A method for high-precision estimation of single-frequency signal parameters

Abstract

The present invention discloses a method for high-precision estimation of single-frequency signal parameters, which filters out power-frequency interference from the signal s r (n), adds a flat-top window after that to obtain the time-domain signal x(n); then uses the multiple autocorrelation algorithm to process the time-domain signal x(n), which can effectively enhance the signal for low signal-to-noise ratio signals, accurately and stably estimate the amplitude and phase of the signal, and finally correct the relative deviation of the signal frequency to obtain the accurate single-frequency signal frequency. This method has a fast processing speed, high efficiency and estimation accuracy, and is easy to implement in engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and particularly to a method for high-precision estimation of single-frequency signal parameters. Background Art

[0002] Single-frequency signals are widely used in actual detection systems. Due to the very complex underwater acoustic and electromagnetic environments, the background noise usually not only contains white noise, but also a large amount of in-band colored noise, making it very difficult to estimate single-frequency signal parameters. Amplitude estimation is mainly used for threshold setting and characterization of acoustic and magnetic field intensities, and frequency estimation is mainly used for determining effective acoustic and magnetic echoes, Doppler estimation, etc. If the signal amplitude and frequency can be accurately estimated under complex backgrounds, it is of great significance for improving the capabilities of detection systems.

[0003] Current single-frequency signal estimation usually adopts adaptive enhancement algorithms, which can effectively extract weak signals from noise but cannot accurately estimate the amplitude; frequency estimation algorithms based on interpolation have high frequency estimation accuracy but are easily affected by noise interference and have poor estimation stability. Summary of the Invention

[0004] In view of the above problems, the inventors provide a method for high-precision estimation of single-frequency signal parameters based on multiple autocorrelations, which can accurately estimate signal amplitude and frequency under strong noise interference backgrounds, has good stability, and small computational complexity.

[0005] The present invention provides a method for high-precision estimation of single-frequency signal parameters, including:

[0006] Step 1: Perform power frequency interference filtering on the signal s r (n) to obtain the signal s(n); subtract a narrowband FIR filter through an all-pass network. The FIR filter is characterized by having narrowband signal processing and the same delay and gain, so as to obtain a notch filter with sharp notch characteristics. The power frequency interference is 50 Hz. Design the upper and lower cut-off frequencies of the stopband to be 49 Hz and 51 Hz to eliminate the 50 Hz power frequency interference and obtain the signal s(n) after filtering the power frequency interference.

[0007] Step 2: Add a flat-top window to the signal s(n) to obtain the windowed time-domain signal x(n), where x(n) = s(n)ω(n),

[0008] The expression of the flat-top window ω(n) is:

[0009]

[0010] where a 0 = 0.2156, a 1 = 0.4166, a 2 = 0.2773, a 3= 0.0836, a 4 = 0.0069, where L is the length of the flat-top window.

[0011] Step 3: Process the time-domain signal x(n) using the multiple autocorrelation algorithm to obtain the amplitude-corrected signal y m (n). For the time-domain signal x(n), its autocorrelation R x (n) is:

[0012]

[0013] Step 4: Search for the amplitude of the signal y m (n) to obtain the discrete frequency index k 0 ,

[0014]

[0015] indicating the discrete frequency index corresponding to the maximum value of Y(k) searched within the range, where Y(k) is the amplitude spectrum of the signal y m (n).

[0016] Step 5: Extract the discrete frequency index k 0 and its two adjacent discrete frequency indices k 0 -1 and k 0 +1 corresponding amplitude spectrum results A l , A m and A r ; where, A l = Y(k 0 -1), A m = Y(k 0 ), A r = Y(k 0 +1).

[0017] Extract the ratio a 0 of the discrete Fourier transform of the discrete frequency index k 0 -1 to the discrete Fourier transform of the discrete frequency index k l , and extract the ratio a 0 of the discrete Fourier transform of the discrete frequency index k 0 +1 to the discrete Fourier transform of the discrete frequency index k r ;

[0018] Step 6: According to A l , A m , A r , a l and a rCalculate the relative frequency deviation of the single-frequency signal ;

[0019] Step 7: Based on interpolation estimation, calculate the frequency of the single-frequency signal according to the relative frequency deviation of the single-frequency signal Calculate the frequency of the single-frequency signal.

