CN102707157A - Single-frequency impulse signal parameter estimating method based on power spectrum - Google Patents

Abstract

The invention discloses a single-frequency impulse signal parameter estimating method based on a power spectrum. The method comprises the following steps: extracting the single-frequency impulse signal power spectrum whose value is to be estimated, mapping a frequency axis of the power spectrum to a time axis to obtain the power time signal; performing the Fourier transform on the power time signal to obtain the magnitude spectrum and the phase spectrum of the power time signal respectively; calculating the impulse width according to the relationship between the impulse width and the magnitude spectrum of the single-frequency impulse signal; calculating a carrier frequency according to the relationship between the carrier frequency and the phase spectrum of the single-frequency impulse signal to estimate the value of the single-frequency impulse signal. According to the single-frequency impulse signal parameter estimating method disclosed by invention, the problem in the prior art that the single-frequency impulse signal parameter cannot be exactly estimated under the environment having low signal to noise ratio is solved; the estimating method is applicable to the cases of spectral peak wrap, oblique change and submersed zero crossing point of a main lobe of the single-frequency impulse signal power spectrum, resulting from noise influences.

Description

A kind of pure-tone polse signal parameter estimation method based on power spectrum

Technical field

The present invention relates to signal processing technology, particularly a kind of pure-tone polse signal parameter estimation method based on power spectrum.

Background technology

The valuation of signal parameter always is the focus of communications field research and application, all is extremely important for military electronic countermeasure and the supervision of civilian frequency spectrum.Valuation is meant measured signal analysis, obtains the useful parameter of signal, so that confirm signal purposes and restoring signal.For pure-tone polse signal parameter estimation algorithm, simple parameters valuation scheme is the trend and the main flow of modulation parameter valuation relatively at present, but the noiseproof feature of algorithm is poor.

The pure-tone polse signal is a signal form commonly used in radar and the sonar, is meant that carrier frequency is to immobilize in each pulse of sending, and has advantage convenient, fast, that be easy to realize.Can be expressed as:

Wherein: A is a signal intensity, and τ is a pulse width, f _cBe carrier frequency,

It is the signal initial phase.

Power spectrum signal is expressed as:

P(f)＝A ²τ ²sinc ²[τ(f-f _c)]

Pure-tone polse signal parameter commonly used has carrier frequency, pulse width.The signal carrier frequency can characterization signal the radiation frequency range, can reflect function of radar and purposes, to the bearing accuracy that improves the sonar tracking measuring system with to improve tracking effect significant.It generally not in time the place change and change, be a comparatively fixing sorting parameter.Pulse width is the time width between end-of-pulsing time and time of arrival, and it is an important parameter describing pulse characteristics.

Pure-tone polse signal estimation method commonly used at present comprises instantaneous correlation method and zero crossing detection method, but all has the shortcoming of noiseproof feature difference, is not suitable under complex environment, estimating.

Summary of the invention

The object of the invention is: overcome the problem that can not estimate signal parameter under the low signal-to-noise ratio environment exactly that existing pure-tone polse signal estimation technology exists, be applicable to that the pure-tone polse power spectrum signal is owing to the spectrum peak that noise effect causes twists, tiltedly becomes and the covered situation of main lobe zero crossing.

Technical scheme of the present invention is: the invention provides a kind of pure-tone polse signal parameter estimation method based on power spectrum, it is characterized in that this method comprises:

Step 1, extraction pure-tone polse power spectrum signal P (f) to be valuated; The frequency axis of said power spectrum is mapped to time shaft; Receive the intensity and the time relation of power spectrum; Be called power time signal P (t); Said power time signal is carried out Fourier transform, obtains the amplitude spectrum of said power time signal respectively | F ' (x) | and phase spectrum

Wherein: with said power spectrum P (f)=A ²τ ²Sinc ²[τ (f-f _c)] frequency axis be mapped to time shaft according to the principle of f=t, obtain said power time signal P (t), A is said pure-tone polse signal intensity, expression formula is as follows:

P(t)＝A ²τ ²sinc ²[τ(t-f _c)]

Said power time signal P (t) is carried out Fourier transform obtain F (x), x is the quadrature component after the conversion, $\mathrm{Rect}\left(\frac{x}{\mathrm{\&tau;}}\right)=\left\{\begin{array}{cc}1& 0<x<\mathrm{\&tau;}\\ 0& \mathrm{Other}\end{array}\right.,$ F (x) expression formula is represented as follows:

