CN108469602B - Pulse signal type automatic discrimination method based on spectral feature extraction - Google Patents

Pulse signal type automatic discrimination method based on spectral feature extraction Download PDF

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CN108469602B
CN108469602B CN201810276193.1A CN201810276193A CN108469602B CN 108469602 B CN108469602 B CN 108469602B CN 201810276193 A CN201810276193 A CN 201810276193A CN 108469602 B CN108469602 B CN 108469602B
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CN108469602A (en
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姚帅
方世良
王晓燕
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Abstract

The invention discloses a pulse signal type automatic distinguishing method based on spectral feature extraction, which comprises the following steps: the first step is as follows: acquiring a sampling data sequence of a pulse signal to be distinguished; the second step is that: initializing parameters; the third step: calculating a magnitude spectrum of the sampling data sequence; the fourth step: carrying out iterative smoothing processing on the amplitude spectrum to obtain a smooth amplitude spectrum; the fifth step: searching a discrete frequency index corresponding to the maximum value of the smooth amplitude spectrum and a starting discrete frequency index and a stopping discrete frequency index corresponding to the half amplitude value of the main lobe; and a sixth step: respectively calculating the signal-to-noise ratio of the peak main lobe of the original amplitude spectrum and the smooth amplitude spectrum; the seventh step: and judging the type of the pulse signal. The judgment method of the invention uses the ratio of the signal-to-noise ratio of the peak main lobe before and after the amplitude spectrum is smoothed as the characteristic parameter of the automatic judgment of the single-frequency pulse signal and the frequency modulation pulse signal, can realize the automatic judgment of the high accuracy of the two types of pulse signals, has small operand and strong practicability, and is suitable for processing the signals in real time.

Description

Pulse signal type automatic discrimination method based on spectral feature extraction
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to an automatic pulse signal type distinguishing method based on spectral feature extraction.
Background
The pulse signal type judgment is to realize the automatic judgment of the signal type through a signal processing algorithm under the condition of no prior knowledge. The single-frequency pulse signal and the frequency modulation pulse signal are most widely applied to the fields of radar and sonar, the signal types of the two types of signals are automatically judged, a basis can be provided for further fine estimation of signal parameters and target identification, important theoretical and application values are achieved in the fields of sonar, radar, electronic warfare and the like, and the occupied position is more prominent particularly in radar and sonar signal processing.
At present, scholars at home and abroad propose a plurality of automatic pulse signal type judgment methods, which mainly comprise the following steps: (1) the method based on pulse signal intra-pulse instantaneous feature identification, for example, uses information such as instantaneous amplitude, instantaneous phase and instantaneous frequency of a signal as the basis of classification judgment, and the method has clear physical concept and simple principle, but is greatly influenced by signal-to-noise ratio; (2) the discrimination method based on the Transform domain characteristics is characterized in that at present, more classical Short-Time Fourier Transform (STFT) and wavelet Transform exist, Morlet wavelet Transform, Marr wavelet Transform, Harr wavelet Transform and the like, S Transform, Wigner-Ville distribution (WVD), Hilbert-Huang Transform (HHT) and the like are mainly used, wherein the S Transform is extension or popularization of the ideas of the Short-Time Fourier Transform and continuous wavelet Transform, the lower limit of the signal-to-noise ratio adaptable by the method is superior to the method based on pulse signal intra-pulse instantaneous characteristic extraction, but the operation amount is huge, and the classification effect is not obvious; (3) the discrimination method for zero crossing point detection has good classification effect under high signal-to-noise ratio, but generally requires higher data sampling rate, and the discrimination effect is rapidly deteriorated along with the reduction of the signal-to-noise ratio; (4) based on the maximum likelihood method, the method theoretically ensures the optimal classification result under the Bayesian rule, but has the defects that more prior information is needed, and the classification judgment effect is poor under the condition of no prior knowledge.