CN102685053A - Communication signal modulating and identifying method based on generalized S transformation - Google Patents

Abstract

The invention provides a communication signal modulating and identifying method based on generalized S transformation. The communication signal modulating and identifying method comprises the following steps of: (1) carrying out analytic signal configuration on an input modulating signal according to the characteristic of an input signal to noise ratio modulating signal to obtain an analytic signal to be used as a signal for carrying out generalized S transformation; (2) configuring a Gaussian window function needed by the generalized S transformation; (3) determining a Gaussian window width factor sigma according to an expression formula of the generalized S transformation; carrying out the generalized S transformation on an input modulation signal by combining short-time Fourier transformation and the Gaussian window function to obtain time-frequency energy distribution images of the modulation signal; and (4) comparing energy images of all modulation signals according to the time-frequency energy distribution images obtained by the step (3) to find out a difference between the time-frequency energy distribution images of all modulation signals which are subjected to the generalized S transformation; selecting a frequency strip quantity with concentrated energy, a maximum value ratio of high-frequency component energy to low-frequency component energy, energy time domain distribution, high-frequency and low-frequency component extreme value time domain distribution and high-frequency component extreme value distribution so as to identify all modulation signals. According to the invention, a high identification rate is achieved under the condition of a low signal to noise ratio, and the method is suitable for modulating and identifying communication signals under a heavy clutter environment.

Description

A kind of Modulation Recognition of Communication Signal method based on generalized S-transform

Technical field

The invention belongs to the Modulation Recognition of Communication Signal field, relate to a kind of Modulation Recognition of Communication Signal method based on generalized S-transform.

Technical background

The basic task of Modulation Recognition of Communication Signal is to determine the modulation system and other signal parameters that receives signal at many signal environments under the condition of noise jamming with having, thereby for further analyzing and processing signals provides foundation.The signal of communication recognition technology is the modulation system of identification communication signal automatically; It is to constitute based on the general purpose receiver of software radio and important technology basis that can only modulator-demodulator, aspect the interconnected and software radio crucial application is arranged also in many systems communications.

Utilize signal time-the frequency Joint Distribution portrays the Energy distribution characteristic of signal, the information of more reflected signal energy in time and frequency domain Joint Distribution can be provided.Time-Frequency Analysis Method commonly used has Short Time Fourier Transform, Wigner-Ville distribution and wavelet transformation etc., and these methods all exist the deficiency of self, and Short Time Fourier Transform has only fixed resolution, and multiple resolution can't be provided; There is not phase factor in wavelet transformation, and the phase information of signal can't be provided; And the Wigner-Ville distribution is non-linear time-frequency representation, has the interference of the cross term of Cohen class distribution.During the S conversion of propositions such as R.G.Stockwell in recent years people study an important tool of the time-frequency distributions of non-stationary signal.But the basic small echo form in the S conversion is fixed, and has limited its application and flexibility in time frequency analysis.Subsequently in practical applications to S conversion promote, generalized S-transform has been proposed.

In recent years; Method based on the non-stationary signal analysis of generalized S-transform has been applied to seismic data processing, medical signals is handled and field such as power technology; And still be in the starting stage in the Modulation Recognition of Communication Signal field; The ripe without comparison method of utilizing generalized S-transform to carry out Modulation Identification occurs; Generalized S-transform has combined the Fourier in short-term of present main flow and the characteristics of wavelet transformation, and has remedied some defectives of these two kinds of methods, therefore under complex electromagnetic environment, has very big potentiality aspect the Modulation Recognition of Communication Signal.

But do not see the bibliographical information that has based on the Modulation Recognition of Communication Signal method of generalized S-transform at present both at home and abroad.

