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CN104316160A - Underwater sound signal instantaneous frequency demodulation method based on wavelet ridges - Google Patents

Underwater sound signal instantaneous frequency demodulation method based on wavelet ridges Download PDF

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CN104316160A
CN104316160A CN201410668406.7A CN201410668406A CN104316160A CN 104316160 A CN104316160 A CN 104316160A CN 201410668406 A CN201410668406 A CN 201410668406A CN 104316160 A CN104316160 A CN 104316160A
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wavelet
ridge
frequency
signal
instantaneous frequency
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CN104316160B (en
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张晓琳
张烈山
唐文彦
邹斌
王军
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Harbin Institute of Technology
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Abstract

The invention belongs to the technical field of underwater sound signal detection, and relates to underwater sound signal instantaneous frequency demodulation, in particular to an underwater sound signal instantaneous frequency demodulation method based on wavelet ridges. The method solves the problems that an existing conventional signal demodulation method is a spectral analysis method which cannot determine the instantaneous frequency of underwater sound signals, frequency detecting precision depends on a set frequency spectrum threshold value when the frequency of the underwater sound signals is calculated, and gross errors occur frequently. According to the technical scheme, signal wavelets are converted to obtain a wavelet conversion coefficient, the distribution positions of wavelet ridge points at all moments are obtained through a local mode maximum value method, center sizes of the wavelet ridges at all moments are calculated according to the distribution positions of the wavelet ridge points, and instantaneous frequencies of all moments are resolved according to the center sizes of the wavelet ridges. The underwater sound signal instantaneous frequency demodulation method based on the wavelet ridges is applicable to the fields of detection of sound generation frequency of an underwater sound generation target, detection of liquid surface sound wave frequency and measurement of vibration frequency of micro amplitude machines.

Description

Based on the underwater signal instantaneous frequency demodulation method of Wavelet Ridge
Technical field
The present invention relates to the demodulation of underwater signal instantaneous frequency, particularly relate to a kind of underwater signal instantaneous frequency demodulation method based on Wavelet Ridge, belong to underwater signal Detection Techniques field.
Background technology
The outside radiative acoustic wave of underwater sound source, can form the water surface sound wave of horizontal transmission at water surface, the vibration frequency of water surface sound wave is consistent with the audible frequency of underwater sound source, and therefore water surface sound wave carries the relevant information of underwater signal.Therefore, due to the needs of Underwater Target Detection, more and more pay attention to the detection to water surface sound wave and utilization.Laser interference method can obtain the frequency information of underwater signal from dynamic water surface, utilizes laser interference to become study hotspot to detect water surface sound wave gradually with the information obtaining underwater signal.Laser doppler detecting underwater acoustic signal is utilized to become one of important means obtaining underwater signal at present.
But in the current detection utilizing the underwater signal of laser interference method to detect to be only limitted to frequency stabilization signal, in practical application, the audible frequency of underwater signal often time become, conventional signal demodulating method is frequency spectrum analysis method, the method can not determine the instantaneous frequency of underwater signal; Moreover, when calculating the frequency of underwater signal by frequency spectrum analysis method, the detection accuracy of this method to frequency depends on the setting of frequency spectrum threshold value, usually occurs gross error.
Summary of the invention
The object of the invention is to propose a kind of underwater signal instantaneous frequency demodulation method based on Wavelet Ridge, be frequency spectrum analysis method with the signal demodulating method solved for existing routine, frequency spectrum analysis method can not determine the instantaneous frequency of underwater signal; When calculating the frequency of underwater signal, the detection accuracy of frequency is depended on to the setting of frequency spectrum threshold value, usually occur the problem of gross error.
The present invention for solving the problems of the technologies described above adopted technical scheme is:
A kind of underwater signal instantaneous frequency demodulation method based on Wavelet Ridge of the present invention, realizes according to following steps:
Step one, utilize Michelson laser interference system detect water surface;
Step 2, collection laser interference signal, described gatherer process is: interference signal by photoelectric detector, and is translated into electric signal, and this electric signal sends host computer to after being gathered by data collecting card;
Step 3, spectrum analysis is carried out to the interference signal collected;
Step 4, determine the observing result of wavelet transformation;
Step 5, wavelet transformation is carried out to interference signal;
Step 6, extract Wavelet Ridge according to the mould of wavelet conversion coefficient;
Step 7, filtering noise point;
Step 8, determine the Wavelet Ridge center yardstick in each moment;
Step 9, calculate each moment underwater signal instantaneous frequency according to Wavelet Ridge center yardstick.
The invention has the beneficial effects as follows:
1, the present invention can realize the extraction of underwater signal instantaneous frequency, namely can realize the detection of frequency conversion underwater signal, and solving routine can not the shortcoming of demodulation instantaneous frequency.