[0020] Further, the said step 3 includes:

[0021] Step 31: Perform a discrete Fourier transform of length 2N on the time-domain signal x(n), convert the time-domain signal x(n) to the frequency domain, and obtain the frequency-domain signal X(k); N is the total number of time-domain signal points, that is, the length of the one-dimensional signal discrete sequence.

[0022] The autocorrelation R(k) of the frequency-domain signal X(k) is:

[0023] R(k) = X(k)X * (k)

[0024] X * (k) is the conjugate of X(k).

[0025] Step 32: Convert the autocorrelation R(k) of the frequency domain X(k) to the time domain to obtain the time-domain signal r(n) after autocorrelation calculation.

[0026] Step 33: Intercept the sequence of length N / 2 to N / 3 of the time-domain signal r(n) to obtain the signal y′(n) after autocorrelation processing,

[0027] Step 34: Repeat Step 31, Step 32, and Step 33 to obtain the signal y′ m (n);

[0028] Step 35: Correct the signal y′ m (n) to obtain the signal y m (n);

[0029]

[0030] Further, the said step 6 includes:

[0031] Calculate the discrete frequency index k 0 -1 and k 0 +1 of the relative frequency deviation δ 1 and δ 2 ;

[0032]

[0033] If δ 1 , δ 2 > 0 or A l<A r , then the relative frequency deviation is:

[0034]

[0035] If δ 1 , δ 2 <0, then the relative frequency deviation is:

[0036]

[0037] Further, the step 7 includes:

[0038] Performing non - linear regression fitting on the signal s r (n), and setting the frequency f 0 as:

[0039]

[0040] where Δf = 0.1, k is the index value at the frequency point, F s is the sampling rate, and N is the number of sampling points;

[0041] Interpolating and estimating the signal frequency

[0042]

[0043] Compared with the prior art, the beneficial effects of the present invention:

[0044] (1) This method can effectively suppress power - frequency interference, prevent spectral leakage caused during the FFT calculation process, can effectively enhance the signal for low - signal - to - noise - ratio signals, and accurately, quickly, and stably estimate the amplitude and phase of the signal.

[0045] (2) By fitting the deviation correction through non - linear regression, the estimation accuracy is effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 (a) is the spectrum of the original signal s r (n) in Embodiment 1;

[0047] Figure 1 (b) is the spectrum of the signal s(n) in Embodiment 1;

[0048] Figure 2 is the filter frequency response diagram in Embodiment 1;

[0049] Figure 3 is the spectrum of the signal x(n) after windowing the signal s(n) in Embodiment 1;

[0050] Figure 4 (a) is the spectrum of the signal y′ after the first autocorrelation processing in Embodiment 1 1 (n);

[0051] Figure 4 (b) is the spectrum of the signal y′ after the fourth autocorrelation processing in Embodiment 1 4 (n);

[0052] Figure 5 is the spectrum of the signal y after autocorrelation amplitude correction in Embodiment 1 m (n). Specific Embodiment

[0053] The present invention will be further described in detail below with reference to the accompanying drawings through specific embodiments.

[0054] Embodiment 1

[0055] Design a simulation signal s r (n) = cos(2π×125n) + N(n) + 0.5cos(2π×50n), the last term represents the 50Hz power frequency interference term, the signal-to-noise ratio is -10dB, and the spectrum of the simulation signal s r (n) is as shown in Figure 1 (a).

[0056] Step 1: Perform power frequency interference filtering on the signal s r (n) to obtain the signal s(n); subtract a narrowband FIR filter through an all-pass network. The FIR filter is characterized by narrowband signal processing and having the same delay and gain, so as to obtain a notch filter with sharp notch characteristics. The power frequency interference is 50Hz, and the upper and lower cut-off frequencies of the stopband are designed to be 49Hz and 51Hz to eliminate the 50Hz power frequency interference and obtain the signal s(n) after filtering the power frequency interference. Its spectrum is as shown in Figure 1 (b). The frequency response of the filter is as shown in Figure 2 shown.

