CN103915102B - 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 signalses

Technical field

The invention belongs to field of signal processing is and in particular to a kind of noise suppressing method of lfm underwater sound multi-path signalses.

Background technology

Noise reduction techniques are always an important subject of field of signal processing.Existing many noise reduction techniques It is suggested, such as adaptive-filtering, time domain average method, noise reduction techniques based on wavelet analysis or neutral net etc., these are made an uproar Sound suppression technology different properties, are respectively suitable for different application requirements.

Linear frequency modulation (lfm) signal is the basis of a big class manual signal, and it is early as a kind of ripe non-stationary signal It has been widely used in underwater sound field, such as sea-floor relief detection, seafloor sediment classification, seabed subbottom survey, underwater acoustic channel are visited Survey, under water small target detection etc..Due to the heterogeneity of underwater acoustic channel medium, many Underwater Detection signals are multi-path signalses. In order to realize high-resolution, detected with high accuracy, meet the requirement to process signal high s/n ratio for a lot of signal processing algorithms, to flooding Lfm underwater sound multi-path signalses in noise are made noise suppressed treatment research and are had extensive realistic meaning and engineering significance.

Lfm noise reduction techniques can be achieved using filtering method, but cannot make an uproar in band only with filtering technique Sound is effectively suppressed；Because lfm signal is typical time varying signal, uncomfortable for the fixing wiener wave filter of parameter Close and it is processed；Although kalman wave filter has a parameter of time-varying, and it is applied to the process of nonstationary random signal, Must could obtain optimal filter result with the statistical property of noise by known signal, and generally cannot learn these in practical application The priori of statistical property, therefore cannot realize optimal filter and process；Although sef-adapting filter can adjust automatically current when The filtering parameter carved, to realize optimal filter to adapt to unknown or non-stationary the statistical property of signal and noise, but self adaptation There is the characteristic of asymptotic convergence in wave filter, when detection data amount is few, adaptive-filtering enhanced signal waveform start-up portion Error highly significant.Many defects that existing noise suppressing method exists make it unsuitable for lfm underwater sound multi-path signalses are carried out Noise suppressed is processed.

Fractional order fourier conversion (fractional fourier transform, frft) is a kind of important fraction Rank converts, and with lfm signal as orthogonal basis, and has good energy accumulating in Fractional Fourier Domain (u domain).Generally u Domain is equally considered that time domain obtains through the rotation of α=p pi/2 angle, and p converts exponent number for frft.U when u domain coordinate system When axle is vertical with chirp signal time-frequency distributions, will obtain lfm signal focusing effect, claim now be transformed to optimum fractional order Fourier converts, and u domain now is called optimal transformation u domain, and conversion exponent number p now is optimal transformation exponent number (optimal Order), use p_optRepresent.In essence, the information in time domain and frequency domain for the signal has been merged in expression on u domain for the lfm signal, Therefore, frft is considered as a kind of Time-Frequency Analysis Method, and frft is one-dimensional linear transform, and it is realized and much two-dimentional time-frequencies Analysis tool is compared, and not only has on computation complexity and has great advantage, and there is not the interference of cross term.The present invention is abundant Linear transformation, rotation and the energy accumulating characteristic being had using this time frequency processing technology of frft, joint band-pass filtering, Time-frequency domain filters in-band noise, realizes the noise suppressed of lfm underwater sound multi-path signalses.

Content of the invention

It is an object of the invention to provide one kind improves signal to noise ratio further, amount of calculation is little, can be with engineering real-time implementation The lfm underwater sound more than way noise suppressing method.

The purpose of the present invention through the following steps that realize:

(1) the optimal transformation exponent number p of optimum fractional order fourier conversion is obtained according to deterministic signal parameter_opt；

(2) lfm multi-path signalses are carried out with bandpass filtering pretreatment, suppresses out-of-band noise；

(3) bandpass filtering output signal is done with hilbert conversion, obtains analytic signal；

(4) p is done to analytic signal_optRank fractional order fourier converts；

(5) make frequency spectrum in Fractional Fourier Domain to hide every process, suppress in-band noise；

(6) it is-p_optRank fractional order fourier inverse transformation, the high s/n ratio multi-path signalses of the noise that is inhibited.

