A high-precision frequency estimation method for real sinusoidal signals based on window sampling

Abstract

The application discloses a high-precision frequency estimation method for real sine signals based on window sampling, and relates to the technical field of signal processing. The method can perform real-time and high-precision estimation on the frequency of dynamic sine signals, and can dynamically identify subtle changes in frequency information. The method comprises the following steps: performing window sampling on a to-be-measured real sine signal to obtain a discrete sequence of the real sine signal in the window; performing spectrum transformation on the discrete sequence of the real sine signal to obtain an amplitude spectrum and a phase spectrum after spectrum transformation; extracting an initial estimation frequency of the peak position of the amplitude spectrum, and calculating a phase corresponding to the initial estimation frequency; calculating the full-phase order frequency of the discrete sequence of the real sine signal in the window by using the initial estimation frequency and the phase corresponding to the initial estimation frequency; and jointly estimating the corrected frequency of the to-be-measured real sine signal by using the full-phase order frequency, the truncated signal phase and the initial phase of the un-truncated signal.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a high-precision frequency estimation method for real sinusoidal signals based on window sampling. Background Technology

[0002] In engineering applications of signal processing and communication, frequency estimation of real sinusoidal signals is an important problem, and frequency estimation of dynamic sinusoidal signals has always been one of the research hotspots in the field of signal processing. The goal of frequency estimation is to accurately estimate the frequency of a sinusoidal signal from a discretely sampled noisy signal, which is crucial for many applications, such as communication systems, radar, audio processing systems, and spectral processing systems.

[0003] Currently, frequency estimation algorithms, both domestically and internationally, can be categorized into time-domain and frequency-domain estimation algorithms based on their computational domain. In the time-domain, linear prediction models are common for parameter estimation. While first-order linear prediction models are computationally simple, they can only predict one frequency parameter, resulting in low frequency estimation accuracy. Higher-order linear prediction models can estimate multiple parameters with higher accuracy, but their computational complexity is high. Maximum likelihood estimation is theoretically the best performing algorithm, but its high computational complexity makes it difficult to apply in real-time signal processing. While least squares linear regression methods can estimate signal frequencies relatively accurately, they suffer from periodic ambiguity.

[0004] Frequency domain estimation algorithms typically sample the sinusoidal signal in the time domain, transform it to the frequency domain using the Discrete Fourier Transform (DFT), and then estimate the frequency based on spectral analysis. However, due to the insufficient frequency resolution of the DFT, frequency interpolation or refinement is generally required. The most representative direct interpolation methods are Rife interpolation and Quinn interpolation. Rife interpolation uses the maximum spectral line and its adjacent second-largest spectral line for interpolation. Its drawback is that the accuracy of frequency estimation is related to the frequency distribution density. Quinn interpolation uses the real part of the ratio of the complex values ​​of the coefficients of the second-largest spectral line within the main lobe to the coefficients of the maximum spectral line for frequency interpolation. It requires only one DFT operation, resulting in low computational cost, but it also suffers from significant estimation errors when the signal frequency is close to the quantization frequency and is highly sensitive to noise. Summary of the Invention

[0005] One of the objectives of this invention is, at least, to provide a high-precision frequency estimation method for real sinusoidal signals based on window sampling, which addresses the problems existing in the prior art and enables dynamic high-resolution real-time frequency estimation of sinusoidal signals, thus meeting the requirements for dynamic high-resolution frequency estimation in engineering applications such as communication, power analysis, and spectral analysis.

[0006] To achieve the above objectives, the technical solution adopted by the present invention includes the following aspects.

[0007] A high-precision frequency estimation method for real sinusoidal signals based on window sampling includes the following steps:

[0008] Step S1: The real sinusoidal signal to be measured Perform window sampling to obtain the discrete sequence of real sinusoidal signals within the window. ;

[0009] Step S2: Discretize the real sinusoidal signal sequence Perform a spectrum transformation to obtain the amplitude spectrum and phase spectrum after the spectrum transformation;

[0010] Step S3: Extract the initial estimated frequency of the amplitude spectrum peak position. And calculate the initial estimated frequency. Corresponding phase ;

[0011] Step S4: Use the initial estimated frequency The discrete sequence of real sinusoidal signals within the initial estimation frequency and phase calculation window. full-phase order frequency ;

[0012] Step S5: Passing through the full-phase order frequency 1. Truncation of signal phase; 2. Initial phase of untruncated signal Jointly estimate the corrected frequency of the real sinusoidal signal to be measured .

