CN115184876A - 2FSK signal parameter estimation method based on wavelet transformation and waveform shaping - Google Patents

Abstract

A2 FSK signal parameter estimation method based on wavelet transform and waveform shaping adopts frequency spectrum shaping to carry out frequency estimation, adopts Morlet wavelet transform to obtain wavelet coefficients, adopts phase space reconstruction and singular value decomposition filtering to carry out noise reduction processing on the wavelet coefficients, carries out wavelet ridge line extraction on the basis, comprehensively uses mean value filtering and median filtering to filter the wavelet ridge line, then carries out wavelet ridge line shaping according to signal frequency, and then carries out estimation on the pulse width and the number of code elements; the method can shape the frequency spectrum under the condition of 0dB or even less than 0dB, accurately extract the signal frequency value, detect the hopping time of the code element and further accurately obtain the 2FSK signal parameter estimation result.

Description

A 2FSK Signal Parameter Estimation Method Based on Wavelet Transform and Waveform Shaping

technical field

The invention relates to the technical field of signal processing, in particular to a 2FSK signal parameter estimation method based on wavelet transform and waveform shaping.

Background technique

Low Probability of Interception (LPI) is an important tactical requirement that modern radars should meet. At present, there is no specific standard to define it. Researchers usually regard the term LPI as a signal characteristic of radar, such as low transmit power, low side lobes, large bandwidth and frequency variation, which makes it difficult for enemy receivers to intercept. A detected feature. Through the design of radar waveform, the signal can obtain a large time-width-bandwidth product, which can have a good effect on improving the low-acquisition performance of the radar. Frequency coding (Frequency Shift Keying, FSK) signal is a commonly used modulation style of LPI radar, it is a kind of pulse compression signal, this kind of signal uses pseudo-random sequence, the energy is relatively scattered, and jumps between different frequencies, Therefore, it has better performance with low probability of interception.

For a long time, the accurate and rapid estimation of 2FSK signal parameters has been a technical difficulty in the field of radar reconnaissance. The parameter estimation method based on phase difference is commonly used, but the anti-noise performance of this method is poor, and it is difficult to accurately detect the transition moment of the symbol, and it is difficult to obtain the accurate symbol width and number of symbols. estimated results.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a 2FSK signal parameter estimation method based on wavelet transform and waveform shaping, and comprehensively use Morlet wavelet transform, spectrum waveform shaping, wavelet ridge waveform shaping processing technology, and realize the 2FSK signal under the condition as low as 0dB. Accurate estimation of pulse width, frequency, symbol width, number of symbols, and bandwidth.

To achieve the above object, the present invention provides the following technical solutions:

A 2FSK signal parameter estimation method based on wavelet transform and waveform shaping, comprising the following steps:

1) Input the 2FSK signal sequence containing the intrapulse modulation information;

2) Estimate the pulse width of the signal sequence in step 1), and divide the sequence into a single pulse signal according to the pulse width;

3) FFT transformation is carried out to the single pulse signal in step 2), and the frequency spectrum is shaped to obtain the frequency and bandwidth of the 2FSK signal;

4) Morlet wavelet transform is performed on the single pulse signal in step 2), and filter processing is performed to obtain a wavelet ridge;

5) Shaping the wavelet ridge to obtain the self-pulse width and the number of symbols;

6) Output the estimated 2FSK signal frequency, bandwidth, pulse width, sub-pulse width and number of symbols.

The specific method of performing pulse width estimation on the signal sequence in step 1) and dividing the sequence into a single pulse signal according to the pulse width is:

S21: Sort and modulate the intercepted signal to obtain a 2FSK signal sequence containing intrapulse modulation information, which is expressed as x(k), k=1,2,...,K, where K is the number of sampling points, and the sampling frequency is f _s ; perform amplitude normalization processing on x(k), and the processed signal sequence is expressed as

进行脉冲宽度估计，估计的脉宽表示为PW₁，PW₂，…，PW_N，其中1，2，…，N表示脉冲序号；将

截取为单个脉冲宽度的信号序列，表示为

其中1，2，…，N表示脉冲序号，每个脉冲的时长都是一个脉冲宽度。S22: yes

Pulse width estimation is performed, and the estimated pulse widths are expressed as PW ₁ , PW ₂ , . . . , PW _N , where 1, 2, .