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems and the defects of the existing method, the invention provides the pulse signal type automatic judging method based on the spectral feature extraction, the method can meet the requirements of radar and sonar signal processing, can realize the automatic judgment of single frequency and frequency modulation pulse signals with high accuracy rate by very small computation amount under the condition of lower signal to noise ratio, and has strong engineering practicability.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme: a pulse signal type automatic discrimination method based on spectral feature extraction comprises the following steps:
(1) acquiring a pulse signal sampling data sequence to be distinguished: receiving real-time acquisition data of N sampling points from a sensor as a data sequence x (N) to be distinguished, wherein N is 0,1, …, N-1, or extracting N sampling point data containing the whole pulse signal from a memory as the data sequence x (N) to be distinguished, N is 0,1, …, N-1, wherein N is the number of sampling points containing the whole pulse signal and is an integer power of 2;
(2) initializing parameters related to iterative smoothing and pulse signal type judgment: setting a maximum iteration number threshold I and a precision control threshold epsilon of iterative smoothing, setting an iterative smoothing window length M, and judging a single frequency and frequency modulation pulse signal-to-noise ratio threshold eta;
(3) calculating a pulse signal amplitude spectrum P (k) according to the data sequence x (n);
(4) carrying out iterative smoothing processing on the P (k) to obtain a smoothed magnitude spectrum S (k);
(5) search for S (k) maximum valueCorresponding discrete frequency index kMAnd the start and end discrete frequency indices k corresponding to the main lobe half-amplitudeLAnd kR；
(6) Respectively calculating the SNR of the peak main lobe of the original amplitude spectrum and the SNR of the smooth amplitude spectrumpAnd SNRS；
(7) According to SNRpAnd SNRSAnd judging the type of the pulse signal.
Preferably, in the step (2), a maximum iteration number threshold I and a precision control threshold epsilon of iterative smoothing are set, a length M of an iterative smoothing window is determined, and a single-frequency and frequency modulation pulse signal-to-noise ratio threshold eta is determined, wherein the value of I is a positive integer greater than 2, epsilon is a positive number less than 1, the length of the iterative smoothing window is an odd number with M being greater than or equal to 3 and less than or equal to N/2-3, and eta is an arbitrary number with eta being greater than or equal to 1.5 and less than or equal to 2.5. Preferably, I is 10, ε is 0.01, M is 5, and η is 2.0.
Preferably, in the step (3), fast fourier transform is performed on the data sequence x (n), and discrete fourier transform x (l) and magnitude spectrum p (k) of the data sequence are obtained through calculation, specifically including the following steps:
(3-1) calculating the discrete Fourier transform of x (n)
Figure BDA0001612517250000021
Where I is the discrete frequency index of X (l) and j represents an imaginary unit, i.e.
Figure BDA0001612517250000022
This equation can be implemented by fast fourier transform.
(3-2) calculating the amplitude spectrum of x (n) according to X (l)
Figure BDA0001612517250000023
Where k is the discrete frequency index of P (k), and | represents the modulo operation.
Preferably, in the step (3), the discrete fourier transform x (l) of the step (3-1) of calculating x (n) can be realized by fast fourier transform;
preferably, in the step (4), the iterative smoothing processing is performed on p (k) to obtain a smoothed magnitude spectrum s (k), and the method specifically includes the following steps:
(4-1) initializing the iteration number i as 0, and smoothing the result S by the first iteration0(k) Is composed of
S0(k)＝P(k)，k＝0，1，2…，N/2-1
(4-2) let the iteration number i be i +1, and smooth the result S for the last iterationi-1(k) Performing smoothing to obtain current smoothing result Si(k)
Figure BDA0001612517250000031
(4-3) judging whether the maximum iterative smoothing times is reached, namely judging whether I is less than or equal to I, if so, entering the step (4-4), and otherwise, jumping to the step (4-6);
(4-4) calculating last smoothing results S, respectivelyi-1(k) And current smoothing result Si(k) Sum of squares J of residuals from original amplitude spectrum p (k)i-1And JiAre respectively as
Figure BDA0001612517250000032
(4-5) judgment of | Ji-1-Ji|≤εJiIf yes, entering the step (4-6), otherwise, returning to the step (4-2);
(4-6) let S (k) be Si(k) And k is 0,1,2 …, N/2-1, and a smoothed amplitude spectrum s (k) is obtained.
