the search interval [ a, b ] using a loss function based on the normalized frequency value error value of the minimum fundamental wave constructed by the relation between the positive and negative spectral components]The fibonacci iteration is adopted to calculate the accurate position index of the fundamental frequency;
s105, calculating the fundamental wave frequency in the noise distortion signal v (n) according to the accurate position index of the fundamental wave frequency.
In step S101 of the present embodiment, the sampling frequency f is specified s Sampling the noise distortion signal v (N) to obtain an N-point discrete sequence, wherein the discrete signal model for obtaining the noise distortion signal v (N) is as follows:
in the above formula, p (n) is a noise interference signal, A h The amplitude of the h harmonic; f (f) h The frequency of the h harmonic; θ h The phase of the h harmonic; h is the number of total harmonics in the noise distorted signal. A is that h 、f h 、θ h H and p (n)) Are all unknown parameters. Specifically, the time domain expression of the noise distortion signal in this embodiment is:
in the above equation, p (t) is a noise interference component at time t.
Performing discrete sampling on the noise distortion signal to obtain a voltage discrete sequence with the signal length of N=1024:
in the above formula, n=0, 1,2, …, N-1; the first part is a fundamental component with the frequency of 50Hz, the second part is a harmonic component with the frequency of 150Hz, and p (n) is a scattered noise interference component.
When the Hanning window is windowed in step S101, the windowing of the discrete noise distortion signal v (N) is performed by using a Hanning window w (N) with a length of N, so as to obtain a windowed noise distortion signal x (N):
x(n)＝v(n)·w(n)，
in the above equation, represents the dot product of the noise distortion signal v (n) and the Hanning window w (n).
The functional expression of the Hanning window w (n) is as follows:
w(n)＝0.5(1-cos(2πn/N)),n＝0,1,...,N-1，
specifically, in this embodiment, the discretized noise distortion signal v (n) is windowed by using a Hanning window w (n) with a length of 1024 to obtain a weighted noise distortion signal x (n).
In step S102, the function expression for obtaining the discrete spectrum X (l) by performing discrete fourier transform on the windowed noise distortion signal X (n) is:
wherein W (·) represents the discrete Fourier transform of the Hanning window W (n)As a result, l is the line index, l=0, 1,2, …, N-1.k (k) h For the normalized frequency value of the h harmonic frequency, when h=1, i.e. k 1 Normalized frequency values for the fundamental wave are: k (k) 1 ＝f 1 The fundamental frequency f is denoted by/. DELTA.f 1 Wherein A is a normalized frequency value of 1 For the amplitude parameter of the estimated signal fundamental wave, θ 1 Is the phase parameter of the fundamental wave of the estimated signal.
In step S104 of the present embodiment, the index l is indexed according to the maximum spectral line position 1 Second largest line position index l 2 Determining search intervals [ a, b ]]When determining the search interval [ a, b]Comprising the following steps: index the maximum spectral line position l 1 And the next largest spectral line position index l 2 Comparing if l 1 >l 2 A=l 1 -a 1 ，b＝l 2 +a 2 The method comprises the steps of carrying out a first treatment on the surface of the If l 1 <l 2 A=l 1 -a 2 ，b＝l 2 +a 1 Wherein a is 1 And a 2 Is a parameter less than 1 and has a 1 Greater than a 2 For example a in the present embodiment 1 ＝0.7，a 2 =0.3, then specifically: if l 1 >l 2 A=l 1 -0.7，b＝l 2 +0.3; if l 1 <l 2 A=l 1 -0.3，b＝l 2 +0.7。
In step S104 of this embodiment, the calculation of the accurate position index of the fundamental frequency using fibonacci iteration in the search interval [ a, b ] includes:
s201, initializing an iteration variable i to be 1, and a trial point z of the 1 st fibonacci iteration 1 And y 1 ：
In the above formula, a and b are search intervals [ a, b, respectively]Lower and upper boundaries of ρ 1 Compression ratio for fibonacci iteration 1, and has:
in the above, ρ i For the compression ratio of the ith fibonacci iteration, F (i+2-I) is the i+2-I element of fibonacci sequence F, F (i+3-I) is the i+3-I element of fibonacci sequence F, and there are:
and has the following steps:
in the above formula, F (m), F (m-1) and F (m-2) are respectively the m < th >, m-1 and m-2 > elements of the fibonacci sequence F; the range of the number r of elements of the fibonacci sequence F is [3, + -infinity);
s202, comparing test points z of ith fibonacci iteration by using a loss function based on a normalized frequency value error value of a minimum fundamental wave constructed by a relation between positive and negative frequency spectrum components i And y i If the loss function value of (1) is at test point z i The loss function value is greater than the test point y i Then update y according to the following i Loss function value of (a) and search interval [ a, b ]]Is defined by the lower boundary a:
a＝z i ，
z i ＝y i ，
y i ＝a+(1-ρ i+1 )*(b-a)，
otherwise, z is updated according to i Loss function value of (a) and search interval [ a, b ]]Upper boundary b of (b):
b＝z i ，
y i ＝z i ，
z i ＝a+ρ i+1 *(b-a)，
wherein ρ is i+1 Compression ratio for the i+1th fibonacci iteration;
s203, adding 1 to the iteration variable I, and if the iteration variable I after adding 1 is smaller than or equal to the preset maximum iteration number I, jumping to the step S202; otherwise, jump to step S204;
s204, calculating the accurate position index of the fundamental wave frequency according to the updated search interval [ a, b ].
