CN103915102A - Method for noise abatement of LFM underwater sound multi-path signals - Google Patents

Abstract

The invention belongs to the field of signal processing, and particularly relates to a method for noise abatement of LFM underwater sound multi-path signals. The method includes the steps that an optimal transformation order popt on which optimal fractional Fourier transformation is conducted is acquired according to deterministic signal parameters; band-pass filtering preprocessing is conducted on the LFM multi-path signals, and out-of-band noise is abated; Hilbert transformation is conducted on band-pass filtering output signals, and then analytic signals are acquired; popt and fractional Fourier transformation is conducted on the analytic signals; frequency spectrum shielding and isolating processing is conducted on a fractional Fourier domain, and in-band noise is abated; -popt and fractional Fourier inverse transformation is conducted, and then high-signal-to-noise-ratio multi-path signals with the abated noise are acquired. The method is mainly achieved through the FFT algorithm, the calculated amount is small, and project real-time implementation can be achieved. Signal processing is not disturbed by cross terms due to FrFT linear transformation characteristics, so that the method is especially suitable for processing the multi-path or multi-component LFM signals.

Description

A kind of noise suppressing method of LFM underwater sound multi-path signals

Technical field

The invention belongs to signal process field, be specifically related to a kind of noise suppressing method of LFM underwater sound multi-path signals.

Background technology

Noise reduction techniques is an important subject of signal process field always.Existing many noise reduction techniques are suggested, and as auto adapted filtering, time domain average method, noise reduction techniques based on wavelet analysis or neural network etc., these noise reduction techniques performances are different, are applicable to respectively different application requirements.

Linear frequency modulation (LFM) signal is the basis of a large class manual signal, it is widely used in underwater sound field already as a kind of non-stationary signal of maturation, as submarine topography detection, sediment classification, seabed subbottom survey, underwater acoustic channel are surveyed, small target detection etc. under water.Due to the heterogeneity of underwater acoustic channel medium, many Underwater Detection signals are multi-path signals.In order to realize high-resolution, detected with high accuracy, meet the requirement of a lot of signal processing algorithms to processing signals high s/n ratio, make squelch and process research and there is realistic meaning and engineering significance being widely submerged in LFM underwater sound multi-path signals in noise.

LFM noise reduction techniques can utilize filtering method to be achieved, but only adopts filtering technique effectively to suppress in-band noise; Because LFM signal is typical time varying signal, for the fixing Wiener wave filter of parameter, be not suitable for it to process; The parameter becoming when although Kalman wave filter has, and be applicable to the processing of nonstationary random signal, but must known signal and the statistical property of noise could obtain optimal filtering result, and in practical application, conventionally cannot learn the priori of these statistical properties, therefore cannot realize optimal filtering processing; Although sef-adapting filter can be adjusted the filtering parameter of current time automatically, realize optimal filtering with adaptation signal and statistical property noise the unknown or non-stationary, but there is the characteristic of asymptotic convergence in sef-adapting filter, in the time that detection data amount is few, the signal waveform start-up portion error highly significant after auto adapted filtering strengthens.Many defects that existing noise suppressing method exists make it be not suitable for LFM underwater sound multi-path signals to carry out squelch processing.

Fractional Fourier Transform (Fractional Fourier Transform, FrFT) is a kind of important fractional order conversion, take LFM signal as orthogonal basis, and has good energy accumulating at Fractional Fourier Domain (u territory).Conventionally u territory is thought that time domain obtains through the rotation of α=p pi/2 angle equivalently, and p is FrFT conversion exponent number.In the time that the u axle of u territory coordinate system is vertical with Chirp signal time-frequency distributions, the focusing effect of LFM signal will be obtained, claim the optimum Fractional Fourier Transform that is transformed to now, claim that u territory is now optimal transformation u territory, conversion exponent number p is now optimal transformation exponent number (Optimal Order), uses p _optrepresent.In essence, the information of signal at time domain and frequency domain has been merged in the expression of LFM signal on u territory, therefore, FrFT is considered to a kind of Time-Frequency Analysis Method, and FrFT is one-dimensional linear conversion, it is realized compared with a lot of two-dimentional time frequency analyzing tool, and not only on computation complexity, tool has great advantage, and does not have the interference of cross term.The present invention makes full use of linear transformation, rotation and the energy accumulating characteristic that this time frequency processing technology of FrFT has, and associating band-pass filtering, at time-frequency domain filtering in-band noise, realizes the squelch of LFM underwater sound multi-path signals.