Summary of the invention

The technical problem that the present invention will solve is: overcome the deficiency of prior art, a kind of Modulation Recognition of Communication Signal method based on generalized S-transform is provided, utilize the robustness of S conversion to improve the reliability of signal time frequency analysis; And in S conversion window function, introduce regulatory factor, make its ability that possesses adaptively changing window function in time-frequency domain, and obtain the similar characteristic of differentiating more, thereby draw corresponding generalized S-transform; Simultaneously; Utilize the time-frequency energy profile of the various modulation systems of generalized S-transform acquisition; Choose suitable parameters and characteristic (like frequency band bar number, the ratio of low-and high-frequency energy maximum, time domain continuous parameter; Low-and high-frequency maximum time domain distributes, high frequency maximum distribution etc.) modulation system of signal is discerned.

The technical solution adopted for the present invention to solve the technical problems is: a kind of Modulation Recognition of Communication Signal method based on generalized S-transform comprises following step:

(1) according to the characteristic of the signal to noise ratio modulation signal of importing, the modulation signal of importing is carried out the analytic signal structure, obtain analytic signal, as the signal that carries out generalized S-transform,

(2) the needed Gaussian window function of structure generalized S-transform;

(3) confirm Gaussian window width factor σ according to the expression formula of generalized S-transform, the modulation signal of importing is carried out generalized S-transform, obtain the time-frequency energy profile of modulation signal in conjunction with Short Time Fourier Transform and Gaussian window function;

The expression formula of said generalized S-transform is following:

$S_{\mathrm{GST}}=(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{+\&infin;}u\left(t\right)\frac{\mathrm{\&sigma;}\left|f\right|}{\sqrt{2\mathrm{\&pi;}}}{e}^{-\frac{{\mathrm{\&sigma;}}^2{(\mathrm{\&tau;}-t)}^2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{2}}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}t}\mathrm{dt}$

$u\left(t\right)={\&Integral;}_{-\&infin;}^{+\&infin;}\left\{{\&Integral;}_{-\&infin;}^{+\&infin;}{S}_{\mathrm{GST}}(\mathrm{\&tau;},f)d\mathrm{\&tau;}\right\}{e}^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{df}$

Wherein, S _GST(τ f) is generalized S-transform signal afterwards; U (t) is a quadractically integrable function; σ is the Gaussian window width factor, and σ＞0, and when 1＞σ＞0, Gaussian window function width and amplitude slow down with frequency change speed, when σ＞1, and, Gaussian window function width and amplitude then speed up with frequency change; T is the time; F is a frequency;

(4) the time-frequency energy profile that obtains according to step (3); Contrast the energy diagram picture of various modulation signals; Find out the difference between the time-frequency energy diagram picture behind the various modulation signal generalized S-transforms, choose that the frequency band bar number of concentration of energy, ratio, energy time domain that low-and high-frequency is divided the energy maximum distribute, low-and high-frequency component maximum time domain distributes and high fdrequency component maximum distributes.Various modulation signals are discerned; Said various modulation signal comprises FSK, BPSK, ASK, FM, AM, QPSK, QAM;

The said process that various modulation signals are discerned is: if concentration of energy on 4 frequency bands, can judge then that modulation signal is a fsk signal; If concentration of energy is on 1 frequency band, then modulation signal is ASK and BPSK, otherwise is FM, AM, SSB, QPSK and QAM; When concentration of energy is on 1 frequency band, if on this frequency band energy on time domain continuously, if promptly the length that distributes in time domain of energy can be thought that Energy distribution on whole time-domain, is bpsk signal, otherwise be the ASK signal greater than 9/10 of time domain total length; When concentration of energy is on 2 frequency bands; Confirm that high frequency obtains the moment of maximum, if the energy value that high frequency is obtained peaked moment low frequency less than 0.5 times of global maximum, at this moment because the maximum of low-and high-frequency on time domain, interlock; Be the FM signal, otherwise be other signals; When concentration of energy on 2 frequency bands; And when being not the FM signal; Confirm the peaked size of high fdrequency component and low frequency component energy, if high fdrequency component maximum and low frequency component maximum are basic identical, if promptly the maximum of low frequency component energy is greater than high fdrequency component energy peaked 4/5; Then be the AM signal, otherwise be other signals; Before on the basis judged, confirm all maximum of high fdrequency component, confirm maximum and minimum value in the maximum, if maximum is no more than 1.5 times of minimum value in the maximum, then is the QPSK signal, otherwise is the QAM signal.