[0013] Preferably, step S1 specifically includes: selecting the starting point of the window. Let the sampling frequency be . With N sampling points, obtain the discrete sequence of real sinusoidal signals within the window. , Represented as:

[0014] .

[0015] Preferably, in step S1, a discrete sequence of real sinusoidal signals is obtained through window sampling. Then, the discrete sequence of the real sinusoidal signal... Perform a Hilbert transform to obtain a complex sinusoidal signal. Complex sinusoidal signal Represented as:

[0016] .

[0017] Preferably, in step S2, Zoom FFT or Z-transform is used to perform spectral transformation on the discrete sequence of real sinusoidal signals.

[0018] Preferably, the spectral transformation result using the Z-transform is:

[0019] ;

[0020] Let the sampling frequency of the spectral transform be... Then we have:

[0021] .

[0022] Preferably, in step S3, the specific process of extracting the initial estimated frequency of the amplitude spectrum peak position and calculating the phase of the phase spectrum corresponding to the initial estimated frequency includes:

[0023] Let the theoretical maximum amplitude spectral line after spectral transformation be... The maximum spectral line The frequency value represented by the corresponding position is set as ,but When performing discrete signal transformation, the number of signal cycles within the window is directly calculated. ,set up At this point, the main frequency position is calculated based on the frequency and the number of cycles within the window. equal;

[0024] After spectral transformation, the phase at each frequency point is:

[0025] ;

[0026] in, The coordinates representing the position of the dominant frequency in the spectrum, when When the amplitude spectrum of the spectral transform is at its peak position, the phase of the dominant frequency position is... Represented as:

[0027] .

[0028] Preferably, the initial estimated frequency The result was obtained using the least squares fitting peak-finding algorithm.

[0029] Preferably, in step S4, the full-phase order frequency of the discrete sinusoidal signal sequence within the window... The calculation process includes: based on the calculated main frequency position The position of the main frequency is calculated by arctangent. Point-wrap phase, then obtain through phase unwrapping algorithm. Full phase of the point Then the known Value and full phase value Substituting these values ​​into the calculation formula, we obtain the full-phase order frequencies of the discrete sinusoidal signal sequence within the window. , Represented as: .

[0030] Preferably, step S5 specifically includes: combining the number of sampling points N and the sampling frequency. ,according to Calculate the frequency of the corrected real sinusoidal signal to be measured. The estimated value.

[0031] In summary, by adopting the above technical solution, the present invention has at least the following beneficial effects:

[0032] By performing window sampling on the real sinusoidal signal to be measured, a shorter number of observation points can be obtained. By performing spectral transformation on the discrete sequence of the real sinusoidal signal within the obtained window, a fine amplitude spectrum and phase spectrum can be obtained, which can dynamically identify subtle changes in frequency information.

[0033] The initial estimated frequency of the amplitude spectrum peak position is calculated by the least squares fitting peak-finding algorithm, which provides a higher resolution for the initial frequency estimate than the interpolation method and avoids the problem of large error in the ratio direction when it is close to the quantization frequency caused by the ratio method.

[0034] By calculating the full-phase order frequency of the discrete sequence of real sinusoidal signals within the window using the initial estimated frequency and the corresponding phase, the frequency resolution level is improved, enhancing the ability to capture minute frequency dynamics.

[0035] The estimation method of this invention can improve the frequency estimation accuracy without using iterative methods and significantly increasing the computational load. It can achieve dynamic high-resolution real-time frequency estimation of sinusoidal signals and is suitable for application scenarios with high requirements for real-time performance and frequency estimation resolution (such as engineering application fields such as communication, power analysis, and spectral analysis). Attached Figure Description

[0036] Figure 1 This is a flowchart illustrating high-precision frequency estimation of a real sinusoidal signal based on window sampling, an exemplary embodiment of the present invention.