The preset maximum iteration number I value rule in this embodiment is that when the value of m satisfies the following formula, the value of m is the maximum iteration number I:
in the above formula, F (m+3) is the m+3th element of the fibonacci sequence F, a and b are the lower boundary and the upper boundary of the search interval [ a, b ] respectively, and L is the preset last interval length (1 e-3 is less than or equal to L is less than or equal to 1 e-10). For example, the last interval length is specifically defined as l=1e-3 in this embodiment. It should be noted that, fibonacci sequence F is a known sequence, and its expression is:
F＝{0,1,1,2,3,5,8,13,21,34,...}。
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:
in the above-mentioned method, the step of,for the exact position index of the fundamental frequency, a and b are updated search intervals [ a, b, respectively]Lower and upper boundaries of (2).
In this embodiment, a loss function based on the error value of the normalized frequency value of the minimum fundamental wave is used to solve the normalized frequency value k of the fundamental wave 1 . In an ideal case, the real and imaginary parts of the positive and negative frequency parts of the discrete spectrum of the signal are symmetrical; however, in practical situations, the aforementioned symmetry cannot be satisfied because the power system signal is disturbed by various noises. The loss function provides the estimation accuracy of the normalized frequency value of the fundamental wave by obtaining the square values of the real part and the imaginary part of the positive frequency part and the negative frequency part in the discrete frequency spectrum of the signal, namely, taking the error influence caused by the asymmetry of the positive frequency part and the negative frequency part into consideration. Concrete embodimentsIn step S104 of this embodiment, the function expression of the loss function based on the error value of the normalized frequency value of the minimum fundamental wave constructed by the relationship between the positive and negative spectral components is:
g(ξ)＝(Im[Q - (ξ)]-Im[Q + (ξ)]) 2 +(Re[Q - (ξ)]+Re[Q - (ξ)]) 2 ，
in the above formula, g (ζ) is a loss function, and ζ represents a normalized frequency value k of the fundamental wave 1 When l is 1 >l 2 When xi is in the range of (l) 2 ,l 1 ) The method comprises the steps of carrying out a first treatment on the surface of the When l 1 <l 2 When xi is in the range of (l) 1 ,l 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Im is the imaginary part, re is the real part, Q - (ζ) and Q + (ζ) is a pair of symmetrical conjugated eliminating factors. Wherein the functional expression of the symmetrical conjugate cancellation factor is:
in the above, X (l) 1 ) Index l for maximum spectral line position 1 Discrete spectrum at, X (l 2 ) Index l for the next largest spectral line position 2 Discrete frequency spectrum at.
The functional expression for calculating the fundamental frequency of the noise distortion signal in step S105 of the present embodiment is:
in the above, f 1 Is the fundamental frequency of the noise distortion signal v (n), f s Is the sampling frequency of the noise distortion signal v (N), N is the number of sampling points of the noise distortion signal v (N),indexing the exact location of the fundamental frequency.
Finally, the spectrum analysis results obtained in this example are shown in table 1.
Table 1: and a spectrum analysis result table.