Preferably, in step (5), the discrete frequency index k corresponding to the maximum value of s (k) is searchedMAnd the start and end discrete frequency indices k corresponding to the main lobe half-amplitudeLAnd kRThe method specifically comprises the following steps:
(5-1) searching a discrete frequency index k corresponding to the maximum value of S (k)M
Figure BDA0001612517250000033
Wherein
Figure BDA0001612517250000034
Representing that the discrete frequency index corresponding to the maximum value of S (k) is searched within the range of 1 ≦ k ≦ N/2-1;
(5-2) performing maximum value normalization processing on the S (k) to obtain a normalized smooth amplitude spectrum Z (k):
Z(k)＝S(k)/S(kM)，k＝0，1，2…，N/2-1
(5-3) searching S (k) initial discrete frequency index k corresponding to main lobe half amplitudeLThe searching process comprises the following steps:
(5-3-1) initializing initial search discrete frequency index kl＝1；
(5-3-2) judgment of kM-k l0 or Z (k)M-kl) -0.5 < 0, if yes, jump to (5-3-4), otherwise go to (5-3-3);
(5-3-3) order kl＝kl+1, and back (5-3-2);
(5-3-4) order kL＝kM-klObtaining the initial discrete frequency index k corresponding to the half amplitude of the main lobeL。
(5-4) searching S (k) termination discrete frequency index k corresponding to main lobe half amplitudeRThe searching process comprises the following steps:
(5-4-1) initial termination of search for discrete frequency index kr＝1；
(5-4-2) judgment of kM+krN/2-1 or Z (k)M+kr) -0.5 < 0, if yes, jump to (5-4-4), otherwise go to (5-4-3);
(5-4-3) order kr＝kr+1, and back (5-4-2);
(5-4-4) order kR＝kM-krObtaining the final discrete frequency index k corresponding to the main lobe half amplitudeR。
Preferably, in step (6), the raw materials are calculated separatelyPeak mainlobe signal-to-noise ratio SNR of amplitude spectrum and smooth amplitude spectrumpAnd SNRS：
Figure BDA0001612517250000041
Preferably, in step (7), the SNR is determinedpAnd SNRSThe method for judging the pulse signal type comprises the following steps:
(7-1) calculating the ratio SNRR of the signal-to-noise ratio of the peak main lobe before and after smoothing of the magnitude spectrum
Figure BDA0001612517250000042
(7-2) judging whether the SNRR < eta is satisfied, if so, judging the signal to be a frequency modulation pulse signal, otherwise, judging the signal to be a single-frequency pulse signal.
Has the advantages that: compared with the prior art, the method has the following beneficial effects:
(1) when the amplitude spectrum of the signal is obtained by the estimation method, the whole pulse signal is utilized, the signal processing gain of approximate matched filtering can be obtained, the lower limit of the applicable signal-to-noise ratio is low, the estimation method can be realized by fast Fourier transform, and the calculation amount is small;
(2) according to the estimation method, after the amplitude spectrum of the pulse signal is obtained by utilizing Fourier transform, iterative smoothing processing is carried out on the amplitude spectrum of the signal, the requirement of pulse signal half-amplitude bandwidth estimation on the signal-to-noise ratio can be reduced, and a precondition is provided for further accurately estimating the peak value main lobe signal-to-noise ratio;
(3) the estimation method defines the ratio of the signal-to-noise ratio of the main lobe of the front peak value and the back peak value of the amplitude spectrum before smoothing as the characteristic quantity parameter of the automatic judgment of the signal type, the characteristic parameter has better discrimination on the single frequency and the frequency modulation pulse signal, and the high-accuracy automatic judgment of the single frequency and the frequency modulation pulse signal can be realized with very small operation amount under the lower signal-to-noise ratio.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a graph of the amplitude spectrum of the simulated pulse signal of example 1;
FIG. 3 is a graph of the smoothed amplitude spectrum of the simulated pulse signal of example 1;
FIG. 4 is a graph of the amplitude of the simulated pulse signal in example 2;
fig. 5 is a simulation pulse signal smooth amplitude spectrum of example 2.