[0057] Step 2: Perform windowing on the filtered signal s(n) to prevent spectrum leakage caused by the FFT calculation process and to accurately estimate the signal amplitude, obtaining the windowed time-domain signal x(n), x(n) = s(n)ω(n), and the flat-top window expression ω(n) is:[[]]

[0058]

[0059] The spectrum of the windowed time-domain signal x(n) is as shown in Figure 3 shown.

[0060] Step 3: Perform multiple autocorrelation processing on the signal x(n) for noise suppression. Use the multiple autocorrelation algorithm to enhance the signal. For the time-domain signal x(n), its autocorrelation R x (n) is:

[0061]

[0062] Step 31: For the time-domain signal x(n), where n = 1, 2, …, N, perform a discrete Fourier transform of length 2N to convert the time-domain signal x(n) to the frequency domain, obtaining the frequency-domain signal X(k); the autocorrelation R(k) of the frequency-domain signal X(k) is:

[0063] (k) = X(k)X * (k)

[0064] X * (k) is the conjugate of X(k).

[0065] Step 32: Convert R(k) to the time domain to obtain the time-domain signal r(n) after autocorrelation calculation.

[0066] Step 33: Intercept the time-domain signal r(n) sequence with a length from N / 2 to N / 3 to obtain the signal y′(n) after autocorrelation processing.

[0067] Step 34: Repeat Step 31, Step 32, and Step 33 to obtain the signal y′ m (n) after m-fold autocorrelation processing; at this time, the signal amplitude becomes 2 m times the original due to autocorrelation calculation.

[0068] The number of multiple autocorrelations m = 5. The spectrum of the signal y′ 1 (n) after the first autocorrelation processing is as shown in Figure 4 (a), and the spectrum of the signal y′ 4 (n) after the fourth autocorrelation processing is as shown in Figure 4 (b). It can be seen that the noise amplitude is well suppressed.

[0069] Step 35: Correct the signal y′ m (n) to obtain the signal y m (n) after amplitude correction;

[0070]

[0071] Step 4: Search for the amplitude of the signal y m (n) to obtain the discrete frequency index k corresponding to the maximum value of its amplitude spectrum 0 ,

[0072]

[0073] Indicates that in the range search, the discrete frequency index corresponding to the maximum value of Y(k); Y(k) is the magnitude spectrum of the signal y m (n), and in this embodiment, k 0 = 2501.

[0074] Step 5: Extract the discrete frequency index k 0 and its two adjacent discrete frequency indices k 0 -1 and k 0 +1 and the corresponding magnitude spectrum results A l , A m and A r ; where A l = Y(k 0 -1), A m = Y(k 0 ), A r = Y(k 0 +1). A m = 1.0553, A l = 1.0504, A r = 1.0541.

[0075] Extract the discrete Fourier transform of the discrete frequency index k 0 -1 and the ratio a 0 of the discrete Fourier transform of the discrete frequency index k l , extract the discrete Fourier transform of the discrete frequency index k 0 +1 and the ratio a 0 of the discrete Fourier transform of the discrete frequency index k r ;

[0076] Step 6: Calculate the frequency relative deviation of the single-frequency signal according to A l , A m , A r , a l and a r ; ;

[0077] Calculate the frequency relative deviations δ 0 -1 and k 0 +1 1 and δ 2 ;

[0078]

[0079] If δ 1 , δ 2 > 0 or A l<A r , then the relative frequency deviation is:

[0080]

[0081] If δ 1 , δ 2 <0, then the relative frequency deviation is:

[0082]

[0083] In this embodiment, δ 1 = 216.39,, δ 2 = 908.09,

[0084] Step 7: Correct the relative frequency deviation of the signal based on the semi-supervised method. First, perform non-linear regression fitting on the signal s r (n). Set the frequency f 0 as:

[0085]

[0086] where Δf = 0.1, k is the index value at the frequency point, F s is the sampling rate, and N is the number of sampling points.