Referring to table 1, it can be seen that the noise distortion signal estimation method of the windowed FFT algorithm of this embodiment can accurately estimate the fundamental frequency of the noise distortion signal, and compared with the conventional three-point iterative interpolation method, the iteration time of the noise distortion signal estimation method of the windowed FFT algorithm of this embodiment is shorter, so that the fundamental frequency of the noise distortion signal in the power system can be estimated more rapidly.
The fundamental wave parameter is accurately detected from the power system signal, so that the method has important engineering practical value for the stable operation of the power system, and is also the basis of the detection research work of partial harmonic waves and inter-harmonic waves. The fundamental frequency of the noise distortion signal in the power system is accurately estimated, the basic periodicity of the signal can be better grasped, the frequency and the amplitude of the harmonic wave can be accurately determined, and therefore the harmonic problem can be better analyzed and processed, and the main frequency component in the frequency spectrum can be accurately determined. The periodicity, harmonic components and spectral characteristics of the noise distortion signals are understood and analyzed, so that the analysis of power system fault diagnosis is facilitated, and a more accurate basis is provided for applications such as signal processing, feature extraction and pattern recognition.
In summary, the method of the embodiment uses fibonacci iteration to calculate the accurate position index of the fundamental frequency, and the ratio between the values in the fibonacci sequence approaches to the golden section ratio (about 0.618), so that the method of the invention can quickly and efficiently approach to the optimal solution, and can effectively solve the technical problem that the windowing interpolation discrete fourier transform effect is rapidly reduced in a short period, and the existing frequency estimation method cannot realize the efficient and accurate measurement of the frequency of the noise distortion signal.
In addition, the embodiment also provides a noise distortion signal estimation device of the windowed FFT algorithm, which comprises a microprocessor and a memory which are connected with each other, wherein the microprocessor is programmed or configured to execute the noise distortion signal estimation method of the windowed FFT algorithm. The present embodiment also provides a computer-readable storage medium having stored therein a computer program for being programmed or configured by a microprocessor to perform the noise distortion signal estimation method of the windowed FFT algorithm.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may 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, and the like) having computer-usable program code embodied therein. The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may 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 means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. 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 such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above examples, and all technical solutions belonging to the concept of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to the present invention may occur to one skilled in the art without departing from the principles of the present invention and are intended to be within the scope of the present invention.
Claims (10)
1. The noise distortion signal estimation method of the windowed FFT algorithm is characterized by comprising the following steps of:
s101, sampling a noise distortion signal v (n) at a specified sampling frequency and windowing a window function;
s102, performing discrete Fourier transform on the windowed noise distortion signal X (n) to obtain a discrete frequency spectrum X (l);
s103, searching the maximum spectral line position index l in the |X (l) | for the discrete spectrum X (l) 1 Second largest line position index l 2 ；
S104, indexing according to the maximum spectral line position 1 Second largest line position index l 2 Determining search intervals [ a, b ]]In the search interval [ a, b ] using a loss function based on the normalized frequency value error value of the minimum fundamental wave constructed by the relation between the positive and negative spectral components]The fibonacci iteration is adopted to calculate the accurate position index of the fundamental frequency;
s105, calculating the fundamental wave frequency in the noise distortion signal v (n) according to the accurate position index of the fundamental wave frequency.