The structure of the analytic signal in the described step (1) has utilized Hilbert transform, and expression formula is:

$\hat{f}\left(t\right)=\frac{1}{\mathrm{\&pi;}}{\&Integral;}_{-\&infin;}^{+\&infin;}\frac{f\left(\mathrm{\&tau;}\right)}{t-\mathrm{\&tau;}}\mathrm{dt}$

F (t) is a real signal;

constructs analytical function Z (t) expression formula that obtains for the Hilbert transform of real signal:

$Z\left(t\right)=f\left(t\right)+j\hat{f}\left(t\right)$

Wherein Z (t) is an analytic signal; F (t) is a real signal;

also can be write as for the Hilbert transform of real signal:

Z(t)＝A(t)e ^-jφ(t)

Wherein, A (t) is called the envelope of Hilbert transform; φ (t) is called transient response signals.

The expression formula of the Gaussian window function in the described step (2) is following:

a＞0,C∈R,w ₀＝const

Wherein, the amplitude factor of C for arbitrarily choosing; T is the time; w ₀Be phase factor; A is a window function decline exponential factor; R is a real number.

Gaussian window is a kind of window index; Gaussian window spectrum does not have negative secondary lobe, and this is on the occasion of being consistent with generalized S-transform time-frequency Energy distribution, and its first side lobe attenuation reaches-55dB; The main lobe broad of Gaussian window spectrum; So frequency resolution is low, the Gaussian window function often is used to block some nonperiodic signals, therefore is fit to the intercepting of signal of communication.

Principle of the present invention is: the S conversion is a kind of Time-Frequency Analysis Method that adopts the product of monochromatic wave and Gaussian function as basic small echo; And exist close contact between the result of S conversion and the Fourier spectrum; Thereby the S conversion has the characteristics of wavelet transformation and Short Time Fourier Transform; Simultaneously in conversion Gaussian window function, introduce regulatory factor, make its ability that possesses adaptively changing window function characteristic in time-frequency domain, and obtain to be similar to the characteristics of differentiating more; The application and the flexibility of S conversion have been improved; Add the robustness that the S conversion possesses itself, can obtain the clear and evident characteristic time-frequency energy profile of various modulation systems, thereby carry out the identification of modulation system.

The present invention is with the advantage of prior art: compare with Short Time Fourier Transform, continuous wavelet variation and S conversion, generalized S-transform of the present invention has adopted the variable Gaussian function with frequency dependence, has added Gaussian window width factor σ, and σ＞0.When 1＞σ＞0, Gaussian window function width and amplitude slow down with frequency change speed; When σ＞1, its width and amplitude then speed up with frequency change, have promptly overcome the fixing deficiency of Short Time Fourier Transform resolution, have also overcome the application of S conversion in time frequency analysis and the deficiency of flexibility; Compare with wavelet transformation, contain phase factor in the generalized S-transform, this is the not available characteristic of wavelet transformation; Compare with most of Modulation Recognition of Communication Signal method; Modulation Recognition of Communication Signal method based on generalized S-transform has very strong robustness; The relative consistency that can keep the time-frequency energy profile; Thereby guaranteed to utilize the time-frequency energy profile to carry out the feasibility and the reliability of Modulation Identification method, and it is littler, more succinct to utilize image information to carry out the parameter recognition amount of calculation.

Description of drawings

Fig. 1 is the Modulation Identification method flow diagram based on generalized S-transform of the present invention;

Fig. 2 is a generalized S-transform noiseproof feature sketch map;

Fig. 3 is the Modulation Identification flow chart after the generalized S-transform.

Embodiment

Introduce the present invention in detail below in conjunction with accompanying drawing and embodiment.

As shown in Figure 1, the practical implementation step of the Modulation Mode Recognition method based on generalized S-transform of the present invention is following:

(1) because generalized S-transform is the conversion that analytic signal is carried out, so when the signal of input is real signal, need utilize Hilbert transform that input signal is carried out the analytic signal structure.