2, experiment shows, the demodulation accuracy of instantaneous frequency of the present invention is better than 100Hz.
3, for the extraction of the underwater signal frequency of frequency stabilization, the method that the present invention adopts has better anti-interference than conventional frequency spectrum analysis method, and the present invention is to the frequency measurement of frequency stabilization underwater signal, and precision can be better than 1Hz.
Accompanying drawing explanation
Fig. 1 is the basic light channel structure figure of typical Michelson interference system;
Fig. 2 is in embodiment one, the general step schematic diagram of Wavelet Ridge method determination underwater signal instantaneous frequency;
Fig. 3 is in experimental verification of the present invention, not the ridge feature schematic diagram of wavelet transformation in the same time, and wherein (a) is t=t 3500the ridge feature schematic diagram of the wavelet transformation in moment, (b) is t=t 3600the ridge feature schematic diagram of the wavelet transformation in moment;
Fig. 4 is in experimental verification of the present invention, wavelet module value distribution plan;
Fig. 5 is in experimental verification of the present invention, Wavelet Ridge distribution plan;
Fig. 6 is in experimental verification of the present invention, frequency change fitting a straight line result schematic diagram;
Embodiment
Composition graphs 1, Fig. 2 further describe the specific embodiment of the present invention.
Embodiment one: a kind of underwater signal instantaneous frequency demodulation method based on Wavelet Ridge described in present embodiment, comprises the following steps:
Step one, utilize Michelson laser interference system detect water surface;
Step 2, collection laser interference signal, described gatherer process is: interference signal by photoelectric detector, and is translated into electric signal, and this electric signal sends host computer to after being gathered by data collecting card;
Step 3, spectrum analysis is carried out to the interference signal collected, for determining the frequency distribution scope of underwater signal;
Step 4, determine the observing result of wavelet transformation;
After step 3, just can know the frequency range of signal spectrum, the observing result of wavelet transformation can be determined according to this scope in conjunction with morther wavelet centre frequency, sample frequency.
Step 5, wavelet transformation is carried out to interference signal;
Spectrum analysis described in step 3 is to determine range scale, is not necessary program code book being in reason.Here interference signal is exactly the signal referring to that data collecting card collects.
Step 6, extract Wavelet Ridge according to the mould of wavelet conversion coefficient;
Step 7, filtering noise point;
Carry out filtering by setting the method for threshold value exactly, have a setting to the minimum value of the mould of wavelet coefficient corresponding to Wavelet Ridge exactly, only have the mould when wavelet coefficient corresponding to Wavelet Ridge to be greater than this value, this ridge point is just considered to effective.
Step 8, determine the Wavelet Ridge center yardstick in each moment;
Step 9, calculate each moment underwater signal instantaneous frequency according to Wavelet Ridge center yardstick.
Laser interferance method detecting underwater acoustic signal is described below:
Underwater sound source sends the surface acoustic wave that acoustical signal can cause water surface horizontal transmission, and usually adopt homodyne optical interference circuit principle to detect water surface, typical homodyne interferometric method light path as shown in Figure 1.
Laser interference detecting underwater acoustic signal is all realized by the mode of detection water surface sound wave, by laser beam, detection light and reference light are divided into by spectroscope for homodyne interferometric method detection system light path, detection light incides water surface, return to meet with reference beam after being subject to the modulation of water surface sound wave and interfere, interference signal is by photoelectric detector, by photoelectric detector interference signal, and be translated into electric signal, this electric signal can be read by host computer by data collecting card and capture program, done process further by the interference signal that host computer reads and can demodulate the frequency of underwater sound source, such as do FFT conversion.
According to aforementioned measuring principle, the distribution of amplitudes of reference light can be expressed from the next:
E b(t)=A b sin(ω 0t+kz b+φ) (1)
In formula, ω 0---reference light angular frequency,
K---wave number, k = 2 π λ ;
The initial phase of Ф---laser beam.
The distribution of amplitudes measuring light can have following formula to state:
E m(t)=A msin(ω 0t+kz m+φ) (2)
Conjunction amplitude after two-beam converges is stated by following formula:
E(t)=E b(t)+E m(t)=A m sin(ω 0t+kz m+φ)+A b sin(ω 0t+kz b+φ) (3)
Therefore interference light intensity can be stated by following formula:
Light intensity is by photoelectric detector, and detector is not to front 3 high frequency items response (namely changing direct current signal into), and therefore, the light intensity signal that removal DC component receives can be stated by following formula:
I d=KA mA b cos[k(z m-z b)]=A d cos[k(z m-z b)] (5)
In formula, K---photodetector enlargement ratio.
