A frequency estimation method of zero-padding signal based on iteration

Abstract

The present invention relates to a zero-padding signal frequency estimation method based on iteration, which comprises the following steps: zero-padding the sine wave signal s(n) to obtain the signal #imgabs0# after zero-padding. The length of the original signal s(n) is M, and the length of the signal #imgabs1# after zero-padding is N; performing FFT on the signal #imgabs2# after zero-padding to obtain the signal #imgabs3#; estimating the frequency offset value x0 of the frequency of the signal to be measured at the frequency point k0 by using the amplitude maximum value #imgabs5# of #imgabs4# and #imgabs6##imgabs7#; calculating the shifted frequency point k1 = k0 + x0 by using the frequency offset value x0, and respectively calculating the discrete-time Fourier transform amplitude values corresponding to the frequency points k1 - 1, k1, and k1 + 1 #imgabs8#; estimating the frequency offset value x1 of the frequency of the signal to be measured at the frequency point k1 again according to the value of #imgabs9#, letting x0 = x1, and performing multiple iterations to obtain the estimated value of the frequency #imgabs10#. The present invention performs frequency shift on each estimation result, so that the peak frequency after frequency shift gradually approaches the quantization frequency point, and better estimation performance is obtained through multiple iterations.

Description

Technical Field

[0001] The invention relates to the field of signal processing, and in particular to an iteration-based zero-filling signal frequency estimation method. Background Art

[0002] In the field of communication and radar signal processing, frequency estimation of a sine wave submerged in noise is a classic problem. This is because most target parameter estimation problems can be transformed into frequency estimation problems for single-frequency signals. The quality of the frequency estimation algorithm directly determines the final performance of parameter estimation to a large extent. Due to the fence effect of FFT, when the frequency of the sampling sequence is not an integer multiple of the FFT frequency resolution, the energy spectrum of the sinusoidal signal leaks, and the real frequency of the signal falls between the discrete FFT spectrum lines in the main lobe, resulting in the frequency estimation accuracy being at the same level as the FFT frequency resolution, which cannot meet the accuracy requirements. Most traditional algorithms perform spectrum interpolation based on the frequency domain of the original signal to obtain a more accurate frequency estimate.

[0003] However, in practical applications, zero padding is usually required before performing FFT. For example, the FFT operation on most hardware platforms (such as FPGA or DSP) is implemented based on a signal length of 2L, where L is an integer. However, due to the sampling rate of the analog-to-digital converter (ADC), the actual signal length will not be equal to 2L. Therefore, the original time domain signal should be zero-padded. Due to the difference in signal models, the performance of traditional frequency estimation algorithms is greatly reduced.

[0004] Although the TF method (using the amplitude values ​​of the main peak of the spectrum and the two adjacent peaks to estimate the frequency of any length) can be used to estimate any zero-padded signal, due to theoretical limitations, the closer the original signal length M is to the signal length N after zero padding, the more biased the estimated value becomes and the lower the estimation accuracy becomes. Summary of the invention

[0005] The purpose of the present invention is to provide an iterative zero-padded signal frequency estimation method to solve the problem that the closer the original signal length M is to the zero-padded signal length N, the more biased the estimated value is and the lower the estimation accuracy is.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for estimating the frequency of a zero-filled signal based on iteration comprises the following steps:

[0008] Step 1: Pad the sine wave signal s(n) with zeros to obtain the signal after zero padding. The original signal s(n) has a length of M, and the signal after zero padding is The length is N;

[0009] Step 2: Zero-filled signal Perform FFT to get the signal

[0010] Step 3: Utilization The maximum amplitude as well as Estimate the frequency offset value of the signal to be measured at the frequency point k0

[0011] Step 4: Use the frequency offset value x0 to calculate the moved frequency point k1=k0+x0, and calculate the discrete time Fourier transform amplitude values ​​corresponding to the frequency points k1-1, k1, and k1+1 respectively.

[0012] Step 5: According to The value of is used to estimate the frequency offset value x1 of the signal to be measured at the frequency point k1 again, and x0=x1 is set. Steps 4-5 are repeated until the number of repetitions reaches the set number.