If real-valued function is f (t), wherein t ∈ (x-x), then the Hilbert transform of f (t) is:

$\hat{f}\left(t\right)={\&Integral;}_{-\&infin;}^{+\&infin;}\frac{f\left(\mathrm{\&tau;}\right)}{\mathrm{\&pi;}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\left(1\right)$

Wherein, f (t) is a real signal;

often is designated as for the Hilbert transform of real signal:

$\hat{f}\left(t\right)=H\left[f\left(t\right)\right]---\left(2\right)$

Next introduce analytical function Z (t):

$Z\left(t\right)=f\left(t\right)+j\hat{f}\left(t\right)---\left(3\right)$

Wherein Z (t) is an analytic signal; F (t) is a real signal;

also can be write as for the Hilbert transform of real signal:

Z(t)＝A(t)e ^-jφ(t) （4）

Wherein, A (t) is called the envelope of Hilbert transform; φ (t) is called transient response signals.

(2) but shape as shown in the formula the infinite dead slow speed that has multiple twiddle factor smooth window function falls:

a＞0,C∈R,w ₀＝const （5）

Be called Gauss Gaussian window function.

Wherein, the amplitude factor of C for arbitrarily choosing; T is the time; w ₀Be phase factor; A is a window function decline exponential factor; R is a real number.

Gaussian window is a kind of window index; Gaussian window spectrum does not have negative secondary lobe, and this is on the occasion of being consistent with generalized S-transform time-frequency Energy distribution, and its first side lobe attenuation reaches-55dB; The main lobe broad of Gaussian window spectrum; So frequency resolution is low, the Gaussian window function often is used to block some nonperiodic signals, like exponential damping signal etc.Because the uncertainty of signal of communication, we choose the Gaussian window function and carry out the intercepting of signal.

(3) the S conversion is a kind of Time-Frequency Analysis Method that adopts the product of monochromatic wave and Gaussian function as basic small echo that is proposed by people such as Stockwell, and its definition is:

$S_{\mathrm{ST}}(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{+\&infin;}u\left(t\right)\frac{\left|f\right|}{\sqrt{2\mathrm{\&pi;}}}{e}^{-\frac{{(\mathrm{\&tau;}-t)}^2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{2}}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{dt}---\left(6\right)$

In the formula, u (t) ∈ L ²(R), be quadractically integrable function; Basic small echo:

$w(t,f)=\frac{\left|f\right|}{\sqrt{2\mathrm{\&pi;}}}{e}^{-\frac{t^2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{2}}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}---\left(7\right)$

And to S _ST(τ f) carries out the Fourier spectrum F that integration just can obtain input signal u (t) along time shaft _u(f), promptly

${\&Integral;}_{-\&infin;}^{+\&infin;}{S}_{\mathrm{ST}}(\mathrm{\&tau;},f)\mathrm{d\&tau;}={\&Integral;}_{-\&infin;}^{+\&infin;}u\left(t\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{dt}=F_u\left(t\right)---\left(8\right)$

Exist close getting in touch between clear S transformation results of this property list and the Fourier spectrum, thereby make it have clear physical meaning more.

But the basic small echo form in the S conversion is fixed, and has limited its application and flexibility in time frequency analysis.For this reason, in S conversion Gaussian window function, introduce regulatory factor, make its ability that possesses adaptively changing window function characteristic in time-frequency domain, and obtain the similar characteristic of differentiating more, thereby can draw corresponding generalized S-transform [9].So generalized S-transform and inverse transformation thereof can be expressed as:

$S_{\mathrm{GST}}(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{+\&infin;}u\left(t\right)\frac{\mathrm{\&sigma;}\left|f\right|}{\sqrt{2\mathrm{\&pi;}}}{e}^{-\frac{{\mathrm{\&sigma;}}^2{(\mathrm{\&tau;}-t)}^2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{2}}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{dt}---\left(9\right)$

