A method for estimating frequency of sinusoidal signal based on minimum amplitude difference strategy

Abstract

The application discloses a sine wave frequency estimation method based on a minimum amplitude difference strategy, which comprises the following steps: receiving a sine wave signal, performing fast Fourier transform on the received sine wave signal to obtain discrete spectral lines; finding the position and amplitude of the peak spectral line and adjacent spectral lines of the signal discrete spectrum; and interpolating two spectral lines at the middle position of the peak spectral line and adjacent spectral lines of the signal discrete spectral line; selecting the double spectral line with the minimum amplitude difference from the peak spectral line, the adjacent spectral line and the interpolated spectral line as a reference spectral line, and constructing a ratio equation according to the selected reference spectral line to estimate the frequency. The application selects the double spectral line with stronger anti-noise capability through the minimum amplitude difference strategy to perform frequency estimation, so that the estimation accuracy of different frequency signals is improved, and the frequency estimation accuracy and stability are good, and the calculation complexity is low.

Description

Technical Field

[0001] This invention relates to the field of signal estimation and identification technology in radar communication and electronic countermeasures, specifically a sinusoidal signal frequency estimation method based on the minimum amplitude difference strategy. Background Technology

[0002] Frequency estimation of sinusoidal signals in additive white Gaussian noise is a classic problem in many fields, including radar communication and electronic countermeasures. This technique is widely used in communication and radar signal estimation and identification processing. Therefore, accurate and rapid frequency estimation is of great significance in this field.

[0003] Traditional frequency estimation methods based on Discrete Fourier Transform (DFT) mainly focus on high-precision frequency estimation under low signal-to-noise ratio (SNR) conditions. However, the estimation accuracy may vary significantly when estimating sinusoidal signals of different frequencies, leading to unstable performance. While achieving better stability through spectrum shifting or iterative estimation inevitably increases computational complexity. Summary of the Invention

[0004] This invention addresses the problem that when estimating the frequency of a sinusoidal signal, methods such as spectrum shifting or iterative estimation are needed, which increase computational complexity in order to improve the accuracy and stability of frequency estimation. It provides a sinusoidal signal frequency estimation method based on the minimum amplitude difference strategy.

[0005] To improve the accuracy and stability of frequency estimation for sinusoidal signals in additive white Gaussian noise with lower computational complexity, this invention selects bispectral lines with stronger noise resistance for frequency estimation using a minimum amplitude difference strategy, thereby improving the estimation accuracy of signals at different frequencies.

[0006] This invention provides a method for estimating the frequency of a sinusoidal signal based on a minimum amplitude difference strategy, comprising the following steps:

[0007] (1) Receive a sine wave signal and perform a fast Fourier transform on the received sine wave signal to obtain the discrete spectrum of the signal;

[0008] (2) Locate the peak spectral lines and the positions and amplitudes of adjacent spectral lines in the discrete spectrum of the signal;

[0009] (3) Interpolate two spectral lines at the midpoint between the peak spectral line and its adjacent spectral lines of the discrete spectral line of the signal;

[0010] (4) Compare the amplitudes of the two interpolated spectral lines of the sinusoidal wave received signal, determine the sign of the frequency fractional multiple frequency shift of the sinusoidal wave signal, and group the peak spectral line, adjacent spectral lines and interpolated spectral lines into pairs according to the sign of the frequency fractional multiple frequency shift.

[0011] (5) Select the bispectral line with the smallest amplitude difference as the reference spectral line, and use different ratio equations to estimate the fractional frequency shift based on the selected reference spectral line combination.

[0012] (6) The estimated frequency of the sine wave signal is calculated based on the position of the spectral peak and the estimated fractional frequency offset.

[0013] Furthermore, in step (1), let the emitted sinusoidal signal be s(n). Where A is the signal amplitude, θ is the initial phase of the signal, and T... s Where N is the sampling period, N is the number of signal sampling points, and f0 is the actual frequency of the signal;

[0014] Let the received sinusoidal signal be r(n), r(n) = s(n) + w(n), where w(n) is complex Gaussian noise. Discrete spectrum lines are obtained by performing a fast Fourier transform on the received sinusoidal signal.