A signal sequence truncated to a single pulse width, expressed as

Among them, 1, 2, ..., N represents the pulse number, and the duration of each pulse is a pulse width.

The single pulse signal in step 2) is all subjected to FFT transformation, and the frequency spectrum is subjected to shaping processing to estimate the frequency and bandwidth of the 2FSK signal. The specific method is:

为例进行后续的参数估计工作，其他单个脉冲参数估计与此相同，针对

进行FFT变换并求绝对值，表示为F₁，其中FFT点数表示为NFFT，取为最靠近0的2的T次幂的值，T为1个脉冲宽度的采样点数；设maxd1为F₁的最大值，I_d为最大值所对应的横坐标序号，寻找F₁从1到

个取值范围内等于maxd1的值，表示为K_e；2FSK信号的两个频率值中的一个，表示为f₁，S31: with

As an example, the subsequent parameter estimation work is performed, and other single pulse parameter estimation is the same.

Perform FFT transformation and find the absolute value, which is expressed as F ₁ , and the number of FFT points is expressed as NFFT, which is the value of the T power of 2 closest to 0, and T is the number of sampling points of 1 pulse width; let maxd1 be the value of F ₁ Maximum value, I _d is the abscissa number corresponding to the maximum value, find F ₁ from 1 to

A value equal to _maxd1 within a range of values, denoted as Ke; one of the two frequency values of the 2FSK signal, denoted as f ₁ ,

S32: Perform logarithmic calculation on F ₁ according to the following formula:

F _1d = 10log ₁₀ (F ₁ )

Find the maximum value of F _1d , expressed as maxd2=max(F _1d ), find out the sequence points that are not less than maxd2-3 in the value sequence of F _1d , and count the number of these points, expressed as L;

范围时，令F₁的纵坐标取值为零，得到新的序列表示为F₂；其中ceil(·)表示向上取整，fix(·)表示靠近0取整；针对序列F₂，按照步骤S31所示方法估计2FSK信号的另一个频率点，表示为f₂；2FSK信号的带宽可通过下式计算：S33: Perform spectrum shaping for the F ₁ sequence; traverse all the abscissas of F ₁ , when the sequence number of the abscissa is in the

In the range, let the ordinate value of F ₁ be zero, and a new sequence is obtained as F ₂ ; where ceil(·) means rounding up, and fix(·) means rounding close to 0; for the sequence F ₂ , follow the steps The method shown in S31 estimates another frequency point of the 2FSK signal, expressed as f ₂ ; the bandwidth of the 2FSK signal can be calculated by the following formula:

BW=f ₂ -f ₁

The single pulse signal in step 2) is subjected to Morlet wavelet transform, and filtering is performed to obtain the specific method of wavelet ridge:

采用快速Morlet小波变换估计码元宽度和码元个数；对

进行小波变换，表示为

cwt函数表示基于Morlet的连续小波函数，1表示小波变换的尺度，cmor3-3表示小波基函数的名称；S41: For

Use fast Morlet wavelet transform to estimate symbol width and number of symbols;

Perform wavelet transform, which is expressed as

The cwt function represents the continuous wavelet function based on Morlet, 1 represents the scale of the wavelet transform, and cmor3-3 represents the name of the wavelet basis function;

即

的采样点数，采样间隔τ＝1；重构及滤波后的信号取绝对值，表示为yy₁；针对yy₁，计算其相位，通过相位差分法计算相位差，得到小波脊线。S42: For y ₁ , perform filtering processing through phase space reconstruction and singular value decomposition, the number of reconstructed rows is M, which can be set according to the number of points of y ₁ , and the number of columns is

which is

The number of sampling points of , sampling interval τ=1; the reconstructed and filtered signal takes the absolute value, expressed as yy ₁ ; for yy ₁ , calculate its phase, calculate the phase difference by the phase difference method, and obtain the wavelet ridge.