Detailed Description
The invention is further described with reference to the following figures and examples:
as shown in fig. 1, an automatic pulse signal type discrimination method based on spectral feature extraction includes the following steps:
(1) acquiring a pulse signal sampling data sequence to be distinguished: the method comprises the steps of receiving real-time acquisition data of N sampling points from a sensor as a data sequence x (N) to be distinguished, wherein N is 0,1, … and N-1, or extracting N sampling point data containing the whole pulse signal from a memory as the data sequence x (N) to be distinguished, N is 0,1, … and N-1, wherein N is the number of sampling points containing the whole pulse signal and is an integer power of 2.
(2) Initializing parameters related to iterative smoothing and pulse signal type judgment: setting a maximum iteration number threshold I and a precision control threshold epsilon of iterative smoothing, and determining a single-frequency and frequency modulation pulse signal-to-noise ratio threshold eta by the length M of an iterative smoothing window, wherein the value of I is a positive integer larger than 2, the value of epsilon is a positive number smaller than 1, the length of the iterative smoothing window is an odd number with the length M larger than or equal to 3 and smaller than or equal to N/2-3, and the value range of eta is an arbitrary number with the length eta larger than or equal to 1.5 and smaller than or equal to 2.5.
In the step (2), in order to take account of the calculation amount and the estimation accuracy of the present invention, the preferred value of I is 10, the value of epsilon is 0.01, the value of M is 5, and the value of eta is 2.0.
(3) Calculating a pulse signal amplitude spectrum P (k) from the data sequence x (n): performing fast Fourier transform on the data sequence x (n), and calculating to obtain discrete Fourier transform X (l) and a magnitude spectrum P (k) of the data sequence, wherein the method specifically comprises the following two steps:
(3-1) calculating the discrete Fourier transform of x (n)
Figure BDA0001612517250000051
Where l is the discrete frequency index of X (l), and j represents an imaginary unit, i.e.
Figure BDA0001612517250000052
This equation can be implemented by fast fourier transform.
(3-2) calculating the amplitude spectrum of x (n) according to X (l)
Figure BDA0001612517250000053
Where k is the discrete frequency index of P (k), and | represents the modulo operation.
In the step (3), the discrete fourier transform x (l) for calculating x (n) in the step (3-1) can be realized by fast fourier transform, so that the calculation efficiency of the algorithm is improved.
(4) Performing iterative smoothing processing on the P (k) to obtain a smoothed magnitude spectrum S (k), and specifically comprising the following steps:
(4-1) initializing the iteration number i as 0, and smoothing the result S by the first iteration0(k) Is composed of
S0(k)＝P(k)，k＝0，1，2…，N/2-1
(4-2) let the iteration number i be i +1, and smooth the result S for the last iterationi-1(k) Performing smoothing to obtain current smoothing result Si(k)
Figure BDA0001612517250000061
(4-3) judging whether the maximum iterative smoothing times is reached, namely judging whether I is less than or equal to I, if so, entering the step (4-4), and otherwise, jumping to the step (4-6);
(4-4) calculating last smoothing results S, respectivelyi-1(k) And current smoothing result Si(k) Sum of squares J of residuals from original amplitude spectrum p (k)i-1And JiAre respectively as
Figure BDA0001612517250000062
(4-5) judgment of | Ji-1-Ji|≤εJiIf yes, entering the step (4-6), otherwise, returning to the step (4-2);
(4-6) let S (k) be Si(k) And k is 0,1,2 …, N/2-1, and a smoothed amplitude spectrum s (k) is obtained.