$F\left(x\right)=4{\mathrm{\&pi;}}^2{A}^2[(\mathrm{\&tau;}+x)\mathrm{rect}\left(\frac{x+\mathrm{\&tau;}}{\mathrm{\&tau;}}\right)+(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)]\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001655013600021.png,HDA00001655013600031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{c}x)$

Because the frequency shift property F (x) of Fourier transform is about longitudinal axis symmetry, the part F ' that gets x >=0 (x) analyzes, and expression formula is as follows:

$F^{\&prime;}\left(x\right)=4{\mathrm{\&pi;}}^2{A}^2(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001655013600021.png,HDA00001655013600031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{c}x)$

Obtain the amplitude spectrum of said power time signal | F ' (x) |, expression formula is as follows:

$\left|F^{\&prime;}\left(x\right)\right|=4{\mathrm{\&pi;}}^2{A}^2(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)$

Phase spectrum

expression formula that obtains said power time signal is as follows:

Step 2, according to the pulse width τ of said pure-tone polse signal and the amplitude spectrum of said power time signal | F ' (x) | between relation, calculate the pulse width τ of said pure-tone polse signal;

Wherein:, calculate the first zero crossing x of said power time signal amplitude spectrum according to the expression formula of said power time signal amplitude spectrum ₀, said first zero crossing x ₀Be the pulse width τ=x of said pure-tone polse signal ₀

Step 3, according to the carrier frequency f of said pure-tone polse signal _cPhase spectrum with said power time signal

Between relation, calculate the carrier frequency f of said pure-tone polse signal _c

Wherein:, calculate the horizontal ordinate x of first maximum value in the phase spectrum of said power time signal according to the expression formula of said power time signal phase spectrum ₁Horizontal ordinate x with last maximum value _N, N is the maximum value number, the horizontal ordinate x of said two maximum value ₁And x _NDifference be Δ x=x _N-x ₁, the carrier frequency f of said pure-tone polse signal _cExpression formula as follows:

$f_c=\frac{N-1}{\mathrm{\&Delta;x}}=\frac{N-1}{x_N-x_1}.$

The invention has the beneficial effects as follows: the present invention is through extracting pure-tone polse power spectrum signal to be valuated, and the frequency axis of said power spectrum is mapped to time shaft, obtains the power time signal; Said power time signal is carried out Fourier transform, obtain the amplitude spectrum and the phase spectrum of said power time signal respectively; According to the pulse width of said pure-tone polse signal and the relation between the said amplitude spectrum, calculate said pulse width; According to the carrier frequency of said pure-tone polse signal and the relation between the said phase spectrum, calculate said carrier frequency, realize the valuation of pure-tone polse signal.The invention solves the pure-tone polse signal parameter problem that can not estimate exactly in the prior art under the low signal-to-noise ratio environment, be applicable to that the pure-tone polse power spectrum signal is owing to the spectrum peak that noise effect causes twists, tiltedly becomes and the covered situation of main lobe zero crossing.

Description of drawings

Fig. 1 is the process flow diagram of the pure-tone polse signal parameter valuation based on power spectrum provided by the invention;

Fig. 2 is the synoptic diagram of embodiment of the invention power time signal;

Fig. 3 is the amplitude spectrum of embodiment of the invention power time signal;

Fig. 4 is the phase spectrum of embodiment of the invention power time signal;

Fig. 5 is the pure-tone polse signal pulse width valuation graph of errors of embodiment of the invention signal to noise ratio (S/N ratio)-10dB to 10dB;

Fig. 6 is the pure-tone polse signal carrier frequency valuation graph of errors of embodiment of the invention signal to noise ratio (S/N ratio)-10dB to 10dB.

Embodiment

Below will describe with reference to Fig. 1-6 specific embodiments of the invention.

As shown in Figure 1, the embodiment of the invention carries out comprising the following steps: based on the pure-tone polse signal parameter estimation method of power spectrum

Step 1, extract pure-tone polse power spectrum signal P (f) to be valuated, the frequency axis of said power spectrum is mapped to time shaft, obtain the intensity and the time relation of power spectrum, be called power time signal P (t); Said power time signal is carried out Fourier transform, obtains the amplitude spectrum of said power time signal respectively | F ' (x) | and phase spectrum

Wherein, definite method of the amplitude spectrum of the time signal of power described in the step 1 and phase spectrum specifically comprises:

With said power spectrum P (f)=A ²τ ²Sinc ²[τ (f-f _c)] frequency axis be mapped to time shaft according to the principle of f=t, obtain said power time signal P (t), A is said pure-tone polse signal intensity, expression formula is as follows:

P(t)＝A ²τ ²sinc ²[τ(t-f _c)]