The specific method of shaping the wavelet ridge to obtain the self-pulse width and the number of symbols by estimation is as follows:

S51: For the wavelet ridge line Mdiff1, perform mean value filtering and median filtering, and the size of the filter window can be set according to the number of wavelet ridge line points; the filtered wavelet ridge line is represented as Mdiff1, and its abscissa is the occurrence corresponding to each frequency point. Time, the ordinate is the frequency value of the 2FSK signal changing with time;

S52: According to the estimated 2FSK signal frequencies f ₁ and f ₂ , shape the filtered wavelet ridge line Mdiff1; set f _m =min(f ₁ , f ₂ ), traverse all the ordinate values of the wavelet ridge line , when its value is greater than or equal to 1.1f _m , set these values to 1, otherwise set them to zero, and get a new sequence Mdiff2; the abscissa of Mdiff2 is still the sampling time, and the ordinate is 0 or 1 that changes with the sampling time value;

整形后的序列表示为Mdiff3；S53: Perform shaping processing again for Mdiff2 to eliminate noise interference; the pulse width threshold of the discarded small pulses can be set to the width of a single pulse width

The reshaped sequence is represented as Mdiff3;

S54: For Mdiff3, the radar pulse repetition interval estimation method of blind source separation is used to estimate the sub-pulse width, and the estimated sub-pulse widths are arranged in descending order of width, expressed as y_pw(i), i=1,2,...,p , p is the number of sub-pulse widths;

的子脉冲宽度；S55: Estimate a pulse by y _pw (i), i=1,2,...,p

The sub-pulse width of ;

If p=1, the estimated sub-pulse width is τ _e =y _pw (1); if p>1, the sub-pulse width is estimated as follows:

子脉冲宽度估计值为

其中round(·)表示按照四舍五入规则取整；Let j=1:p-1,

The estimated sub-pulse width is

where round( ) means rounding according to the rounding rules;

S56: Estimate the number of symbols, _Ne =round(PW ₁ /τ _e ).

Compared with the prior art, the beneficial effects of the present invention are:

A 2FSK signal parameter estimation method based on wavelet transform and waveform shaping, which comprehensively uses Morlet wavelet transform, spectrum waveform shaping, and wavelet ridge waveform shaping processing technology to realize the 2FSK signal pulse width, frequency, code under the condition as low as 0dB. Accurate estimation of element width, number of symbols, and bandwidth; it solves the problem of the traditional parameter estimation method based on phase difference, which causes poor anti-noise performance, and it is difficult to accurately detect the transition time of symbols. It is difficult to obtain the accurate estimation result of the symbol width and the number of symbols.

Description of drawings

Fig. 1 is a flowchart of 2FSK signal parameter estimation processing;

Fig. 2 is the waveform diagram of the absolute value of the wavelet coefficient modulus value after wavelet transformation of the signal;

Fig. 3 is the waveform diagram of the absolute value of wavelet coefficient modulus value after phase space reconstruction and singular value decomposition filtering;

Fig. 4 is a wavelet ridge waveform diagram;

Fig. 5 is the wavelet ridge waveform diagram after mean filtering;

Fig. 6 is the wavelet ridge waveform diagram after median filtering;

Fig. 7 is the wavelet ridge shaping waveform after the first shaping;

Fig. 8 is the wavelet ridge shaping waveform after the extremely narrow interference pulse caused by noise is discarded.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

1-8, the present invention provides a 2FSK signal parameter estimation method based on wavelet transform and waveform shaping, including the following steps:

1) Input the 2FSK signal sequence containing the intrapulse modulation information;

2) Estimate the pulse width of the signal sequence in step 1), and divide the sequence into a single pulse signal according to the pulse width;

S21: Sort and modulate the intercepted signal to obtain a 2FSK signal sequence containing intrapulse modulation information, which is expressed as x(k), k=1,2,...,K, where K is the number of sampling points, and the sampling frequency is f _s ; perform amplitude normalization processing on x(k), and the processed signal sequence is expressed as

进行脉冲宽度估计，估计的脉宽表示为PW₁，PW₂，…，PW_N，其中1，2，…，N表示脉冲序号；将

截取为单个脉冲宽度的信号序列，表示为

其中1，2，…，N表示脉冲序号，每个脉冲的时长都是一个脉冲宽度。S22: yes

Pulse width estimation is performed, and the estimated pulse widths are expressed as PW ₁ , PW ₂ , . . . , PW _N , where 1, 2, .