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

$x_{\mathrm{\α}}\left(u\right)=\left\{f^{\mathrm{\α}}\right[x\left(t\right)\left]\right\}\left(u\right)={\&integral;}_{-\∞}^{\∞}x\left(t\right)k_{\mathrm{\α}}(t,u)\mathrm{dt}$

In formula, α=p pi/2 is the corresponding coordinate system anglec of rotation, the transformation kernel k of fourier conversion_α(t, u) is:

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

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

$x\left(t\right)={\&integral;}_{-\∞}^{+\∞}{x}_p\left(u\right)k_{-p}(t,u)\mathrm{du}.$

The frequency band range that step (5) intermediate frequency spectrum hides every processing is:

Wherein, t ' is the length choosing pending signal；t_lfmFor transmission signal pulsewidth；T is actual treatment signal length, δτ_maxFor the corresponding maximum delay of component of signal each in multi-path signalses, meet t≤2t_lfm+2f_l/ k, otherwise, by treating in selection 0 is mended, " [] " represents interval range after process signal.

The beneficial effects of the present invention is:

Present invention employs frft technology, on the basis of bandpass filtering pretreatment, make full use of the revolving property of frft Lfm underwater sound multi-path signalses optimal order is transformed to u domain, frequency spectrum is carried out according to the spectral range of u domain multi-path signalses and hides every process, press down In-band noise composition processed, further increases the signal to noise ratio of lfm underwater sound multi-path signalses.Because frft fast algorithm adopts fft real Existing, therefore this method is mainly realized by fft algorithm, and amount of calculation is little, can be with engineering real-time implementation.Frft linear transformation characteristic makes Signal transacting is not subject to cross term interference, therefore, the invention is particularly suited to processing many ways or multi -components lfm signal.

Brief description

Fig. 1 is the noise suppressing method flow chart of lfm underwater sound multi-path signalses；

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 domain distribution map of lfm underwater sound multi-path signalses；

Fig. 4 is bandpass filtering and u domain hides every Combined Treatment noise suppressed schematic diagram；

Fig. 5 a is the time domain waveform that signal to noise ratio is multi-path signalses during 3db；

Fig. 5 b is the only multi-path signalses matched filtering output through bandpass filtering pretreatment；

Fig. 5 c is the matched filtering output of multi-path signalses after this method noise suppressed；

Fig. 5 d is the matched filtering output of multi-path signalses during noiseless.

Specific embodiment

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

The present invention relates to a kind of noise suppressing method for lfm underwater sound multi-path signalses, the algorithm flow that method is realized is such as Shown in Fig. 1, whole flow process is decomposed into following 6 steps and completes:

Step (1), by known lfm signal parameter, calculates optimum fractional order according to formula α=arctank+ pi/2 Fourier converts exponent number, and for the optimal order fractional order fourier conversion of lfm underwater sound multi-path signalses, wherein k is lfm signal Frequency change rate；

Step (2) carries out bandpass filtering pretreatment to underwater sound multi-path signalses, and the noise beyond filtering appts working band becomes Point, can reach the purpose of u domain signal in-band noise in suppression subsequent treatment, improve u domain Signal-to-Noise；

Step (3) makees hilbert conversion to bandpass filtering output signal, converts thereof into analytic signal form.This be by In frft analytic signal is carried out process can get single-side belt frequency spectrum it is ensured that after signal conversion signal energy aggregation properties, real Signal is contrasted as shown in Fig. 2 obvious analytic signal has with the aggregation of the optimal order frft output signal energy of its analytic signal There is more preferable aggregation, be more beneficial for u domain and hide every process, fully demonstrated and become, using hilbert, real signal of changing commanders and be converted into it The necessity of analytic signal form；

Step (4) makees p to analytic signal_optRank frft, obtains a series of impulse signals in u domain for the multi-path signalses correspondence.