Said power time signal P (t) is carried out Fourier transform obtain F (x), x is the quadrature component after the conversion, $\mathrm{Rect}\left(\frac{x}{\mathrm{\&tau;}}\right)=\left\{\begin{array}{cc}1& 0<x<\mathrm{\&tau;}\\ 0& \mathrm{Other}\end{array}\right.,$ F (x) expression formula is represented as follows:

$F\left(x\right)=4{\mathrm{\&pi;}}^2{A}^2[(\mathrm{\&tau;}+x)\mathrm{rect}\left(\frac{x+\mathrm{\&tau;}}{\mathrm{\&tau;}}\right)+(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)]\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001655013600021.png,HDA00001655013600031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{c}x)$

Because the frequency shift property F (x) of Fourier transform is about longitudinal axis symmetry, the part F ' that gets x >=0 (x) analyzes,, expression formula is as follows:

$F^{\&prime;}\left(x\right)=4{\mathrm{\&pi;}}^2{A}^2(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00001655013600021.png,HDA00001655013600031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{c}x)$

Obtain the amplitude spectrum of said power time signal | F ' (x) |, expression formula is as follows:

$\left|F^{\&prime;}\left(x\right)\right|=4{\mathrm{\&pi;}}^2{A}^2(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)$

Phase spectrum

expression formula that obtains said power time signal is as follows:

Step 2, according to the pulse width τ of said pure-tone polse signal and the amplitude spectrum of said power time signal | F ' (x) | between relation, calculate the pulse width τ of said pure-tone polse signal;

Wherein, the method for the said pure-tone polse signal pulse width of calculating specifically comprises in the step 2:

According to the expression formula of said power time signal amplitude spectrum, calculate the first zero crossing x of said power time signal amplitude spectrum ₀, said first zero crossing x ₀Be the pulse width τ=x of said pure-tone polse signal ₀

Need to prove:

Confirm that the method that concerns between the amplitude spectrum of pulse width and said power time signal of pure-tone polse signal specifically comprises:

The amplitude spectrum expression formula of power time signal is as follows:

$\left|F^{\&prime;}\left(x\right)\right|=4{\mathrm{\&pi;}}^2{A}^2(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)$

According to rectangular function $\mathrm{Rect}\left(\frac{x}{\mathrm{\&tau;}}\right)=\left\{\begin{array}{cc}1& 0<x<\mathrm{\&tau;}\\ 0& \mathrm{Other}\end{array}\right.$ Can know, when x>=τ | F ' (x) |=0, obtain the first zero crossing x of amplitude spectrum thus ₀Pulse width τ=x for the pure-tone polse signal ₀

Step 3, according to the carrier frequency f of said pure-tone polse signal _cPhase spectrum with said power time signal

Between relation, calculate the carrier frequency f of said pure-tone polse signal _c

Wherein, the method for the said pure-tone polse signal carrier frequency of calculating specifically comprises in the step 3:

According to the expression formula of said power time signal phase spectrum, calculate the horizontal ordinate x of first maximum value in the phase spectrum of said power time signal ₁Horizontal ordinate x with last maximum value _N, N is the maximum value number, the horizontal ordinate x of said two maximum value ₁And x _NDifference be Δ x=x _N-x ₁, the carrier frequency f of said pure-tone polse signal _cExpression formula as follows:

$f_c=\frac{N-1}{\mathrm{\&Delta;x}}=\frac{N-1}{x_N-x_1}.$

Need to prove:

Confirm that the method that concerns between the phase spectrum of carrier frequency and said power time signal of pure-tone polse signal specifically comprises:

The phase spectrum expression formula of power time signal is as follows:

The frequency that can draw phase spectrum according to the expression formula of phase spectrum is the carrier frequency of signal, obtains the carrier frequency f of pure-tone polse signal thus _cExpression formula as follows:

$f_c=\frac{N-1}{\mathrm{\&Delta;x}}=\frac{N-1}{x_N-{\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="HDA00001655013600012.png,HDA00001655013600021.png"\; state="\{\{state\}\}">x</figure-callout>}}_1}.$

The present invention is that embodiment is elaborated to the inventive method with the pure-tone polse signal.

The embodiment of the invention can be applied to military electronic countermeasure and civilian frequency spectrum supervision field; Under the low signal-to-noise ratio environment, estimate signal parameter exactly; Can reflect function of radar and purposes, to the bearing accuracy that improves the sonar tracking measuring system with to improve tracking effect significant.