(5) Searching for a discrete frequency index k corresponding to the maximum value of S (k)MAnd the start and end discrete frequency indices k corresponding to the main lobe half-amplitudeLAnd kRThe method specifically comprises the following steps:
(5-1) searching a discrete frequency index k corresponding to the maximum value of S (k)M
Figure BDA0001612517250000063
Wherein
Figure BDA0001612517250000064
Representing that the discrete frequency index corresponding to the maximum value of S (k) is searched within the range of 1 ≦ k ≦ N/2-1;
(5-2) performing maximum value normalization processing on the S (k) to obtain a normalized smooth amplitude spectrum Z (k):
Z(k)＝S(k)/S(kM)，k＝0，1，2…，N/2-1
(5-3) searching S (k) initial discrete frequency index k corresponding to main lobe half amplitudeLThe searching process comprises the following steps:
(5-3-1) initializing initial search discrete frequency index kl＝1；
(5-3-2) judgment of kM-k l0 or Z (k)M-kl) -0.5 < 0, if yes, jump to (5-3-4), otherwise go to (5-3-3);
(5-3-3) order kl＝kl+1, and back (5-3-2);
(5-3-4) order kL＝kM-klTo obtain the initial discrete frequency corresponding to the half amplitude of the main lobeIndex kL。
(5-4) searching S (k) termination discrete frequency index k corresponding to main lobe half amplitudeRThe searching process comprises the following steps:
(5-4-1) initial termination of search for discrete frequency index kr＝1；
(5-4-2) judgment of kM+krN/2-1 or Z (k)M+kr) -0.5 < 0, if yes jump to (5-4-4), otherwise go into (5-4-3):
(5-4-3) order kr＝kr+1, and back (5-4-2);
(5-4-4) order kR＝kM-krObtaining the final discrete frequency index k corresponding to the main lobe half amplitudeR。
(6) Respectively calculating the SNR of the peak main lobe of the original amplitude spectrum and the SNR of the smooth amplitude spectrumpAnd SNRS：
Figure BDA0001612517250000071
(7) According to SNRpAnd SNRSThe method for judging the pulse signal type comprises the following steps:
(7-1) calculating the ratio SNRRR of the signal-to-noise ratio of the peak main lobe before and after smoothing of the amplitude spectrum
Figure BDA0001612517250000072
(7-2) judging whether the SNRR < eta is satisfied, if so, judging the signal to be a frequency modulation pulse signal, otherwise, judging the signal to be a single-frequency pulse signal.
In the embodiment of the invention, the simulation received pulse signal model is as follows:
Figure BDA0001612517250000073
where a is the amplitude of the signal and,
Figure BDA0001612517250000074
for the initial phase, τ is the pulse width, f1For signal start frequency, μ ═ f2-f1) τ is the frequency modulation rate, f2For signal termination frequency, when f2＝f1When mu is 0, the signal is a single-frequency pulse signal, otherwise, the signal is a frequency modulation pulse signal. w (t) is mean 0 and variance σ2White Gaussian noise, variance σ2Is determined by the signal-to-noise ratio SNR: SNR is 10log (A)2/2σ2)。
At a sampling frequency fsThe pulse signal is subjected to discrete sampling to obtain a pulse signal sampling data sequence:
Figure BDA0001612517250000075
wherein N isτ＝int(fsτ), int () represents the rounding operation.
Example 1:
the simulation signal parameters are respectively set as: signal amplitude a 2, initial phase
Figure BDA0001612517250000076
Pulse width τ of 0.512s, signal start frequency f1300Hz, signal termination frequency f2300Hz, the frequency modulation rate mu is 0Hz/s, i.e. the simulation signal is a single-frequency pulse signal, the sampling frequency fs2000Hz, 1024 points of observation data sequence, and 0dB SNR.