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

$x_{\mathrm{\α}}\left(u\right)=\left\{f^{\mathrm{\α}}\right[x\left(t\right)\left]\right\}\left(u\right)={\&integral;}_{-\∞}^{\∞}x\left(t\right)k_{\mathrm{\α}}(t,u)\mathrm{dt}---\left(1\right)$

In formula, α=p pi/2 is the frft computing corresponding coordinate system anglec of rotation.The transformation kernel k of frft_α(t, u) is expressed as:

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

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

$x\left(t\right)={\&integral;}_{-\∞}^{+\∞}{x}_p\left(u\right)k_{-p}(t,u)\mathrm{du}---\left(3\right)$

When signal is done with optimal order frft, time domain coordinate system (t-f coordinate system) is to u domain coordinate system (u-v coordinate system) The anglec of rotation is α_opt=π p_opt/2.Frft algorithm generally adopts decomposition method to realize, and its core concept is to realize algorithm using fft In convolution algorithm, thus can be by its multiplying amount by o (n²) it is down to o (nlbn), and the multiplying amount of fft is (n/2) lbn.

Step (5) is made frequency spectrum in Fractional Fourier Domain and is hidden every process, further on the basis of bandpass filtering pretreatment Suppression in-band noise composition, this process carries out frequency spectrum with the distribution of u domain multi-path signalses frequency spectrum and hides every process to u domain signal.

Geometrical relationship, dimensional normalization principle and the frft being distributed in time-frequency domain and u domain by multi-path signalses component each in Fig. 3 Definition it is known that effective spectrum distribution b in u domain for the multi-path signalses is (unit be hz):

Wherein, α_c=α_opt- pi/2, t ' is the length choosing pending signal；t_lfmFor transmission signal pulsewidth；T is to apply this The actual signal length that method is processed, δ τ_maxFor the corresponding maximum delay of component of signal each in multi -components echo-signal, " δ " represents dimensional normalization value；For dimensional normalization time factor；f_sFor sample frequency, " [] " represents interval Scope.

From the geometrical relationship in Fig. 3, it is more than t/2+f when taking peak signal time delay in pending signal_lDuring/k, this letter Number frequency spectrum is located at the negative semiaxis of frequency axis, no actual physical meaning, but works as t≤t/2+f_l/k+t_lfm, i.e. t≤2t_lfm+2f_lDuring/k, This phenomenon is not in necessarily.Therefore, when actual signal is processed it should choose multicomponent data processing length t≤2t_lfm+2f_l/ The maximum delay that k(chooses component of signal is less than t/2+f_l/ k), can be reached by way of mending 0 after choosing pending signal This requirement.

The spectral range being determined according to above formula, hides every process to the frequency spectrum of multi-path signalses, further increases many ways and believes Number signal to noise ratio.In bandpass filtering and step (5) in step (2), u domain frequency spectrum hides that to reach noise suppressed purpose every Combined Treatment former Reason is as shown in figure 4, hide the noise eliminating after the gradually segmentation to time-frequency plane, maximum journey by bandpass filtering and u domain frequency spectrum Degree inhibits the noise contribution in signal band.

Step (6) is-p_optRank fractional order fourier inverse transformation, has fractional order fourier inverse transformation to be inhibited noise High s/n ratio multi-path signalses, finally achieve the noise suppressed of multi-path signalses.

The general principle of the present invention is: first passes through the preliminary signal to noise ratio improving multi-path signalses of bandpass filtering pretreatment, table It is now to improve u domain Signal-to-Noise；Secondly, revolving property and the lfm signal optimal order fractional order of frft are made full use of U domain aggregation properties after fourier conversion, by hiding every the in-band noise suppressing signal further to u domain signal spectrum, enter One step improves the signal to noise ratio of multi-path signalses.Linear transformation characteristic using frft, it is to avoid the interference of cross term during signal transacting, The inventive method is made to be particularly suitable for processing many ways or multi -components lfm signal.Analysis draws, two factors ensure that multi-path signalses In-band noise is effectively suppressed: one is bandpass filtering and u domain hides the noise eliminating after the gradually segmentation to time-frequency plane, In-band noise composition is inhibited, this is any traditional time-domain filtering or frequency domain filtering method all cannot be realized in big degree； Two is that frft itself also has very strong inhibitory action to noise, this be due to frft kernel function be one group of lfm signal complete The characteristic of orthogonal basis determines.