A signal sequence truncated to a single pulse width, expressed as

Among them, 1, 2, ..., N represents the pulse number, and the duration of each pulse is a pulse width.

3) FFT transformation is carried out to the single pulse signal in step 2), and the frequency spectrum is shaped to obtain the frequency and bandwidth of the 2FSK signal;

为例进行后续的参数估计工作，其他单个脉冲参数估计与此相同，针对

进行FFT变换并求绝对值，表示为F₁，其中FFT点数表示为NFFT，取为最靠近0的2的T次幂的值(在Matlab中可用2^nextpow2(T)获得)，T为1个脉冲宽度的采样点数；设maxd1为F₁的最大值，I_d为最大值所对应的横坐标序号，寻找F₁从1到

个取值范围内等于maxd1的值，表示为K_e；2FSK信号的两个频率值中的一个，表示为f₁，S31: with

As an example, the subsequent parameter estimation work is performed, and other single pulse parameter estimation is the same.

Perform FFT transformation and find the absolute value, denoted as F ₁ , where the number of FFT points is denoted as NFFT, which is the value of the T power of 2 closest to 0 (available in Matlab by 2 ^nextpow2(T) ), T is 1 The number of sampling points of the pulse width; let maxd1 be the maximum value of F ₁ , I _d be the abscissa number corresponding to the maximum value, and find F ₁ from 1 to

A value equal to _maxd1 within a range of values, denoted as Ke; one of the two frequency values of the 2FSK signal, denoted as f ₁ ,

S32: Perform logarithmic calculation on F ₁ according to the following formula:

F _1d = 10log ₁₀ (F ₁ )

Find the maximum value of F _1d , expressed as maxd2=max(F _1d ), find out the sequence points that are not less than maxd2-3 in the value sequence of F _1d , and count the number of these points, expressed as L;

范围时，令F₁的纵坐标取值为零，得到新的序列表示为F₂；其中ceil(·)表示向上取整，fix(·)表示靠近0取整；针对序列F₂，按照步骤S31所示方法估计2FSK信号的另一个频率点，表示为f₂；2FSK信号的带宽可通过下式计算：S33: Perform spectrum shaping for the F ₁ sequence; traverse all the abscissas of F ₁ , when the sequence number of the abscissa is in the

In the range, let the ordinate value of F ₁ be zero, and a new sequence is obtained as F ₂ ; where ceil(·) means rounding up, and fix(·) means rounding close to 0; for the sequence F ₂ , follow the steps The method shown in S31 estimates another frequency point of the 2FSK signal, expressed as f ₂ ; the bandwidth of the 2FSK signal can be calculated by the following formula:

BW=f ₂ -f ₁

4) Morlet wavelet transform is performed on the single pulse signal in step 2), and filter processing is performed to obtain a wavelet ridge;

采用快速Morlet小波变换估计码元宽度和码元个数；对

进行小波变换，表示为

cwt函数表示基于Morlet的连续小波函数，1表示小波变换的尺度，cmor3-3表示小波基函数的名称，除了cmor3-3之外，也可以采用其他小波基函数。S41: For

Use fast Morlet wavelet transform to estimate symbol width and number of symbols;

Perform wavelet transform, which is expressed as

The cwt function represents the continuous wavelet function based on Morlet, 1 represents the scale of the wavelet transform, and cmor3-3 represents the name of the wavelet basis function. In addition to cmor3-3, other wavelet basis functions can also be used.

即

的采样点数，采样间隔τ＝1；重构及滤波后的信号取绝对值，表示为yy₁；针对yy₁，计算其相位，通过相位差分法计算相位差，得到小波脊线。S42: For y ₁ , perform filtering processing through phase space reconstruction and singular value decomposition, the number of reconstructed rows is M, which can be set according to the number of points of y ₁ , and the number of columns is

which is

The number of sampling points of , sampling interval τ=1; the reconstructed and filtered signal takes the absolute value, expressed as yy ₁ ; for yy ₁ , calculate its phase, calculate the phase difference by the phase difference method, and obtain the wavelet ridge.