$u\left(t\right)={\&Integral;}_{-\&infin;}^{+\&infin;}\left\{{\&Integral;}_{-\&infin;}^{+\&infin;}{S}_{\mathrm{GST}}(\mathrm{\&tau;},f)\mathrm{d\&tau;}\right\}{e}^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001638811600021.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{df}---\left(10\right)$

In the formula, S _GST(τ f) is generalized S-transform signal afterwards; U (t) is a quadractically integrable function; σ is the Gaussian window width factor, and σ＞0, and when 1＞σ＞0, Gaussian window function width and amplitude slow down with frequency change speed, and when σ＞1, its width and amplitude then speed up with frequency change; T is the time; F be frequency according to signal characteristic, generalized S-transform adopts window when narrow at high band, then can obtain higher time sense; Adopt window when wide in low-frequency range, then obtain higher frequency resolution.On this basis, through choosing suitable regulatory factor σ, generalized S-transform can influence the rate of change of Gaussian window width and amplitude, thereby controls the frequency dependence of its variation tendency neatly.In practical engineering application; The selection of generalized S-transform regulatory factor σ need require to carry out comprehensively to confirm according to the time-frequency characteristics of measured signal and concrete time-frequency resolving power " the general value of σ is 0 ~ 50; in practical application; need signal be carried out generalized S-transform, choose make interested frequency domain part figure clearly σ as the used window width factor of generalized S-transform.The σ that is applicable to general signal of communication is 30 "

In order to check the validity of generalized S-transform in sophisticated signal is analyzed, suppose input signal U (t)=U ₁(t)+U ₂(t), t ∈ [0,2] U wherein ₁(t), U ₂(t), respectively like a among Fig. 2, b shows that wherein a representes u ₂(t)=and sin [2 π * (130-20t) * t], t ∈ [0.2]; B representes u ₂(t)=and sin [2 π * (50-20t) * t], t ∈ [0.2].

Fig. 2 c ~ f has represented under the noiseless ideal conditions; The time-frequency distributions of the input signal U (t) that application formula (9) is obtained; Therefrom can tell with Fig. 2 a; Corresponding each signal component of b, and it has higher frequency resolution in low-frequency range, then has higher temporal resolution at high band.Fig. 2 c ~ f has provided in U (t) the generalized S-transform result who adds behind the zero-mean white noise corresponding to different signal to noise ratios; Can know through comparative analysis; It can keep the basic distribution situation of primary signal at time-frequency domain; Therefore, generalized S-transform has robustness preferably, thereby has further strengthened its reliability in the signal time frequency analysis is used.

(4) owing to the time-frequency energy profile based on generalized S-transform has very strong robustness, so we can utilize different modulated signals to carry out Modulation Identification through the difference of time-frequency energy profile after the generalized S-transform.

The following 7 kinds of typical modulation signal generalized S-transform time-frequency energy profiles of ideal conditions have apparent in view difference; The concentration of energy of FSK (frequency shift keying) signal is on four frequency bands; And on the frequency band in the concentration of energy of BPSK (biphase phase shift keying) signal and ASK (amplitude shift keying) signal ground; Remaining modulation signal FM (frequency modulation(FM)) signal, AM (amplitude modulation(PAM)) signal, QPSK (QPSK) signal, QAM (quadrature amplitude modulation) signal energy concentrate on two frequency bands; The energy distributions situation is also different on each frequency band in addition, has at time domain continuous (for example SSB signal, bpsk signal), discontinuous in addition (for example ASK signal etc.); And these signals Energy distribution between different frequency bands is also different; AM signal low-and high-frequency energy maximum is identical, and QPSK is different with QAM low-and high-frequency energy maximum, and the maximum of QAM high-frequency energy on time domain has tangible difference; And the maximum of FM signal low-and high-frequency is interlocked on time domain, can carry out the Modulation Identification of signal according to these gaps.