[0015] Further, in step (2), the position and amplitude of the peak spectral line and adjacent spectral lines of the discrete spectrum of the signal are found. The frequency of the sine wave signal consists of an integer part and a fractional frequency offset. The peak position p of the discrete spectrum of the signal is set as the integer part of the frequency of the sine wave signal, and the fractional frequency offset is set as x, with a range of -0.5≤x≤0.5.

[0016] The true frequency of the sinusoidal signal is f0 = (p + x)Δf, where Δf = 1 / (NT) s () indicates frequency resolution;

[0017] Let the amplitude at the discrete peak position p of the emitted sinusoidal signal be S0, and the amplitudes at its adjacent spectral lines p-1 and p+1 be S0 and S1, respectively. -1 and S +1 ;

[0018] Let the amplitude at the discrete peak position p of the received sinusoidal signal be R0, and the amplitudes at its adjacent spectral lines p-1 and p+1 be R0 and R1, respectively. -1 and R +1 .

[0019] Further, in step (3), two spectral lines are interpolated at the midpoints p-0.5 and p+0.5 of the peak spectral line and its adjacent spectral lines of the signal spectral line. The amplitudes of the two interpolated spectral lines of the sinusoidal wave transmitted signal at p-0.5 and p+0.5 are S, respectively. -0.5 and S +0.5 ;

[0020] The amplitudes at p-0.5 and p+0.5 of the two interpolated spectral lines of the sinusoidal received signal are R, respectively. -0.5 and R +0.5 .

[0021] Further, step (4) involves comparing the amplitudes of the two interpolated spectral lines of the received sinusoidal signal, i.e., comparing R... +0.5 and R -0.5 Determine the sign of x by its magnitude, and if R ∈ R. +0.5 ≥R -0.5 If x≥0, then R +0.5 <R -0.5 If x < 0, then x < 0;

[0022] The method of grouping peak spectral lines, adjacent spectral lines, and interpolated spectral lines pairwise and subtracting them based on the sign of x is as follows: if x ≥ 0, compare |R0 - R +0.5 |、|R0-R +1 |、|R +0.5 -R -0.5 | size;

[0023] If x < 0, compare |R0 - R -0.5 |、|R0-R -1 |、|R +0.5 -R -0.5 The size of |.

[0024] Further, in step (5), the bispectral line with the smallest amplitude difference is selected as the reference spectral line. Different ratio equations are used to estimate the fractional frequency shift based on the selected reference spectral line combination. Specifically, the method is as follows:

[0025] If |R0-R +0.5 |or|R0-R -0.5 | Minimum, substitute R ±0.5 and R0 to the estimated equation Finally, the Newton-Raphson method was used to solve the equation. Obtain the estimated value

[0026] If |R0-R +1 |or|R0-R -1 | Minimum, substitute R ±1 And R0 to the formula That is, we obtain the estimated value.

[0027] If |R +0.5 -R -0.5 | Minimum, substitute R ±0.5 To the formula That is, we obtain the estimated value.

[0028] Further, step (6) involves using the spectral peak position p and the estimated... Obtain the estimated frequency of the sinusoidal signal.

[0029] CN116449098A describes a method for estimating the frequency of a sinusoidal signal under low signal-to-noise ratio (SNR). This method uses a Fast Fourier Transform (FFT) algorithm to calculate the discrete spectrum of the received sinusoidal signal. The frequency of the sinusoidal signal is estimated based on the spectral lines flanking the peak in the discrete spectrum. The estimated frequencies are then weighted to obtain the actual frequency estimate of the sinusoidal signal under low SNR. This invention requires interpolation at two additional frequency points near the peak, or in other words, estimation at two additional frequency points. A spectral line selection is performed based on the additional interpolated frequencies and the original frequencies. This spectral line selection is crucial and can effectively further improve reliability.

[0030] The sinusoidal signal frequency estimation method of this invention can simultaneously achieve good frequency estimation accuracy and stability, as well as low computational complexity. Attached Figure Description

[0031] Figure 1 This is a flowchart of the sinusoidal signal frequency estimation method of the present invention;

[0032] Figure 2 The discrete Fourier transform (DFT) spectrum and discrete-time Fourier transform (DTFT) spectrum of the transmitted and received sinusoidal signals in the embodiment are shown.

[0033] In the figure, circles represent the amplitude of the transmitted signal DFT sample, triangles represent the amplitude of the received signal DFT sample, and dashed lines represent two interpolation spectral lines. Detailed Implementation

[0034] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but this is not intended to limit the present invention.