5) Shaping the wavelet ridge to obtain the self-pulse width and the number of symbols;

S51: Perform mean filtering and median filtering for the wavelet ridge line Mdiff1. The size of the filter window can be set according to the number of wavelet ridge line points. Generally, the filter window can be set to 20; the filtered wavelet ridge line is represented as Mdiff1, and its abscissa is The appearance time corresponding to each frequency point, the ordinate is the frequency value of the 2FSK signal changing with time;

S52: According to the estimated 2FSK signal frequencies f ₁ and f ₂ , shape the filtered wavelet ridge line Mdiff1; set f _m =min(f ₁ , f ₂ ), traverse all the ordinate values of the wavelet ridge line , when its value is greater than or equal to 1.1f _m , set these values to 1, otherwise set them to zero, and get a new sequence Mdiff2; the abscissa of Mdiff2 is still the sampling time, and the ordinate is 0 or 1 that changes with the sampling time value;

因为2FSK信号所用的Barker码编码长度至多为13，整形后的序列表示为Mdiff3；S53: Perform shaping processing again for Mdiff2 to eliminate noise interference; the pulse width threshold of the discarded small pulses can be set to the width of a single pulse width

Because the coding length of the Barker code used by the 2FSK signal is at most 13, the reshaped sequence is represented as Mdiff3;

S54: For Mdiff3, the radar pulse repetition interval estimation method of blind source separation is used to estimate the sub-pulse width, and the estimated sub-pulse widths are arranged in descending order of width, expressed as y_pw(i), i=1,2,...,p , p is the number of sub-pulse widths;

的子脉冲宽度；S55: Estimate a pulse by y _pw (i), i=1,2,...,p

The sub-pulse width of ;

If p=1, the estimated sub-pulse width is τ _e =y _pw (1); if p>1, the sub-pulse width is estimated as follows:

子脉冲宽度估计值为

其中round(·)表示按照四舍五入规则取整；Let j=1:p-1,

The estimated sub-pulse width is

where round( ) means rounding according to the rounding rules;

S56: Estimate the number of symbols, _Ne =round(PW ₁ /τ _e ).

6) Output the estimated 2FSK signal frequency, bandwidth, pulse width, sub-pulse width and number of symbols.

The present invention will be further described below in conjunction with the experimental test chart.

1. Experimental condition settings:

The experimental verification of the present invention is carried out under computer simulation conditions, and the simulation software adopts MATLABR2010a. In order to fully verify the effectiveness of the present invention, three groups of experimental tests are carried out by applying the technical solution of the present invention.

Example 1:

The sampling frequency is f _s =150MHz, the frequencies of the two frequency points of 2FSK are 14MHz and 19MHz respectively, the signal bandwidth is 5MHz, the encoding method is thirteen-bit Barker code, the symbol width is 1.2μs, and the pulse width is 15.6μs. Under the conditions of different signal-to-noise ratios, the estimated signal parameters are shown in Table 1 through the patent scheme.

Table 1 Parameter estimation results of 2FSK signal in the case of thirteen-digit Barker codes

In the case of -2dB, some key waveforms corresponding to the processing in steps 1) to 6) are shown in Fig. 2-8, which can be used to assist the understanding of wavelet ridge shaping processing.

Example 2:

The sampling frequency is f _s =100 MHz, the frequencies of the two frequency points of 2FSK are 11 MHz and 15 MHz respectively, the signal bandwidth is 4 MHz, the encoding method is seven-bit Barker code, the symbol width is 0.8 μs, and the pulse width is 5.6 μs. Under the conditions of different signal-to-noise ratios, the estimated signal parameters are shown in Table 2 through the patented solution.

Table 2 Parameter estimation results of 2FSK signal in the case of seven-digit Barker code

Example 3:

The sampling frequency is f _s =200MHz, the frequencies of the two frequency points of 2FSK are 18MHz and 23MHz respectively, the signal bandwidth is 5MHz, the encoding method is five-bit Barker code, the symbol width is 1.5μs, and the pulse width is 7.5μs. Under the conditions of different signal-to-noise ratios, the estimated signal parameters are shown in Table 3 through the patent scheme.