Summary of the invention

The object of the present invention is to provide a kind of signal to noise ratio (S/N ratio) that further improves, calculated amount is little, the many ways of LFM underwater sound noise suppressing methods that can engineering real-time implementation.

The object of the invention is to realize by following steps:

(1) obtain the optimal transformation exponent number p of optimum Fractional Fourier Transform according to deterministic signal parameter _opt;

(2) LFM multi-path signals is carried out to bandpass filtering pre-service, inhibition zone external noise;

(3) bandpass filtering output signal is done to Hilbert conversion, obtain analytic signal;

(4) analytic signal is done to p _optrank Fractional Fourier Transform;

(5) make frequency spectrum at Fractional Fourier Domain and hide every processing, suppress in-band noise;

(6) do-p _optrank Fractional Fourier inverse transformation, the high s/n ratio multi-path signals of the noise that is inhibited.

In step (4), the Fourier of analytic signal x (t) is transformed to:

$X_{\mathrm{\α}}\left(u\right)=\left\{F^{\mathrm{\α}}\right[x\left(t\right)\left]\right\}\left(u\right)={\∫}_{-\∞}^{\∞}x\left(t\right)K_{\mathrm{\α}}(t,u)\mathrm{dt}$

In formula, α=p pi/2 is corresponding coordinate system rotation angle, the transformation kernel K of Fourier conversion _α(t, u) is:

$K_p(t,u)=\left\{\begin{array}{c}\sqrt{\frac{1-j\cot \mathrm{\α}}{2\mathrm{\π}}}\exp (j\frac{t^2+u^2}{2}\cot \mathrm{\α}-\mathrm{jtu}\csc \mathrm{\α}),\mathrm{\α}\≠\mathrm{n\π}\\ \mathrm{\δ}(t-u),\mathrm{\α}=2\mathrm{n\π}\\ \mathrm{\δ}(t+u),\mathrm{\α}=(2n\±1)\mathrm{\π}\end{array}\right.$

And the inverse transformation of p rank Fourier conversion is defined as:

$x\left(t\right)={\∫}_{-\∞}^{+\∞}{X}_p\left(u\right)K_{-p}(t,u)\mathrm{du}.$

Step (5) intermediate frequency spectrum hides every the frequency band range of processing:

Wherein, T ' is for choosing the length of pending signal; T _lFMfor the pulsewidth that transmits; T is actual treatment signal length, Δ τ _maxfor maximum delay corresponding to each component of signal in multi-path signals, meet T≤2T _lFM+ 2f _l/ k, otherwise by mending 0 choosing after pending signal, " [] " represents interval range.

Beneficial effect of the present invention is:

The present invention has adopted FrFT technology, on the pretreated basis of bandpass filtering, LFM underwater sound multi-path signals optimal order is transformed to u territory by the revolving property that makes full use of FrFT, carry out frequency spectrum screening every processing according to the spectral range of u territory multi-path signals, noise contribution in inhibition zone, has further improved the signal to noise ratio (S/N ratio) of LFM underwater sound multi-path signals.Realize because FrFT fast algorithm adopts FFT, therefore this method is mainly realized by fft algorithm, and calculated amount is little, can engineering real-time implementation.FrFT linear transformation characteristic makes signal processing not disturbed by cross term, and therefore, the present invention is particularly suitable for processing many ways or many LFM Signal.