From above formula, the signal of photoelectric detector is about reference light and the modulation signal measuring light optical path difference, and the optical path difference of two bundle laser is relevant with water surface Oscillation Amplitude by the initial length of two arms, optical path difference z m-z bcan be expressed from the next:
z m - z b = 2 ( L 1 - L 2 ) + 2 Σ n ( A n sin ( 2 π f n t + φ n ) ) + 2 A s sin ( 2 π f s t + φ s ) - - - ( 6 )
In formula, for the vibration on Natural Water surface, A ssin (2 π f st+ φ s) the water surface vibration that causes for underwater sound source, (L 1-L 2) for the water surface static time two-way light initial optical path difference, be designated as Δ L.Therefore the light intensity signal that photoelectric detector arrives can be stated by formula (7), carries out spectrum analysis and can obtain water surface sound wave frequency, be i.e. the audible frequency of underwater signal to this signal.
I d = A d cos { k [ 2 ΔL + 2 Σ n ( A n sin ( 2 π f n t + φ n ) ) + 2 A s sin ( 2 π f s t + φ s ) ] } - - - ( 7 )
Underwater signal laser interference detection method ultimate principle based on Wavelet Ridge is as follows:
This shortcoming of underwater signal frequency can not be determined in real time, the method process interference signal of research and utilization wavelet transformation for frequency spectrum analysis method.Suppose that the natural fluctuation of water surface is A without loss of generality nsin (2 π f nt+ φ n), so according to trigonometric function with difference eliminate indigestion formula, and Bezier identical relation formula (7) can be decomposed into f further nand f sinteger harmonics item and they with frequency item and difference frequency term sum, shown in (8), in formula, x 1=2kA n, x 2=2kA s.
I d = A d cos ( 2 kΔL ) J 0 ( x 1 ) J 0 ( x 2 ) - 2 A d sin ( 2 kΔL ) J 0 ( x 2 ) Σ m = 0 ∞ J 2 m + 1 ( x 1 ) sin ( ( 2 m + 1 ) ( 2 π f n t + φ n ) ) + 2 A d cos ( 2 kΔL ) J 0 ( x 2 ) Σ m = 0 ∞ J 2 m ( x 1 ) cos ( 2 m ( 2 πf n t + φ n ) ) - 2 A d sin ( 2 kΔL ) J 0 ( x 1 ) Σ m = 0 ∞ J 2 m + 1 ( x 2 ) sin ( ( 2 m + 1 ) ( 2 πf s t + φ s ) ) + 2 A d cos ( 2 kΔL ) J 0 ( x 1 ) Σ m = 1 ∞ J 2 m ( x 2 ) cos ( 2 m ( 2 π f s t + φ s ) ) - 4 A d cos ( 2 kΔL ) [ Σ m = 0 ∞ J 2 m + 1 ( x 1 ) sin ( ( 2 m + 1 ) ( 2 πf n t + φ n ) ) ] [ Σ m = 0 ∞ J 2 m + 1 ( x 2 ) sin ( ( 2 m + 1 ) ( 2 π f s t + φ s ) ) ] - 4 A d sin ( 2 kΔL ) [ Σ m = 1 ∞ J 2 m ( x 1 ) cos ( 2 m ( 2 π f n t + φ n ) ) ] [ Σ m = 0 ∞ J 2 m + 1 ( x 2 ) sin ( ( 2 m + 1 ) ( 2 π f s t + φ s ) ) ] + 4 A d cos ( 2 kΔL ) [ Σ m = 1 ∞ J 2 m ( x 1 ) cos ( 2 m ( 2 π f n t + φ n ) ) ] [ Σ m = 1 ∞ J 2 m ( x 2 ) cos ( 2 m ( 2 π f s t + φ s ) ) ] - 4 A d sin ( 2 kΔL ) [ Σ m = 0 ∞ J 2 m + 1 ( x 1 ) sin ( ( 2 m + 1 ) ( 2 π f n t + φ n ) ) ] [ Σ m = 1 ∞ J 2 m ( x 2 ) cos ( 2 m ( 2 π f s t + φ s ) ) ] - - - ( 8 )
The interference signal expression formula of observing after decomposing is known: the fluctuation due to Natural Water surface is low-frequency fluctuation, and a very important feature has appearred in the spectrum distribution of interference signal, namely with f scentered by a frequency band in there is the spectral line of comparatively dense, and the distribution of spectral line presents strict symmetry.The frequency that each spectral line is corresponding is f s± 2nf nor f s± (2n-1) f n, n ∈ N +.Their amplitude should be proportional to 2A respectively dsin (2k △ L) J 2n(x 1) J 1(x 2) and 2A dcos (2k △ L) J 2n-1(x 1) J 1(x 2), and f sthe amplitude of place's spectral line is then proportional to 2A dsin (2k △ L) J 0(x 1) J 1(x 2).