[0013] Step 6: Get the estimated value of frequency

[0014] After adopting the above scheme, the present invention performs frequency shifting on each estimation result so that the peak frequency after frequency shifting gradually approaches the quantization frequency point, and obtains better estimation performance through multiple iterations, thereby solving the problem that the original signal length M is approximately close to the signal length N after zero padding, and the bias of the estimation value becomes increasingly larger. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a RMSE comparison chart between the improved algorithm of the present invention and the TF method (the signal-to-noise ratio is 10dB);

[0016] Figure 2 This is a RMSE comparison chart between the improved algorithm of the present invention and the TF method (the signal-to-noise ratio is -10dB). DETAILED DESCRIPTION

[0017] The present invention discloses an iterative zero-filled signal frequency estimation method, which comprises the following steps:

[0018] Step 1: Pad the sine wave signal s(n) with zeros to obtain the signal after zero padding. The original signal s(n) has a length of M, and the signal after zero padding is The length is N.

[0019]

[0020] Where A is the amplitude, f0 is the signal frequency, and fs is the sampling rate, is the initial phase, M is the number of sampling points, ω(n) is the mean value of 0 and the variance of σ 2 Complex Gaussian white noise, signal-to-noise power ratio SNR = A 2 / (2σ 2 ).

[0021] Step 2: Zero-filled signal Perform FFT to get the signal

[0022]

[0023] Step 3: Extract the signal spectrum The maximum amplitude as well as The theoretical values ​​are as follows:

[0024]

[0025] In the above formula, x is the frequency offset value.

[0026] use The value of is used to estimate the frequency offset x0 at the frequency point k0;

[0027]

[0028] Step 4: Use the frequency offset value x0 to calculate the frequency point k1=k0+x0 after the shift, and calculate the discrete time Fourier transform (DTFT) amplitude values ​​corresponding to the frequency points k1-1, k1, and k1+1 respectively.

[0029] Step 5: According to The value of is used to estimate the frequency offset value x1 at the frequency point k1 again, and x0=x1 is set. Steps 4-5 are repeated until the number of repetitions reaches the set number.

[0030] Step 6: Get the estimated value of frequency

[0031] In order to illustrate the effect of the present invention, the present invention provides several embodiments based on the above method for detailed description.

[0032] In this embodiment, the signal length M of the original sinusoidal wave signal s(n) is 1024, 1500, and 1800 respectively, and the s(n) signal is padded with zeros to obtain the signal Signal length N = 2048, sampling frequency is 1Hz, the real frequency of the signal is set to f0 = 401.5 / 2048 = 0.1960Hz; the signal-to-noise ratio SNR is 10, -10dB, the number of iterations is set to three; the frequency offset value x = -0.5:0.05:0.5. Substituting these data into the above method, the RMSE (root mean square error) between the frequency estimation method of this embodiment and the existing zero-filling interpolation algorithm is obtained. Figure 1 and Figure 2 As shown. Figure 1 and Figure 2 It can be seen that when the original signal length M is closer to the signal length N after zero padding, the frequency error estimated by the existing method is larger, while the frequency error estimated by the method of the present invention can always maintain a low level.

[0033] The above description is merely an embodiment of the present invention and does not limit the technical scope of the present invention. Therefore, any minor modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for estimating the frequency of a zero-padding signal based on iteration, characterized in that: The method comprises the following steps: Step 1: Pad the sine wave signal s(n) with zeros to obtain the signal after zero padding. The original signal s(n) has a length of M, and the signal after zero padding is The length is N; Step 2: Zero-filled signal Perform FFT to get the signal Step 3: Utilization The maximum amplitude as well as Estimate the frequency offset of the signal to be measured at the frequency point k0 Step 4: Use the frequency offset value x0 to calculate the moved frequency point k1=k0+x0, and calculate the discrete time Fourier transform amplitude values ​​corresponding to the frequency points k1-1, k1, and k1+1 respectively. Step 5: According to The value of is used to estimate the frequency offset value x1 of the signal to be measured at the frequency point k1 again, and x0=x1 is set. Steps 4-5 are repeated until the number of repetitions reaches the set number. Step 6: Get the estimated value of frequency

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