Accompanying drawing explanation

Fig. 1 is the noise suppressing method process flow diagram of LFM underwater sound multi-path signals;

Fig. 2 a is time domain plethysmographic signal;

Fig. 2 b is signal optimal order FrFT output waveform;

Fig. 2 c is the optimal order FrFT output waveform of the corresponding analytic signal of real signal;

Fig. 3 is time-frequency domain and the optimal transformation u territory distribution plan of LFM underwater sound multi-path signals;

Fig. 4 is that bandpass filtering and u territory hide every Combined Treatment squelch schematic diagram;

Fig. 5 a is the time domain waveform of signal to noise ratio (S/N ratio) multi-path signals while being 3dB;

Fig. 5 b is only through the pretreated multi-path signals matched filtering output of bandpass filtering;

Fig. 5 c is the matched filtering output of multi-path signals after this method squelch;

The matched filtering of multi-path signals output when Fig. 5 d is noiseless.

Embodiment

For a more detailed description to the specific embodiment of the present invention below in conjunction with accompanying drawing.

The present invention relates to a kind of noise suppressing method for LFM underwater sound multi-path signals, as shown in Figure 1, whole flow process is decomposed into following 6 steps and completes the algorithm flow that method realizes:

Step (1) is by known LFM signal parameter, calculate optimum Fractional Fourier Transform exponent number according to formula α=arctank+ pi/2, for the optimal order Fractional Fourier Transform of LFM underwater sound multi-path signals, wherein k is the frequency change rate of LFM signal;

Step (2) is carried out bandpass filtering pre-service to underwater sound multi-path signals, and the noise contribution beyond filtering appts working band can reach the object that suppresses u territory signal in-band noise in subsequent treatment, improves u territory Signal-to-Noise;

Step (3) is done Hilbert conversion to bandpass filtering output signal, converts thereof into analytic signal form.This is because FrFT processes and can obtain single-side belt frequency spectrum analytic signal, guarantee the aggregation properties of the rear signal energy of signal conversion, the aggregation of the optimal order FrFT output signal energy of real signal and its analytic signal contrasts as shown in Figure 2, obviously analytic signal has better aggregation, more be conducive to u territory and hide every processing, fully demonstrated the necessity of utilizing Hilbert conversion real signal to be converted to its analytic signal form;

Step (4) is made p to analytic signal _optrank FrFT, obtains a series of impulse signals of multi-path signals correspondence in u territory.

The FrFT of signal x (t) is defined as:

$X_{\mathrm{\α}}\left(u\right)=\left\{F^{\mathrm{\α}}\right[x\left(t\right)\left]\right\}\left(u\right)={\∫}_{-\∞}^{\∞}x\left(t\right)K_{\mathrm{\α}}(t,u)\mathrm{dt}---\left(1\right)$

In formula, α=p pi/2 is coordinate system rotation angle corresponding to FrFT computing.The transformation kernel K of FrFT _α(t, u) is expressed as:

$K_p(t,u)=\left\{\begin{array}{c}\sqrt{\frac{1-j\cot \mathrm{\α}}{2\mathrm{\π}}}\exp (j\frac{t^2+u^2}{2}\cot \mathrm{\α}-\mathrm{jtu}\csc \mathrm{\α}),\mathrm{\α}\≠\mathrm{n\π}\\ \mathrm{\δ}(t-u),\mathrm{\α}=2\mathrm{n\π}\\ \mathrm{\δ}(t+u),\mathrm{\α}=(2n\±1)\mathrm{\π}\end{array}\right.---\left(2\right)$

And the inverse transformation of p rank FrFT is defined as:

$x\left(t\right)={\∫}_{-\∞}^{+\∞}{X}_p\left(u\right)K_{-p}(t,u)\mathrm{du}---\left(3\right)$

In the time that signal is done to optimal order FrFT, time domain coordinate system (t-f coordinate system) to the anglec of rotation of u territory coordinate system (u-v coordinate system) is α _opt=π p _opt/ 2.FrFT algorithm adopts decomposition method to realize conventionally, and its core concept is the convolution algorithm utilizing in FFT implementation algorithm, thereby can be by its multiplying amount by O (N ²) be down to O (NlbN), and the multiplying amount of FFT is (N/2) lbN.