[0087] Use a signal with a signal-to-noise ratio of -10 dB to perform a Monte Carlo experiment for regression fitting. The number of regression fittings is 1000. It is obtained that when , let When , let When let When , let When , let In other cases, let

[0088] Based on interpolation estimation, calculate the frequency of the single-frequency signal according to the relative frequency deviation of the single-frequency signal That is

[0089]

[0090] The calculated interpolation estimation frequency of the signal is The frequency estimation error is less than 0.001.

[0091] The above uses specific examples to elaborate on the present invention, which is only used to help understand the present invention and is not intended to limit the present invention. For those skilled in the art to which the present invention pertains, based on the idea of the present invention, several simple deductions, deformations or substitutions can also be made.

Claims

1. A method for high-precision estimation of single-frequency signal parameters, characterized in that, it includes: Step 1: Perform power frequency interference filtering on the signal s r (n) to obtain the signal s(n); Step 2: Add a flat-top window to the signal s(n) to obtain the windowed time-domain signal x(n); Step 3: Process the time-domain signal x(n) using the multiple autocorrelation algorithm to obtain the amplitude-corrected signal y m (n): Step 4: Search for the amplitude of the signal y m (n), and obtain the discrete frequency index k corresponding to the maximum value of its amplitude spectrum 0 ; Step 5: Extract the discrete frequency index k 0 and its two adjacent discrete frequency indices k 0 -1 and k 0 +1 corresponding to the magnitude spectrum results A l , A m and A r ; Extract the discrete frequency index k 0 The ratio a of the discrete Fourier transform of -1 and the discrete frequency index k 0 to the discrete Fourier transform l Extract the discrete frequency index k 0 The ratio a of the discrete Fourier transform of +1 and the discrete frequency index k 0 to the discrete Fourier transform r ; Step 6: According to A l , A m , A r , a l and a r Calculate the relative frequency deviation of the single-frequency signal Step 7: Based on the interpolation estimation, calculate the frequency of the single-frequency signal according to the relative frequency deviation of the single-frequency signal Calculate the frequency of the single-frequency signal.

2. The method according to claim 1, characterized in that, in the said Step 2, the flat-top window expression is: Among them, a 0 = 0.2156, a 1 = 0.4166, a 2 = 0.2773, a 3 = 0.0836, a 4 = 0.0069, and L is the length of the flat-top window.

3. The method according to claim 1, characterized in that, the said Step 3 includes: Step 31: Perform a discrete Fourier transform of length 2N on the time-domain signal x(n); convert the time-domain signal x(n) to the frequency domain to obtain the frequency-domain signal X(k); N is the total number of time-domain signal points; Step 32: Convert the autocorrelation R(k) of the frequency domain X(k) to the time domain to perform the autocorrelation calculation on the time-domain signal r(n); Step 33: Intercept the time-domain signal r(n) from N / 2 to N / 3 length sequence to obtain the autocorrelation processed signal y′(n); Step 34: Repeat Step 31, Step 32, and Step 33 to obtain the signal y′ m (n) after m-fold autocorrelation processing; Step 35: Correct the signal y′ m (n) to obtain the amplitude-corrected signal y m (n).

4. The method according to any one of claims 1-3, characterized in that, the said Step 6 includes: Calculate the discrete frequency index k 0 -1 and k 0 The relative frequency deviation δ of +1 1 and δ 2 ; If δ 1 , δ 2 > 0 or A l < A r , then the relative frequency deviation is: If δ 1 , δ 2 < 0, then the relative frequency deviation is:

5. The method according to any one of claims 1-3, characterized in that, the said Step 7 includes: Perform non-linear regression fitting on the signal s r (n), and set the frequency f 0 as: where Δf = 0.1, k is the index value at the frequency point, F s is the sampling rate, and N is the number of sampling points; Interpolated estimated signal frequency

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