In the step (2), a maximum iteration time threshold I is set to be 10, a precision control threshold epsilon is 0.01, an iteration smoothing window length M is set to be 5, and a ratio threshold eta of a single frequency and a frequency modulation pulse signal-to-noise ratio is determined to be 2.
According to step (3), calculating the amplitude spectrum P (k) of the data sequence x (n), as shown in FIG. 2.
According to the step (4), performing iterative smoothing processing on p (k) to obtain a smoothed magnitude spectrum s (k), as shown in fig. 3, as can be seen by comparing fig. 2 and fig. 3: after iterative smoothing processing, the main lobe of the single-frequency pulse signal is obviously widened, and the whole frequency band spectrum is smoother.
According to the step (5), searching the discrete frequency index corresponding to the maximum value of S (k) and the initial and final discrete frequency indexes corresponding to the half-amplitude of the main lobe respectively
kM＝155，kL＝148，kR＝162。
According to the step (6), respectively calculating the ratio of the peak main lobe signal-to-noise ratio of the original amplitude spectrum and the smooth amplitude spectrum
SNRp＝8.1592，SNRS＝1.3991。
According to the step (7), calculating the ratio of the signal-to-noise ratio of the peak main lobe before and after the smoothing of the amplitude spectrum
SNRR＝8.9152/1.3991＝6.3719。
Therefore, the SNRR & gteta is known, the pulse signal is judged to be a single-frequency pulse signal, and the signal type is consistent with the set signal type.
Example 2:
the simulation signal parameters are respectively set as: signal amplitude a 1, initial phase
Figure BDA0001612517250000081
Pulse width τ of 0.512s, signal start frequency f1400Hz, signal termination frequency f2460Hz and 117.19Hz/s, i.e. the simulation signal is a frequency modulated pulse signal, the sampling frequency fs2000Hz, 1024 points of observation data sequence, and 3dB SNR.
In the step (2), a maximum iteration time threshold I is set to be 8, a precision control threshold epsilon is set to be 0.005, an iteration smoothing window length M is set to be 7, and a ratio threshold eta of a single frequency and a frequency modulation pulse signal-to-noise ratio is judged to be 1.9.
According to step (3), calculating the amplitude spectrum P (k) of the data sequence x (n), as shown in FIG. 4.
According to the step (4), performing iterative smoothing processing on p (k) to obtain a smoothed magnitude spectrum s (k), as shown in fig. 5, comparing fig. 4 and fig. 5, it can be seen that: after iterative smoothing processing, the width of the main lobe of the frequency modulation pulse signal is basically unchanged, and the whole frequency band spectrum is smoother.
According to the step (5), searching the discrete frequency index corresponding to the maximum value of S (k) and the initial and final discrete frequency indexes corresponding to the half-amplitude of the main lobe respectively
kM＝217，kL＝204，kR＝237。
According to the step (6), respectively calculating the ratio of the peak main lobe signal-to-noise ratio of the original amplitude spectrum and the smooth amplitude spectrum
SNRp＝1.2851，SNRS＝1.218。
According to the step (7), calculating the ratio of the signal-to-noise ratio of the peak main lobe before and after the smoothing of the amplitude spectrum
SNRR＝1.2851/1.218＝1.055。
Therefore, the SNRR < eta is known, and the pulse signal is judged to be a frequency modulation pulse signal and is consistent with the set signal type.