Step (5) is made frequency spectrum at Fractional Fourier Domain and is hidden every processing, noise contribution in further inhibition zone on the pretreated basis of bandpass filtering, and this process is carried out frequency spectrum screening every processing with the distribution range of u territory multi-path signals frequency spectrum to u territory signal.

Definition by each multi-path signals component in Fig. 3 at geometric relationship, dimension normalization principle and the FrFT of time-frequency domain and the distribution of u territory, known multi-path signals is (unit is Hz) at the effective spectrum distribution range B in u territory:

Wherein, α _c=α _opt-pi/2, T ' is for choosing the length of pending signal; T _lFMfor the pulsewidth that transmits; T is the actual signal length that application this method is processed, Δ τ _maxfor maximum delay corresponding to each component of signal in many components echoed signal, " Δ " represents dimension normalized value; for dimension normalization time factor; f _sfor sample frequency, " [] " represents interval range.

From the geometric relationship in Fig. 3, be greater than T/2+f when getting peak signal time delay in pending signal _lwhen/k, this signal spectrum is positioned at the negative semiaxis of frequency axis, without actual physics meaning, but as T≤T/2+f _l/ k+T _lFM, i.e. T≤2T _lFM+ 2f _lwhen/k, this phenomenon must there will not be.Therefore,, in the time that actual signal is processed, should choose many component signals length T≤2T _lFM+ 2f _lthe maximum delay that/k(chooses component of signal is less than T/2+f _l/ k), can be by reaching this requirement choosing 0 the mode of mending after pending signal.

The spectral range definite according to above formula, hides every processing the frequency spectrum of multi-path signals, has further improved the signal to noise ratio (S/N ratio) of multi-path signals.In step (2), in bandpass filtering and step (5), the frequency spectrum screening of u territory reaches squelch object principle as shown in Figure 4 every Combined Treatment, hide every the noise eliminating to after successively the cutting apart of time-frequency plane by bandpass filtering and u territory frequency spectrum, at utmost suppressed the noise contribution in signal band.

Do-p of step (6) _optrank Fractional Fourier inverse transformation, has the be inhibited high s/n ratio multi-path signals of noise of Fractional Fourier inverse transformation, has finally realized the squelch of multi-path signals.

Ultimate principle of the present invention is: first tentatively improve the signal to noise ratio (S/N ratio) of multi-path signals by bandpass filtering pre-service, show as and improved u territory Signal-to-Noise; Secondly, make full use of the u territory aggregation properties after revolving property and the LFM signal optimal order Fractional Fourier Transform of FrFT, by the in-band noise every further Inhibitory signal to the screening of u territory signal spectrum, further improve the signal to noise ratio (S/N ratio) of multi-path signals.Utilize the linear transformation characteristic of FrFT, while having avoided signal to process, the interference of cross term, makes the inventive method be particularly suitable for processing many ways or many LFM Signal.Analysis draws, two factors have guaranteed that multi-path signals in-band noise is effectively suppressed: the one, and bandpass filtering and u territory hide every the noise eliminating to after successively the cutting apart of time-frequency plane, suppressed to the full extent in-band noise composition, this is that any traditional time-domain filtering or frequency domain filtering method all cannot realize; The 2nd, FrFT itself also has very strong inhibiting effect to noise, and this is because the characteristic that FrFT kernel function is one group of Complete Orthogonal base of LFM signal determines.

Method of the present invention is carried out to simulation example, to provide more intuitive description.The in the situation that of the effect of faling apart in the time not considering underwater acoustic channel, the signal model of multi-path signals can be expressed as:

$\begin{array}{cc}y\left(t\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{a}_{i}s(t-{\mathrm{\τ}}_i)+n\left(t\right)& 0\≤t\≤T\end{array}---\left(5\right)$

Wherein, what s (t) was known waveform transmits, and n (t) is white Gaussian noise, M, a _iand τ _iamplitude and the time delay of echoed signal on the number of respective signal travel path, i paths respectively.