[0035] Example

[0036] A frequency estimation method for sinusoidal signals based on the minimum amplitude difference strategy, referring to... Figure 1 It includes the following steps:

[0037] (1) Receive a sine wave signal and perform a fast Fourier transform on the received sine wave signal to obtain the discrete spectrum of the signal;

[0038] (2) Locate the peak spectral lines and the positions and amplitudes of adjacent spectral lines in the discrete spectrum of the signal;

[0039] (3) Interpolate two spectral lines at the midpoint between the peak spectral line and its adjacent spectral lines of the discrete spectral line of the signal;

[0040] (4) Compare the amplitudes of the two interpolated spectral lines of the sinusoidal wave received signal, determine the sign of the frequency fractional multiple frequency shift of the sinusoidal wave signal, and group the peak spectral line, adjacent spectral lines and interpolated spectral lines into pairs according to the sign of the frequency fractional multiple frequency shift.

[0041] (5) Select the bispectral line with the smallest amplitude difference as the reference spectral line, and use different ratio equations to estimate the fractional frequency shift based on the selected reference spectral line combination.

[0042] (6) The estimated frequency of the sine wave signal is calculated based on the position of the spectral peak and the estimated fractional frequency offset.

[0043] Reference Figure 2 A method for frequency estimation of sinusoidal signals based on the minimum amplitude difference strategy is presented, with the following specific steps:

[0044] (1) Let the emitted sinusoidal signal be s(n), Where A is the signal amplitude, θ is the initial phase of the signal, and T... s Where N is the sampling period, N is the number of signal sampling points, and f0 is the actual frequency of the signal;

[0045] Let the received sinusoidal signal be r(n), r(n) = s(n) + w(n), where w(n) is complex Gaussian noise. Discrete spectrum lines are obtained by performing a fast Fourier transform on the received sinusoidal signal.

[0046] (2) Locate the peak spectral line and the position and amplitude of adjacent spectral lines in the discrete spectrum of the signal. The frequency of the sinusoidal signal consists of an integer part and a fractional frequency offset. Set the peak position p of the discrete spectrum of the signal as the integer part of the frequency of the sinusoidal signal, and set the fractional frequency offset as x, with a range of -0.5≤x≤0.5.

[0047] The true frequency of the sinusoidal signal is f0 = (p + x)Δf, where Δf = 1 / (NT) s () indicates frequency resolution;

[0048] Suppose the amplitude at the discrete peak position p of the transmitted sinusoidal signal is S0, such as Figure 2 As shown, the amplitudes at p-1 and p+1 of its adjacent spectral lines are S, respectively. -1 and S +1 ;

[0049] Suppose the amplitude at the discrete spectrum peak position p of the received sinusoidal signal is R0, such as Figure 2 As shown, the amplitudes at adjacent spectral lines p-1 and p+1 are R, respectively. -1 and R +1 .

[0050] Step (3) interpolate two spectral lines at the midpoints p-0.5 and p+0.5 of the peak spectral line and its adjacent spectral lines, such as... Figure 2 As shown, the amplitudes at p-0.5 and p+0.5 of the two interpolated spectral lines of the sinusoidal transmitted signal are S, respectively. -0.5 and S +0.5 ;

[0051] The amplitudes at p-0.5 and p+0.5 of the two interpolated spectral lines of the sinusoidal received signal are R, respectively. -0.5 and R +0.5 .

[0052] Step (4) Compare the amplitudes of the two interpolated spectral lines of the sinusoidal received signal, i.e., compare R. +0.5 and R -0.5 Determine the sign of x by its magnitude, and if R ∈ R. +0.5 ≥R -0.5 If x≥0, then R +0.5 <R -0.5 If x < 0, then x < 0;

[0053] The method of grouping peak spectral lines, adjacent spectral lines, and interpolated spectral lines pairwise and subtracting them based on the sign of x is as follows: if x ≥ 0, compare |R0 - R +0.5 |、|R0-R +1 |、|R +0.5 -R -0.5 | size;

[0054] If x < 0, compare |R0 - R -0.5 |、|R0-R -1 |、|R +0.5 -R -0.5 The size of |.