Claims (8)

1. A pulse signal type automatic distinguishing method based on spectral feature extraction is characterized by comprising the following steps:
(1) acquiring a pulse signal sampling data sequence x (N) to be distinguished, wherein N is 0,1, … and N-1, and N is the number of sampling points corresponding to the pulse width length of a detected pulse signal and is an integer power of 2;
(2) initializing parameters of iterative smoothing and pulse signal type judgment;
(3) calculating an amplitude spectrum P (k) of the pulse signal according to the data sequence x (n), wherein k is a discrete frequency index corresponding to the amplitude spectrum;
(4) performing iterative smoothing on the pulse signal amplitude spectrum P (k) to obtain a smoothed amplitude spectrum S (k);
(5) searching a discrete frequency index corresponding to the maximum value of the smooth amplitude and a starting discrete frequency index and a stopping discrete frequency index corresponding to the half amplitude of the main lobe;
(6) respectively calculating the signal-to-noise ratio of the peak main lobe of the original amplitude spectrum and the smooth amplitude spectrum;
(7) and judging the type of the pulse signal.
2. The method for automatically discriminating the pulse signal type based on the spectral feature extraction according to claim 1, wherein in the step (1), the pulse signal sampling data sequence x (n) to be discriminated is obtained by the following method: receiving real-time acquisition data of N sampling points from a sensor as a data sequence x (N) to be distinguished; or extracting N sampling point data containing the whole pulse signal from the memory as a data sequence x (N) to be distinguished.
3. The method for automatically discriminating the pulse signal type based on the spectral feature extraction according to claim 1, wherein in the step (2), the iterative smoothing and pulse signal type discrimination parameters are initialized by the following method: setting a maximum iteration time threshold I and a precision control threshold epsilon for initializing iterative smoothing, and judging a single-frequency and frequency modulation pulse signal-to-noise ratio threshold eta by an iterative smoothing window length M, wherein the value of I is a positive integer larger than 2, the value of epsilon is a positive number smaller than 1, the iterative smoothing window length is an odd number with the M larger than or equal to 3 and smaller than or equal to N/2-3, and the value range of eta is an arbitrary number with the eta larger than or equal to 1.5 and smaller than or equal to 2.5.
4. The method according to claim 1, wherein in step (3), the pulse signal amplitude spectrum p (k) is calculated from the data sequence x (n) by the following method: fast Fourier transform is carried out on the data sequence x (n), and discrete Fourier transform X (l) and pulse signal amplitude spectrum P (k) of the data sequence are obtained through calculation, and the method comprises the following steps:
(3-1) calculating the discrete Fourier transform of x (n)
Figure FDA0003000983080000011
Where l is the discrete frequency index of X (l), and j represents an imaginary unit, i.e.
Figure FDA0003000983080000012
This formula is implemented by fast fourier transform;
(3-2) calculating the amplitude spectrum of the pulse signal x (n) according to X (l)
Figure FDA0003000983080000013
Where k is the discrete frequency index of P (k), and | represents the modulo operation.
5. The method for automatically discriminating the pulse signal type based on the spectral feature extraction according to claim 1, wherein in the step (4), the following method is adopted to perform iterative smoothing processing on the pulse signal magnitude spectrum p (k) to obtain a smoothed magnitude spectrum s (k), and the method specifically comprises the following steps:
(4-1) initializing the iteration number i as 0, and smoothing the result S by the first iteration0(k) Is composed of
S0(k)＝P(k),k＝0,1,2…,N/2-1，
(4-2) let the iteration number i be i +1, and smooth the result S for the last iterationi-1(k) Smoothing to obtain current smoothing result Si(k)
Figure FDA0003000983080000021
Wherein M is the length of the iteration smoothing window;
(4-3) judging whether the maximum iterative smoothing times is reached, namely judging whether I is less than or equal to I, if so, entering the step (4-4), otherwise, jumping to the step (4-6), and I is the maximum iterative times threshold of iterative smoothing;
(4-4) calculating last smoothing results S, respectivelyi-1(k) And current smoothing result Si(k) Sum of squares J of residuals from original amplitude spectrum p (k)i-1And JiAre respectively as
Figure FDA0003000983080000022
(4-5) judgment of | Ji-1-Ji|≤εJiIf yes, go to step (4-6), if notReturning to the step (4-2), wherein epsilon is a precision control threshold;
(4-6) let S (k) be Si(k) And k is 0,1,2 …, N/2-1, and a smoothed amplitude spectrum s (k) is obtained.