[0037] Figure 2 This is a schematic diagram of a window sampling sequence according to an exemplary embodiment of the present invention. Detailed Implementation

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, so that the objectives, technical solutions, and advantages of the present invention will be clearer. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0039] like Figure 1 As shown, the high-precision frequency estimation method for real sinusoidal signals based on window sampling according to an exemplary embodiment of the present invention includes the following steps:

[0040] Step S1: Perform window sampling on the real sinusoidal signal to be tested to obtain the discrete sequence of the real sinusoidal signal within the window.

[0041] The specific process includes: using a signal acquisition system to process noisy real sinusoidal signals. Fast discrete sampling and preprocessing, selecting the starting point of the window. The discrete sequence of real sinusoidal signals obtained by window sampling is obtained. ; denote the noisy real sinusoidal signal The sampling frequency is The number of sampling points is N (reference) Figure 2 Sampling points can be set. Window start point Discrete sequence of real sinusoidal signals within the window It can be represented as:

[0042]

[0043] in, Indicates the amplitude of a sinusoidal signal. Indicates the initial phase of the signal. Indicates the frequency of the signal to be estimated. Indicates the sampling rate. Indicates the starting point of the window. Represents a discrete time point.

[0044] The preprocessing process is as follows: Discretize the real sinusoidal signal sequence. Perform a Hilbert transform to obtain a complex sinusoidal signal. The complex sinusoidal signal only has a frequency response in the positive frequency band of its spectrum. When the signal under test is a low-frequency signal or the observation period is insufficient, it can suppress positive and negative frequency interference of the signal. The complex sinusoidal signal after Hilbert transform. Represented as:

[0045]

[0046] Step S2: Perform spectral transformation on the discrete sequence of the real sinusoidal signal to obtain the amplitude spectrum and phase spectrum after spectral transformation.

[0047] In the process of spectral transformation, methods such as Zoom FFT and Z-transform can be used to transform the discrete sequence of real sinusoidal signals to obtain a fine and high-resolution spectrum and phase spectrum. In practice, Z-transform is preferred for spectral transformation, and the transformation result is as follows:

[0048]

[0049] in, Represents a point on the complex plane Z-transform value at that location, This represents the complex frequency point used in the Z-transform. This represents the total number of frequency points used in the Z-transform.

[0050] Let the sampling frequency of the spectral transform be... Then we have:

[0051]

[0052] in, Indicates the amplitude of the spectrum. This represents the frequency corresponding to the k-th spectral sampling point.

[0053] Step S3: Extract the initial estimated frequency of the peak position of the amplitude spectrum and calculate the phase corresponding to the initial estimated frequency.

[0054] Let the theoretical maximum amplitude spectral line after spectral transformation be... The maximum spectral line The frequency value represented by the corresponding position is set as ,but When performing discrete signal transformation, the number of signal cycles within the window is directly calculated. Therefore, let's assume At this point, the main frequency position is calculated based on the frequency and the number of cycles within the window. Equal. After spectral transformation, the phase at each frequency point is:

[0055]

[0056] in, The coordinates representing the dominant frequency position (initial estimated frequency) in the spectrum, when When the amplitude spectrum of the spectral transform is at its peak, the initial estimated frequency is... Corresponding phase Represented as:

[0057]

[0058] From the above formula, we can see that the initial estimated frequency Corresponding phase With this initial estimated frequency The relationship is linear; where the initial estimated frequency is... It can be calculated using the least squares fitting peak-finding algorithm.

[0059] Step S4: Calculate the full-phase order frequency of the discrete sequence of the real sinusoidal signal within the window using the initial estimated frequency and the phase corresponding to the initial estimated frequency.

[0060] The specific process includes: based on the calculated initial estimated frequency... The initial estimated frequency is calculated using the arctangent. Point-wrap phase, then obtain through phase unwrapping algorithm. Full phase of the point Then the known Value and full phase value Substitute into the calculation formula ( In the process, the full-phase order frequencies of the discrete sequence of sinusoidal signals within the window are obtained. , Represented as: .

[0061] Step S5: Estimate the corrected frequency of the real sinusoidal signal to be measured by jointly estimating the full-phase order frequency, the truncated signal phase (the phase corresponding to the initial estimated frequency of the discrete sequence of the sinusoidal signal within the window), and the initial phase of the untruncated signal; combine this with the number of sampling points N and the sampling frequency. ,according to:

[0062]

[0063] Calculate the frequency of the corrected real sinusoidal signal to be measured. The estimated value.