Table 3 Estimation results of 2FSK signal parameters in the case of five-digit Barker codes

The above experimental results show that the present invention can accurately estimate the pulse width, sub-pulse width, number of symbols, frequency and bandwidth parameters of the 2FSK signal under conditions as low as 0dB or even -2dB.

Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, it is still possible to modify the technical solutions described in the foregoing embodiments, or to perform equivalent replacements for some of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Note:

进行脉冲宽度估计，估计方法参考申请日为2021.04.28，申请号：202110466533.9的发明专利“一种基于盲源分离的雷达脉冲重复间隔估计方法。1. In step S22, correct

Pulse width estimation is performed, and the estimation method refers to the invention patent with the application date of 2021.04.28 and the application number: 202110466533.9 "A radar pulse repetition interval estimation method based on blind source separation.

2. In step S42, the phase difference is calculated by the phase difference method. Reference [Yao Wenyang. Intrapulse Analysis and Recognition of Radar Signals [D]. Harbin: Harbin Engineering University Master Thesis, 2012.].

3. In step S54, "a radar pulse repetition interval estimation method by blind source separation" is used. For details, please refer to the application date of 2021.04.28, application number: 202110466533.9, and the name of the invention is "a radar pulse based on blind source separation". Methods for Estimating Repeat Intervals".

Claims (5)

1. A2 FSK signal parameter estimation method based on wavelet transformation and waveform shaping is characterized by comprising the following steps:

1) Inputting a 2FSK signal sequence containing intra-pulse modulation information;

2) Performing pulse width estimation on the signal sequence in the step 1), and dividing the sequence into single pulse signals according to the pulse width;

3) Performing FFT conversion on the single pulse signals in the step 2), shaping the frequency spectrum, and estimating the frequency and the bandwidth of the 2FSK signal;

4) Performing Morlet wavelet transform on the single pulse signal in the step 2), and performing filtering processing to obtain a wavelet ridge line;

5) Shaping the wavelet ridge line, and estimating to obtain the pulse width and the number of code elements;

6) And outputting the estimated frequency, bandwidth, pulse width, sub-pulse width and code element number of the 2FSK signal.

2. The method according to claim 1, wherein the method comprises the following steps: the specific method for estimating the pulse width of the signal sequence in step 1) and dividing the sequence into single pulse signals according to the pulse width is as follows:

s21: sorting and modulating and identifying the intercepted signals to obtain a 2FSK signal sequence containing intra-pulse modulation information, wherein the sequence is represented by x (K), K =1,2, \ 8230, K and K are sampling point numbers, and the sampling frequency is f _s (ii) a The amplitude normalization processing is carried out on the x (k), and the processed signal sequence is expressed as

S22: to pair

Pulse width estimation is performed, the estimated pulse width being denoted as PW ₁ ，PW ₂ ，…，PW _N Wherein, 1,2, \8230, N represents pulse sequence number; will be provided with

A sequence of signals truncated to a single pulse width, denoted as

Where 1,2, \8230, N denotes the pulse number, and the duration of each pulse is one pulse width.

3. The method according to claim 1, wherein the 2FSK signal parameter estimation method based on wavelet transform and waveform shaping comprises: the specific method for performing FFT on the single pulse signals in step 2), shaping the frequency spectrum, and estimating the frequency and bandwidth of the 2FSK signal is as follows:

s31: to be provided with

For example, the subsequent parameter estimation work is carried out, and other single pulse parameter estimation is the same as that for

FFT and absolute value, denoted F ₁ The FFT point number is expressed as NFFT, and is taken as the value of the power of T of 2 closest to 0, wherein T is the sampling point number of 1 pulse width; let maxd1 be F ₁ Maximum value of (1), I _d Finding F for the horizontal coordinate serial number corresponding to the maximum value ₁ From 1 to

A value equal to maxd1 in each value range, denoted as K _e (ii) a 2 one of the two frequency values of the FSK signal, denoted f ₁ ，