Concrete Modulation Identification flow process is as shown in Figure 3,

301: if concentration of energy on 4 frequency bands, can judge then that modulation signal is a fsk signal;

302: if concentration of energy on 1 frequency band, then modulation signal is ASK and BPSK, otherwise is FM, AM, SSB, QPSK and QAM;

303: when concentration of energy is on 1 frequency band; If on this frequency band energy on time domain continuously, if promptly the length that distributes in time domain of energy can think that greater than 9/10 of time domain total length Energy distribution is on whole time-domain; Be bpsk signal, otherwise be the ASK signal;

304: when concentration of energy is on 2 frequency bands; Confirm that high frequency obtains the moment of maximum; If the energy value that high frequency is obtained peaked moment low frequency is less than 0.5 times of global maximum; At this moment can on time domain, interlock because of the maximum of low-and high-frequency, be the FM signal, otherwise be other signals;

305: when concentration of energy on 2 frequency bands; And when being not the FM signal; Confirm the peaked size of high fdrequency component and low frequency component energy, if high fdrequency component maximum and low frequency component maximum are basic identical, if promptly the maximum of low frequency component energy is greater than high fdrequency component energy peaked 4/5; Then be the AM signal, otherwise be other signals;

306: before on the basis judged, confirm all maximum of high fdrequency component, confirm maximum and minimum value in the maximum, if maximum is no more than 1.5 times of minimum value in the maximum, then is the QPSK signal, otherwise is the QAM signal.

Wherein: m: the frequency range number of concentration of energy; Length: the time width that has concentration of energy to distribute; W: the width of whole time domain; A: can get simultaneously the value of low frequency energy with the high-frequency energy maximum; P: the global maximum of energy; A1: the energy maximum of low-frequency band; A2: the energy maximum of high frequency band; A3: the maximum in the high band Energy distribution in several maximum; A4: the minimum value of several maximum in the high band Energy distribution.

According to such criterion of identification, the discrimination that in signal to noise ratio is various modulation systems under the situation of 5dB is all more than 90%.Recognition effect is more satisfactory, therefore can be used as a kind of method of satellite communication Modulation Identification.

The content of not doing in the specification of the present invention to describe in detail belongs to this area professional and technical personnel's known prior art.

Although disclose most preferred embodiment of the present invention and accompanying drawing for the purpose of illustration, it will be appreciated by those skilled in the art that: in the spirit and scope that do not break away from the present invention and appended claim, various replacements, variation and modification all are possible.Therefore, the technical scheme that the present invention protected should not be limited to most preferred embodiment and the disclosed content of accompanying drawing.

Claims (5)

1. Modulation Recognition of Communication Signal method based on generalized S-transform is characterized in that: comprise following step:

(1) according to the characteristic of the signal to noise ratio modulation signal of importing, the modulation signal of importing is carried out the analytic signal structure, obtain analytic signal, as the signal that carries out generalized S-transform;

(2) the needed Gaussian window function of structure generalized S-transform;

(3) confirm Gaussian window width factor σ according to the expression formula of generalized S-transform, the modulation signal of importing is carried out generalized S-transform, obtain the time-frequency energy profile of modulation signal in conjunction with Short Time Fourier Transform and Gaussian window function;

The expression formula of said generalized S-transform is following:

$S_{\mathrm{GST}}(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{+\&infin;}u\left(t\right)\frac{\mathrm{\&sigma;}\left|f\right|}{\sqrt{2\mathrm{\&pi;}}}{e}^{-\frac{{\mathrm{\&sigma;}}^2{(\mathrm{\&tau;}-t)}^2{f}^2}{2}}{e}^{-j2\mathrm{\&pi;ft}}\mathrm{dt}$

$u\left(t\right)={\&Integral;}_{-\&infin;}^{+\&infin;}\left\{{\&Integral;}_{-\&infin;}^{+\&infin;}{S}_{\mathrm{GST}}(\mathrm{\&tau;},f)\mathrm{d\&tau;}\right\}{e}^{j2\mathrm{\&pi;ft}}\mathrm{df}$