Simulation example is carried out to the method for the present invention, to provide more intuitive description.Dissipate when not considering underwater acoustic channel In the case of effect, the signal model of multi-path signalses is represented by:

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

Wherein, s (t) is the transmission signal of known waveform, and n (t) is white Gaussian noise, m, a_iAnd τ_iRespectively induction signal is passed Broadcast the number in path, the amplitude of echo-signal and time delay on the i-th paths.

Set lfm underwater sound multi-path signalses in emulation and include 4 echo-signal components, each component of signal respective amplitude is followed successively by 1, 0.9th, 0.7 and 0.6, time delay is followed successively by 0,0.5,1.4 and 2.2ms, and Signal-to-Noise is 3db.Introduce noise after cannot from when Domain distinguishes each component of signal, and this point can clearly be found by Fig. 5 (a)；Fig. 5 (b) is ways many after bandpass filtering treatment The matched filtering output of signal, although matched filtering can suppress out-of-band noise composition effectively, because lfm believes for broadband Number, still suffer from substantial amounts of interference signal in band, lead to still include a large amount of interference components in matched filtering output；Fig. 5 (c) be through This method suppresses the matched filtering output of multi-path signalses after noise, because this method inhibits substantial amounts of in-band noise composition, Join the output signal that filtering output has obtained more high s/n ratio, with the matched filtering output signal providing multi-path signalses during noiseless Fig. 5 (d) compare discovery, this method has drastically increased the signal to noise ratio of multi-path signalses, effectively eliminates observation signal It is suppressed that the in-band noise composition of observation signal, noise suppression effect is obvious for in-band noise.

Frft fast algorithm in the present invention mainly to be realized using fft, its computation complexity and the same magnitude of fft. Because this method is mainly made up of fft and frft, therefore, mainly by fft fast algorithm implementation, amount of calculation is little for this method, can answer For engineering real-time implementation, frft is linear transformation in addition, and processing procedure is not disturbed by cross term, and therefore, this method is also special It is not suitable for processing many ways or multi -components lfm signal.

Claims (1)

1. a kind of noise suppressing method of lfm underwater sound multi-path signalses is it is characterised in that comprise the following steps:

(1) the optimal transformation exponent number p of optimum fractional order fourier conversion is obtained according to deterministic signal parameter_opt；

(2) lfm multi-path signalses are carried out with bandpass filtering pretreatment, suppresses out-of-band noise；

(3) bandpass filtering output signal is done with hilbert conversion, obtains analytic signal；

(4) p is done to analytic signal_optRank fractional order fourier converts；

(5) make frequency spectrum in Fractional Fourier Domain to hide every process, suppress in-band noise；

(6) it is-p_optRank fractional order fourier inverse transformation, the high s/n ratio multi-path signalses of the noise that is inhibited；

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

$x_{\mathrm{\α}}\left(u\right)=\{f^{\mathrm{\α}}\[x\left(t\right)\]\}\left(u\right)={\&integral;}_{-\mathrm{\∞}}^{\mathrm{\∞}}x\left(t\right)k_{\mathrm{\α}}(t,u)dt$

In formula, α=p pi/2 is the corresponding coordinate system anglec of rotation, the transformation kernel k of fourier conversion_α(t, u) is:

$k_p(t,u)=\left\{\begin{array}{cc}\sqrt{\frac{1-j\cot \mathrm{\α}}{2\mathrm{\π}}}\exp (j\frac{t^2+u^2}{2}\cot \mathrm{\α}-jtu\csc \mathrm{\α}),& \mathrm{\α}\&notequal;n\mathrm{\π}\\ \mathrm{\δ}(t-u),& \mathrm{\α}=n\mathrm{\π}\\ \mathrm{\δ}(t+u),& \mathrm{\α}\&notequal;(2n\&plusminus;1)\mathrm{\π}\end{array}\right.$

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

$x\left(t\right)={\&integral;}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{x}_p\left(u\right)k_{-p}(t,u)du;$

The frequency band range that described step (5) intermediate frequency spectrum hides every processing is:

Wherein, t ' is the length choosing pending signal；t_lfmFor transmission signal pulsewidth；T is actual treatment signal length, δ τ_max For the corresponding maximum delay of component of signal each in multi-path signalses, meet t≤2t_lfm+2f_l/ k, otherwise, by pending in selection 0 is mended, " [] " represents interval range after signal.