[0055] Step (5) Select the bispectral line with the smallest amplitude difference as the reference spectral line, and use different ratio equations to estimate the fractional frequency shift based on the selected reference spectral line combination. The specific method is as follows:

[0056] If |R0-R +0.5 |or|R0-R -0.5 | Minimum, substitute R ±0.5 and R0 to the estimated equation Finally, the Newton-Raphson method was used to solve the equation. Obtain the estimated value

[0057] If |R0-R +1 |or|R0-R -1 | Minimum, substitute R +1 And R0 to the formula That is, we obtain the estimated value.

[0058] If |R +0.5 -R -0.5 | Minimum, substitute R ±0.5 To the formula That is, we obtain the estimated value.

[0059] Step (6) Based on the spectral peak position p and the estimated... Obtain the estimated frequency of the sinusoidal signal.

[0060] The present invention provides a sinusoidal signal frequency estimation method that adopts a minimum amplitude difference strategy. By selecting bispectral lines with similar amplitudes and stronger noise resistance for frequency estimation, the estimation accuracy of signals of different frequencies is improved, thus overcoming the problem of obtaining better estimation stability at the cost of increased computational complexity.

Claims

1. A method for estimating the frequency of a sinusoidal signal based on a minimum amplitude difference strategy, characterized in that, Includes the following steps: (1) Receive a sine wave signal and perform a fast Fourier transform on the received sine wave signal to obtain the discrete spectrum of the signal; (2) Locate the peak spectral line and the position and amplitude of adjacent spectral lines in the discrete spectrum of the signal. Specifically: the frequency of a sinusoidal signal consists of an integer part and a fractional frequency offset. Locate the peak position of the discrete spectrum of the signal. Let the integer part of the frequency of the sine wave signal be , and let the fractional frequency offset be . , range ; The true frequency of a sine wave signal ,in Indicates frequency resolution; Let the discrete spectrum peak position of the transmitted sinusoidal signal be... The amplitude at that point is Its adjacent spectral lines place and The amplitudes at the locations are respectively and ; Let the discrete spectrum peak position of the received sinusoidal signal be... The amplitude at that point is Its adjacent spectral lines place and The amplitudes at the locations are respectively and ; (3) Interpolate two spectral lines at the midpoint between the peak spectral line and its adjacent spectral lines of the discrete spectral line of the signal. Specifically, interpolate at the midpoint between the peak spectral line and its adjacent spectral lines of the discrete spectral line of the signal. place and Two interpolated spectral lines for the sinusoidal transmitted signal. place and The amplitudes at the locations are respectively and ; Two interpolated spectral lines of the sine wave received signal place and The amplitudes at the locations are respectively and ; (4) Compare the amplitudes of the two interpolated spectral lines of the sinusoidal wave received signal, determine the sign of the frequency fractional multiple frequency shift of the sinusoidal wave signal, and group the peak spectral line, adjacent spectral lines and interpolated spectral lines into pairs according to the sign of the frequency fractional multiple frequency shift. The comparison refers to the magnitude of the amplitudes of the two interpolated spectral lines of the received sinusoidal signal. and Size, determine The positive and negative, if ,but ,like ,but ; According to The sign of the peak spectral line, adjacent spectral lines, and interpolated spectral lines are grouped pairwise and subtracted. Specifically: if ,Compare , , Size; like ,Compare , , Size; (5) Select the bispectral line with the smallest amplitude difference as the reference spectral line, and use different estimation equations to estimate the fractional frequency shift based on the selected reference spectral line combination. The specific method is as follows: like or minimum, substitute and To the estimated equation , , Finally, the Newton-Raphson method was used to solve the equation. Obtain the estimated value ; like or minimum, substitute and To the formula , That is, to obtain the estimated value ; like minimum, substitute To the formula , That is, to obtain the estimated value ; (6) The estimated frequency of the sine wave signal is calculated based on the position of the spectral peak and the estimated fractional frequency offset.

2. The sinusoidal signal frequency estimation method according to claim 1, characterized in that: In step (1), let the emitted sinusoidal signal be... , ,in The signal amplitude, This is the initial phase of the signal. The sampling period is The number of signal sampling points. The actual frequency of the signal; Let the received sine wave signal be... , ,in It is complex Gaussian noise, and discrete spectral lines are obtained by performing a fast Fourier transform on the received sine wave signal.

3. The sinusoidal signal frequency estimation method according to claim 1, characterized in that: Step (6) involves determining the position of the spectral peaks. and the estimated Obtain the estimated frequency of the sinusoidal signal. .

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