In emulation, establish LFM underwater sound multi-path signals and comprise 4 echoed signal components, each component of signal respective amplitude is followed successively by 1,0.9,0.7 and 0.6, and time delay is followed successively by 0,0.5,1.4 and 2.2ms, and Signal-to-Noise is 3dB.After introducing noise, cannot distinguish each component of signal from time domain, this point can clearly be found by Fig. 5 (a); Fig. 5 (b) is the only matched filtering of multi-path signals output after bandpass filtering treatment, although matched filtering is inhibition zone external noise composition effectively, but because LFM is broadband signal, in band, still there is a large amount of undesired signals, cause still including a large amount of interference components in matched filtering output; Fig. 5 (c) is the matched filtering output of multi-path signals after this method suppresses noise, because this method has suppressed a large amount of in-band noise compositions, matched filtering output has obtained the more output signal of high s/n ratio, Fig. 5 (d) of the matched filtering output signal of multi-path signals relatively finds when providing noiseless, this method has greatly improved the signal to noise ratio (S/N ratio) of multi-path signals, effectively eliminate the in-band noise of observation signal, the in-band noise composition that has suppressed observation signal, noise suppression effect is obvious.

FrFT fast algorithm in the present invention mainly adopts FFT to realize, the same magnitude of its computation complexity and FFT.Because this method is mainly made up of FFT and FrFT, therefore, this method is mainly by FFT fast algorithm implementation, calculated amount is little, can be applicable to engineering real-time implementation, FrFT is linear transformation in addition, and processing procedure is not subject to the interference of cross term, therefore, this method is also particularly suitable for processing many ways or many LFM Signal.

Claims (3)

1. a noise suppressing method for LFM underwater sound multi-path signals, is characterized in that, comprises the following steps:

(1) obtain the optimal transformation exponent number p of optimum Fractional Fourier Transform according to deterministic signal parameter _opt;

(2) LFM multi-path signals is carried out to bandpass filtering pre-service, inhibition zone external noise;

(3) bandpass filtering output signal is done to Hilbert conversion, obtain analytic signal;

(4) analytic signal is done to p _optrank Fractional Fourier Transform;

(5) make frequency spectrum at Fractional Fourier Domain and hide every processing, suppress in-band noise;

(6) do-p _optrank Fractional Fourier inverse transformation, the high s/n ratio multi-path signals of the noise that is inhibited.

2. the noise suppressing method of a kind of LFM underwater sound multi-path signals according to claim 1, is characterized in that the Fourier of analytic signal x (t) in described step (4) is transformed to:

$X_{\mathrm{\α}}\left(u\right)=\left\{F^{\mathrm{\α}}\right[x\left(t\right)\left]\right\}\left(u\right)={\∫}_{-\∞}^{\∞}x\left(t\right)K_{\mathrm{\α}}(t,u)\mathrm{dt}$

In formula, α=p pi/2 is corresponding coordinate system rotation angle, the transformation kernel K of Fourier conversion _α(t, u) is:

$K_p(t,u)=\left\{\begin{array}{c}\sqrt{\frac{1-j\cot \mathrm{\α}}{2\mathrm{\π}}}\exp (j\frac{t^2+u^2}{2}\cot \mathrm{\α}-\mathrm{jtu}\csc \mathrm{\α}),\mathrm{\α}\≠\mathrm{n\π}\\ \mathrm{\δ}(t-u),\mathrm{\α}=2\mathrm{n\π}\\ \mathrm{\δ}(t+u),\mathrm{\α}=(2n\±1)\mathrm{\π}\end{array}\right.$

And the inverse transformation of p rank Fourier conversion is defined as:

$x\left(t\right)={\∫}_{-\∞}^{+\∞}{X}_p\left(u\right)K_{-p}(t,u)\mathrm{du}.$

3. the noise suppressing method of a kind of LFM underwater sound multi-path signals according to claim 1, is characterized in that the screening of described step (5) intermediate frequency spectrum every the frequency band range of processing is:

Wherein, T ' is for choosing the length of pending signal; T _lFMfor the pulsewidth that transmits; T is actual treatment signal length, Δ τ _maxfor maximum delay corresponding to each component of signal in multi-path signals, meet T≤2T _lFM+ 2f _l/ k, otherwise by mending 0 choosing after pending signal, " [] " represents interval range.