Wherein, S _GST(τ f) is generalized S-transform signal afterwards; U (t) is a quadractically integrable function; σ is the Gaussian window width factor, and σ＞0, and when 1＞σ＞0, Gaussian window function width and amplitude slow down with frequency change speed, when σ＞1, and, Gaussian window function width and amplitude then speed up with frequency change; T is the time; F is a frequency;

(4) the time-frequency energy profile that obtains according to step (3); Contrast the energy diagram picture of various modulation signals; Find out the difference between the time-frequency energy diagram picture behind the various modulation signal generalized S-transforms; Choose the frequency band bar number of concentration of energy, ratio, the distribution of energy time domain, the distribution of low-and high-frequency component maximum time domain and the distribution of high fdrequency component maximum that low-and high-frequency is divided the energy maximum, various modulation signals are discerned; Said various modulation signal comprises FSK, BPSK, ASK, FM, AM, QPSK, QAM;

The said process that various modulation signals are discerned is: if concentration of energy on 4 frequency bands, can judge then that modulation signal is a fsk signal; If concentration of energy is on 1 frequency band, then modulation signal is ASK and BPSK, otherwise is FM, AM, SSB, QPSK and QAM; When concentration of energy is on 1 frequency band, if on this frequency band energy on time domain continuously, if promptly the length that distributes in time domain of energy can be thought that Energy distribution on whole time-domain, is bpsk signal, otherwise be the ASK signal greater than 9/10 of time domain total length; When concentration of energy is on 2 frequency bands; Confirm that high frequency obtains the moment of maximum, if the energy value that high frequency is obtained peaked moment low frequency less than 0.5 times of global maximum, at this moment because the maximum of low-and high-frequency on time domain, interlock; Be the FM signal, otherwise be other signals; When concentration of energy on 2 frequency bands; And when being not the FM signal; Confirm the peaked size of high fdrequency component and low frequency component energy, if high fdrequency component maximum and low frequency component maximum are basic identical, if promptly the maximum of low frequency component energy is greater than high fdrequency component energy peaked 4/5; Then be the AM signal, otherwise be other signals; Before on the basis judged, confirm all maximum of high fdrequency component, confirm maximum and minimum value in the maximum, if maximum is no more than 1.5 times of minimum value in the maximum, then is the QPSK signal, otherwise is the QAM signal.

2. a kind of Modulation Recognition of Communication Signal method according to claim 1 based on generalized S-transform, it is characterized in that: the structure of the analytic signal in the described step (1) has utilized Hilbert transform, and expression formula is:

$\hat{f}\left(t\right)=\frac{1}{\mathrm{\&pi;}}{\&Integral;}_{-\&infin;}^{+\&infin;}\frac{f\left(\mathrm{\&tau;}\right)}{t-\mathrm{\&tau;}}\mathrm{dt}$

F (t) is a real signal, and is the Hilbert transform of real signal.

Analytical function Z (t) expression formula that structure obtains:

$Z\left(t\right)=f\left(t\right)+j\hat{f}\left(t\right)$

Wherein Z (t) is an analytic signal; F (t) is a real signal;

also can be write as for the Hilbert transform of real signal:

Z(t)＝A(t)e ^-jφ(t)

Wherein, A (t) is called the envelope of Hilbert transform; φ (t) is called transient response signals.

3. a kind of Modulation Recognition of Communication Signal method according to claim 1 based on generalized S-transform, it is characterized in that: the expression formula of the Gaussian window function in the described step (2) is following:

a＞0,C∈R,w ₀＝const

Wherein, the amplitude factor of C for arbitrarily choosing; T is the time; w ₀Be phase factor; A is a window function decline exponential factor; R is a real number.

4. a kind of Modulation Recognition of Communication Signal method according to claim 1 based on generalized S-transform; It is characterized in that: said σ value is 0 ~ 50; In practical application; Need signal be carried out generalized S-transform, choose make interested frequency domain part figure clearly σ as the used window width factor of generalized S-transform.

5. according to claim 1 or 4 described a kind of Modulation Recognition of Communication Signal methods based on generalized S-transform, it is characterized in that: for signal of communication, said σ is 30.

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