The following content of the present invention is represented the pure-tone polse signal with abbreviation CW, and SNR representes signal to noise ratio (S/N ratio) with abbreviation.Wherein, carrier frequency f _c=500MHz, the power time signal that pulse width τ=the CW signal of 1 μ s obtains is as shown in Figure 2, and the power time signal is carried out Fourier transform, and the amplitude spectrum that obtains the power time signal respectively is as shown in Figure 3 as shown in Figure 4 with phase spectrum.

The present invention estimates the CW signal parameter under the MATLAB6.5 environment.

CW signal carrier frequency f _c=500MHz, pulse width τ=1 μ s, SNR variation range-10dB-10dB.The present invention to the parameter estimation result of CW signal like table 1, shown in 2; Pulse width evaluated error curve is as shown in Figure 5, and carrier frequency evaluated error curve is as shown in Figure 6.Can know by above result, when SNR at-10dB-10dB, pulse width valuation error is less than 0.019, carrier frequency valuation error is 0, analyzes thus and can know that the inventive method still can be carried out parameter estimation to the CW signal under the low signal-to-noise ratio situation, and precision is higher.

Table 1 signal to noise ratio (S/N ratio) changes parameter estimation result down

Table 2 signal to noise ratio (S/N ratio) changes parameter estimation result down

Claims (1)

1. pure-tone polse signal parameter estimation method based on power spectrum is characterized in that this method comprises:

Step 1, extraction pure-tone polse power spectrum signal P (f) to be valuated; The frequency axis of said power spectrum is mapped to time shaft; Receive the intensity and the time relation of power spectrum; Be called power time signal P (t); Said power time signal is carried out Fourier transform, obtains the amplitude spectrum of said power time signal respectively | F ' (x) | and phase spectrum

Wherein: with said power spectrum P (f)=A ²τ ²Sinc ²[τ (f-f _c)] frequency axis be mapped to time shaft according to the principle of f=t, obtain said power time signal P (t), A is said pure-tone polse signal intensity, expression formula is as follows:

P(t)＝A ²τ ²sinc ²[τ(t-f _c)]

Said power time signal P (t) is carried out Fourier transform obtain F (x), x is the quadrature component after the conversion, $\mathrm{Rect}\left(\frac{x}{\mathrm{\&tau;}}\right)=\left\{\begin{array}{cc}1& 0<x<\mathrm{\&tau;}\\ 0& \mathrm{Other}\end{array}\right.,$ F (x) expression formula is represented as follows:

$F\left(x\right)=4{\mathrm{\&pi;}}^2{A}^2[(\mathrm{\&tau;}+x)\mathrm{rect}\left(\frac{x+\mathrm{\&tau;}}{\mathrm{\&tau;}}\right)+(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)]\exp (-j2\mathrm{\&pi;}{f}_{c}x)$

Because the frequency shift property F (x) of Fourier transform is about longitudinal axis symmetry, the part F ' that gets x >=0 (x) analyzes, and expression formula is as follows:

$F^{\&prime;}\left(x\right)=4{\mathrm{\&pi;}}^2{A}^2(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)\exp (-j2\mathrm{\&pi;}{f}_{c}x)$

Obtain the amplitude spectrum of said power time signal | F ' (x) |, expression formula is as follows:

$\left|F^{\&prime;}\left(x\right)\right|=4{\mathrm{\&pi;}}^2{A}^2(\mathrm{\&tau;}-x)\mathrm{rect}\left(\frac{x}{\mathrm{\&tau;}}\right)$

Phase spectrum

expression formula that obtains said power time signal is as follows:

Step 2, according to the pulse width τ of said pure-tone polse signal and the amplitude spectrum of said power time signal | F ' (x) | between relation, calculate the pulse width τ of said pure-tone polse signal;

Wherein:, calculate the first zero crossing x of said power time signal amplitude spectrum according to the expression formula of said power time signal amplitude spectrum ₀, said first zero crossing x ₀Be the pulse width τ=x of said pure-tone polse signal ₀

Step 3, according to the carrier frequency f of said pure-tone polse signal _cPhase spectrum with said power time signal

Between relation, calculate the carrier frequency f of said pure-tone polse signal _c

Wherein:, calculate the horizontal ordinate x of first maximum value in the phase spectrum of said power time signal according to the expression formula of said power time signal phase spectrum ₁Horizontal ordinate x with last maximum value _N, N is the maximum value number, the horizontal ordinate x of said two maximum value ₁And x _NDifference be Δ x=x _N-x ₁, the carrier frequency f of said pure-tone polse signal _cExpression formula as follows:

$f_c=\frac{N-1}{\mathrm{\&Delta;x}}=\frac{N-1}{x_N-x_1}.$

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