6. The method according to claim 1, wherein in step (5), the discrete frequency index k corresponding to the maximum value of the smoothed amplitude spectrum s (k) is searched forMAnd the start and end discrete frequency indices k corresponding to the main lobe half-amplitudeLAnd kRThe method comprises the following steps:
(5-1) searching a discrete frequency index k corresponding to the maximum value of S (k)M
Figure FDA0003000983080000023
Wherein
Figure FDA0003000983080000024
Representing that the discrete frequency index corresponding to the maximum value of S (k) is searched within the range of 1 ≦ k ≦ N/2-1;
(5-2) performing maximum value normalization processing on the S (k) to obtain a normalized smooth amplitude spectrum Z (k):
Z(k)＝S(k)/S(kM),k＝0,1,2…,N/2-1
(5-3) searching S (k) initial discrete frequency index k corresponding to main lobe half amplitudeLThe searching process comprises the following steps:
(5-3-1) initializing initial search discrete frequency index kl＝1；
(5-3-2) judgment of kM-kl0 or Z (k)M-kl) -0.5 < 0, if yes, jump to (5-3-4), otherwise go to (5-3-3);
(5-3-3) order kl＝kl+1, and back (5-3-2);
(5-3-4) order kL＝kM-klObtaining the initial discrete frequency index corresponding to the half amplitude of the main lobekL；
(5-4) searching S (k) termination discrete frequency index k corresponding to main lobe half amplitudeRThe searching process comprises the following steps:
(5-4-1) initial termination of search for discrete frequency index kr＝1；
(5-4-2) judgment of kM+krN/2-1 or Z (k)M+kr) -0.5 < 0, if yes, jump to (5-4-4), otherwise go to (5-4-3);
(5-4-3) order kr＝kr+1, and back (5-4-2);
(5-4-4) order kR＝kM-krObtaining the final discrete frequency index k corresponding to the main lobe half amplitudeR。
7. The method for automatically discriminating pulse signal type based on spectral feature extraction according to claim 1, wherein in step (6), the peak main lobe signal-to-noise ratio SNR of the original amplitude spectrum and the smoothed amplitude spectrum is calculated by the following method respectivelypAnd SNRS：
Figure FDA0003000983080000031
Wherein S (k) smoothed amplitude spectrum, kMIs the discrete frequency index, k, corresponding to the maximum value of S (k)LAnd kRThe initial and final discrete frequency indexes corresponding to the half-amplitude of the main lobe, P (k) is the pulse signal amplitude spectrum, S (k)M) To smooth the maximum value of the amplitude, P (k)M) Is the maximum value of the amplitude of the pulse signal.
8. The method according to claim 1, wherein in the step (7), the pulse signal type is determined according to SNR by using the following methodpAnd SNRSThe pulse signal type is judged, and the steps are as follows:
(7-1) calculating the ratio SNRR of the signal-to-noise ratio of the peak main lobe before and after smoothing of the magnitude spectrum
Figure FDA0003000983080000032
Wherein the SNRpAnd SNRSPeak mainlobe signal-to-noise ratio, max (SNR), for both the original and smoothed amplitude spectraP,SNRS) Expressed as SNRpAnd SNRSMaximum value of (d), min (SNR)P,SNRS) Expressed as SNRpAnd SNRSMinimum value of (d);
(7-2) judging whether the SNRR < eta is true, if true, judging the signal to be a frequency modulation pulse signal, and if not, judging the signal to be a single-frequency pulse signal;
wherein, eta is the threshold of the ratio of the single frequency to the frequency modulation pulse signal-to-noise ratio.
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