[0064] The above description is merely a detailed illustration of specific embodiments of the present invention and is not intended to limit the invention. Various substitutions, modifications, and improvements made by those skilled in the art without departing from the principles and scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A high-precision frequency estimation method for real sinusoidal signals based on window sampling, characterized in that, Includes the following steps: Step S1: The real sinusoidal signal to be measured Perform window sampling to obtain the discrete sequence of real sinusoidal signals within the window. ; Step S2: Discretize the real sinusoidal signal sequence Perform a spectrum transformation to obtain the amplitude spectrum and phase spectrum after the spectrum transformation; Step S3: Extract the initial estimated frequency of the amplitude spectrum peak position. And calculate the initial estimated frequency. Corresponding phase The specific process includes: Let the theoretical maximum amplitude spectral line after spectral transformation be... The maximum spectral line The frequency value represented by the corresponding position is set as ,but , This represents the frequency corresponding to the k-th spectral sampling point; during discrete signal transformation, the number of signal cycles within the window is directly calculated. ,set up , The sampling frequency is N, where N is the number of sampling points. The dominant frequency is then calculated based on the frequency and the number of periods within the window. equal; After spectral transformation, the phase at each frequency point is: ; in, The coordinates representing the position of the dominant frequency in the spectrum, when When the amplitude spectrum of the spectral transform is at its peak position, the phase of the dominant frequency position is... Represented as: ; in, Indicates the initial phase of the signal. Indicates the frequency of the signal to be estimated. Indicates the sampling rate. Indicates the starting point of the window; The initial estimated frequency Calculated using the least squares fitting peak-finding algorithm; Step S4: Use the initial estimated frequency The discrete sequence of real sinusoidal signals within the initial estimation frequency and phase calculation window. full-phase order frequency ; The discrete sequence of real sinusoidal signals within the window full-phase order frequency The calculation process includes: based on the calculated main frequency position The position of the main frequency is calculated by arctangent. Point-wrap phase, then obtain through phase unwrapping algorithm. Full phase of the point Then the known Value and full phase value Substituting these values ​​into the calculation formula, we obtain the full-phase order frequencies of the discrete sinusoidal signal sequence within the window. , Represented as: ; Step S5: Combine the number of sampling points N and the sampling frequency ,according to Calculate the frequency of the corrected real sinusoidal signal to be measured. The estimated value.

2. The high-precision frequency estimation method for real sinusoidal signals based on window sampling according to claim 1, characterized in that, Step S1 specifically includes: selecting the starting point of the window. Let the sampling frequency be... With N sampling points, obtain the discrete sequence of real sinusoidal signals within the window. , Represented as: ； in, Indicates the amplitude of a sinusoidal signal. Indicates the initial phase of the signal. Indicates the frequency of the signal to be estimated. Indicates the sampling rate. Indicates the starting point of the window. Represents a discrete time point.

3. The high-precision frequency estimation method for real sinusoidal signals based on window sampling according to claim 2, characterized in that, In step S1, a discrete sequence of real sinusoidal signals is obtained through window sampling. Then, the discrete sequence of the real sinusoidal signal... Perform a Hilbert transform to obtain a complex sinusoidal signal. Complex sinusoidal signal Represented as: ; in, Indicates the amplitude of a sinusoidal signal. Indicates the initial phase of the signal. Indicates the frequency of the signal to be estimated. Indicates the sampling rate. Indicates the starting point of the window. Represents a discrete time point.

4. The high-precision frequency estimation method for real sinusoidal signals based on window sampling according to claim 2, characterized in that, In step S2, Zoom FFT or Z-transform is used to perform spectral transformation on the discrete sequence of real sinusoidal signals.

5. The high-precision frequency estimation method for real sinusoidal signals based on window sampling according to claim 4, characterized in that, The spectral transformation result using the Z-transform is as follows: ; in, This represents the complex frequency point used in the Z-transform. This represents the total number of frequency points used in the Z-transform; Let the sampling frequency of the spectral transform be... Then we have: ; in, Indicates the amplitude of the spectrum. This represents the frequency corresponding to the k-th spectral sampling point. It is the sampling frequency of the spectrum transform.

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