2. The noise distortion signal estimation method of a windowed FFT algorithm of claim 1, wherein step S104 is based on a maximum line position index l 1 Second largest line position index l 2 Determining search intervals [ a, b ]]When determining the search interval [ a, b]Comprising the following steps: index the maximum spectral line position l 1 And the next largest line position cableLead l 2 Comparing if l 1 >l 2 A=l 1 -a 1 ，b＝l 2 +a 2 The method comprises the steps of carrying out a first treatment on the surface of the If l 1 <l 2 A=l 1 -a 2 ，b＝l 2 +a 1 Wherein a is 1 And a 2 Is a parameter less than 1 and has a 1 Greater than a 2 。
3. The noise-distorted signal estimation method of the windowed FFT algorithm of claim 1, wherein calculating the exact position index of the fundamental frequency in the search interval [ a, b ] using fibonacci iteration in step S104 includes:
s201, initializing an iteration variable i to be 1, and a trial point z of the 1 st fibonacci iteration 1 And y 1 ：
In the above formula, a and b are search intervals [ a, b, respectively]Lower and upper boundaries of ρ 1 Compression ratio for fibonacci iteration 1, and has:
in the above, ρ i For the compression ratio of the ith fibonacci iteration, F (i+2-I) is the i+2-I element of fibonacci sequence F, F (i+3-I) is the i+3-I element of fibonacci sequence F, and there are:
in the above formula, F (m), F (m-1) and F (m-2) are respectively the m < th >, m-1 and m-2 > elements of the fibonacci sequence F; the range of the number r of elements of the fibonacci sequence F is [3, + -infinity);
s202, utilizing the positive and negative frequency spectrum componentsThe relation of the minimum fundamental wave based normalized frequency value error value loss function is compared with the test point z of the ith fibonacci iteration i And y i If the loss function value of (1) is at test point z i The loss function value is greater than the test point y i Then update y according to the following i Loss function value of (a) and search interval [ a, b ]]Is defined by the lower boundary a:
a＝z i ，
z i ＝y i ，
y i ＝a+(1-ρ i+1 )*(b-a)，
otherwise, z is updated according to i Loss function value of (a) and search interval [ a, b ]]Upper boundary b of (b):
b＝z i ，
y i ＝z i ，
z i ＝a+ρ i+1 *(b-a)，
wherein ρ is i+1 Compression ratio for the i+1th fibonacci iteration;
s203, adding 1 to the iteration variable I, and if the iteration variable I after adding 1 is smaller than or equal to the preset maximum iteration number I, jumping to the step S202; otherwise, jump to step S204;
s204, calculating the accurate position index of the fundamental wave frequency according to the updated search interval [ a, b ].
4. The noise distortion signal estimation method of the windowed FFT algorithm of claim 3, wherein the preset maximum iteration number I takes a value rule that when the value of m satisfies the following formula, the value of m is the maximum iteration number I:
in the above formula, F (m+3) is the m+3 element of fibonacci sequence F, a and b are the lower boundary and the upper boundary of the search interval [ a, b ], respectively, and L is the preset last interval length.
5. A noise distortion signal estimation method according to claim 3, wherein the function expression for calculating the exact position index of the fundamental frequency according to the updated search interval [ a, b ] in step S204 is:
in the above-mentioned method, the step of,for the exact position index of the fundamental frequency, a and b are updated search intervals [ a, b, respectively]Lower and upper boundaries of (2).
6. The noise distortion signal estimation method of the windowed FFT algorithm of claim 5, wherein the function expression of the loss function of the normalized frequency value error value based on the minimum fundamental wave constructed by the relation between the positive and negative spectral components in step S104 is:
g(ξ)＝(Im[Q - (ξ)]-Im[Q + (ξ)]) 2 +(Re[Q - (ξ)]+Re[Q - (ξ)]) 2 ，
in the above formula, g (ζ) is a loss function, and ζ represents a normalized frequency value k of the fundamental wave 1 When l is 1 >l 2 When xi is in the range of (l) 2 ,l 1 ) The method comprises the steps of carrying out a first treatment on the surface of the When l 1 <l 2 When xi is in the range of (l) 1 ,l 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Im is the imaginary part, re is the real part, Q - (ζ) and Q + (ζ) is a pair of symmetrical conjugated eliminating factors.
7. The method of claim 6, wherein the function expression of the pair of symmetrical conjugate cancellation factors is:
in the above, X (l) 1 ) Index l for maximum spectral line position 1 Discrete spectrum at, X (l 2 ) Index l for the next largest spectral line position 2 Discrete frequency spectrum at.
8. The noise distortion signal estimation method of the windowed FFT algorithm of claim 1, wherein the function expression for calculating the fundamental frequency of the noise distortion signal in step S105 is:
in the above, f 1 Is the fundamental frequency of the noise distortion signal v (n), f s Is the sampling frequency of the noise distortion signal v (N), N is the number of sampling points of the noise distortion signal v (N),indexing the exact location of the fundamental frequency.
9. A noise-distorted signal estimation device of a windowed FFT algorithm, comprising a microprocessor and a memory connected to each other, characterized in that the microprocessor is programmed or configured to perform the noise-distorted signal estimation method of a windowed FFT algorithm according to any one of claims 1 to 8.
10. A computer readable storage medium having a computer program stored therein, wherein the computer program is for programming or configuring by a microprocessor to perform the noise distortion signal estimation method of the windowed FFT algorithm of any one of claims 1 to 8.
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