S32: to F ₁ Logarithmic calculation was performed as follows:

F _1d ＝10log ₁₀ (F ₁ )

calculating F _1d Is expressed as maxd2= max (F) _1d ) To find out F _1d Sequence points which are not less than maxd2-3 in the value sequence are counted, and the number of the points is represented as L;

s33: for F ₁ Sequence, performing spectral shaping; traverse F ₁ All abscissa, when the serial number of the abscissa is at

In the range, let F ₁ The ordinate of (a) is zero, and a new sequence denoted as F is obtained ₂ (ii) a Wherein ceil (-) represents rounding up and fix (-) represents rounding near 0; for sequence F ₂ Another frequency bin, denoted f, of the 2FSK signal is estimated according to the method shown in step S31 ₂ (ii) a The bandwidth of the 2FSK signal can be calculated by:

BW＝f ₂ -f ₁ 。

4. the method according to claim 1, wherein the 2FSK signal parameter estimation method based on wavelet transform and waveform shaping comprises: the specific method for performing Morlet wavelet transform on the single pulse signal in the step 2) and performing filtering processing to obtain the wavelet ridge line is as follows:

s41: to is directed at

Estimating the code element width and the number of code elements by adopting fast Morlet wavelet transformation; to pair

Performing wavelet transform, expressed as

The cwt function represents a continuous wavelet function based on Morlet, 1 represents the scale of wavelet transform, cmor3-3 represents the name of wavelet basis function;

s42: for y ₁ Filtering by phase space reconstruction and singular value decomposition, the number of reconstructed lines is M, and the filter can be obtained according to y ₁ Is set to the number of columns

Namely, it is

The number of sampling points of (1), the sampling interval τ =1; the reconstructed and filtered signal takes the absolute value, denoted yy ₁ (ii) a For yy ₁ And calculating the phase of the wavelet ridge line, and calculating the phase difference by a phase difference method to obtain the wavelet ridge line.

5. The method according to claim 1, wherein the 2FSK signal parameter estimation method based on wavelet transform and waveform shaping comprises: the specific method for shaping the wavelet ridge line and estimating the pulse width and the number of code elements is as follows:

s51: performing mean filtering and median filtering on the wavelet ridge line Mdiff1, wherein the size of a filtering window can be set according to the number of the wavelet ridge line points; the filtered wavelet ridge line is represented as Mdiff1, the abscissa of the wavelet ridge line is the occurrence time corresponding to each frequency point, and the ordinate of the wavelet ridge line is the frequency value of the 2FSK signal changing along with the time;

s52: according to the estimated 2FSK signal frequency f ₁ And f ₂ Shaping the filtered wavelet ridge line Mdiff 1; let f _m ＝min(f ₁ ,f ₂ ) Traversing all the ordinate values of the wavelet ridge line, and when the value is more than or equal to 1.1f _m Setting the values to 1, otherwise, setting the values to zero to obtain a new sequence Mdiff2; the abscissa of Mdiff2 is still the sampling time, and the ordinate is a value of 0 or 1 which changes along with the sampling time;

s53: reshaping is carried out again for Mdiff2, and noise interference is eliminated; the pulse width threshold of the discarded small pulses may be set to a single pulse width

The shaped sequence is denoted Mdiff3;

s54: aiming at Mdiff3, the estimation of the sub-pulse width is realized by a radar pulse repetition interval estimation method of blind source separation, the estimated sub-pulse widths are arranged according to the width size in a descending order and are represented as y _ pw (i), i =1,2, \ 8230, and p are the number of the sub-pulse widths;

s55: by y _pw (i) I =1,2, \8230, p estimates result in one pulse

The sub-pulse width of (2);

if p =1, the sub-pulse width estimation value is τ _e ＝y _pw (1) (ii) a If p is>1, the sub-pulse width is estimated according to the following method:

let j =1,

the estimated value of the sub-pulse width is

Wherein round (. Cndot.) represents a formula according toRounding off according to a rule to get the whole;

s56: estimating to obtain the number of code elements, N _e ＝round(PW ₁ /τ _e )。

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