According to These characteristics, in this frequency band, may there be two kinds of situations the position of spectrum peak, depending on Bessel's function value J 0(x 1) and initial phase difference 2k Δ L sine and cosine value and determine, or be positioned at f=f splace, or be distributed in f=f symmetrically sthe left and right sides, even if the fluctuation on Natural Water surface has certain randomness, such spectrum distribution feature still runs through whole time domain scale.Therefore, when we carry out wavelet transformation to the interference signal received, observe in yardstick specific, Wavelet Ridge point is always along f splace size distribution, works as f sbe time dependent amount, so Wavelet Ridge point is then along f scorresponding yardstick time curve distributes.Therefore according to this conclusion, we can be judged by the instantaneous frequency (i.e. the instantaneous frequency of underwater signal) of position to water surface sound wave calculating Wavelet Ridge point.
Embodiment two: present embodiment and embodiment one unlike: the spectrum analysis described in step 3, refers to and adopts fast fourier transform algorithm, i.e. fft algorithm to the interference signal collected.Other step is identical with embodiment one.
Embodiment three: present embodiment and embodiment one or two unlike: the detailed process of the wavelet transformation described in step 5 is:
Select Morlet small echo to be morther wavelet, its mathematical expression formula is
ψ ( t ) = exp ( - t 2 2 σ ) exp ( j ω 0 t ) - - - ( 10 )
In formula, ω 0for the center angular frequency of morther wavelet, σ is Gaussian function parameter, and j is imaginary symbols, and t is the time, and its corresponding Fourier transform is:
ψ ( ω ) = 2 πσ exp [ - σ ( ω - ω 0 ) 2 2 ] - - - ( 11 )
ω is angular frequency, then as follows to the wavelet conversion coefficient computing formula of interference signal:
W f ( a , b ) = 1 α ∫ f ( t ) ψ ( t - b a ) dt - - - ( 12 )
In formula, be the family of functions that is morther wavelet with Morlet small echo, a is scale factor, and b is shift factor, namely by to the translation of wavelet mother function and the flexible family of functions obtained, the interference signal of f (t) for collecting, W f(a, b) is wavelet conversion coefficient.
Other step is identical with embodiment one or two.
Embodiment four: one of present embodiment and embodiment one to three unlike: the detailed process that the mould according to wavelet conversion coefficient described in step 6 extracts Wavelet Ridge is:
Wavelet conversion coefficient W is obtained according to wavelet conversion coefficient computing formula f(a, b), to wavelet conversion coefficient delivery value, then utilize local model maximum value-based algorithm to calculate local model maximum value, local model maximum value point is Wavelet Ridge point, obtains the distributing position (t of Wavelet Ridge point 0, a 0), t here 0be exactly the Wavelet Ridge point place moment, a 0it is exactly the yardstick at Wavelet Ridge point place.
The computation process of actual Wavelet Ridge point distributing position is as follows: what obtain after completing wavelet transformation is a series of wavelet coefficients, if time span is m, the scale length of calculating is n, and so wavelet coefficient is exactly the matrix of m*n, and we wonder t 0the Wavelet Ridge point distribution in moment, just t=t 0the wavelet coefficient in this moment is taken out, the wavelet coefficient at this time taken out is exactly the sequence of (1*n), there is which position in the maximum value calculating this sequence, that is which value of the sequence of calculation is maximum value, and scale-value corresponding to this maximum value is exactly the scale-value a of Wavelet Ridge point distributing position 0.Other step is identical with one of embodiment one to three.
Embodiment five: one of present embodiment and embodiment one to four unlike: the detailed process of the Wavelet Ridge center yardstick in each moment of determination described in step 8 is:
The position of Wavelet Ridge point or be positioned on dimension line corresponding to underwater signal frequency, or symmetrical point is listed in the upper and lower of dimension line.Therefore, for the moment only having a ridge point, this ridge point place yardstick is Wavelet Ridge center yardstick;
For the moment having two ridge points, then the mid point place yardstick of these two ridge points is Wavelet Ridge center yardstick, and the frequency that Wavelet Ridge center yardstick is corresponding is the instantaneous frequency in this moment.
Wavelet Ridge center yardstick is exactly the yardstick corresponding to Zhi Ge Wavelet Ridge dot center, hereafter there is explanation, two kinds of Wavelet Ridge states are carved with time different, one only has a ridge point, one is two ridge points, and for the situation only having a ridge point, Wavelet Ridge center yardstick is exactly yardstick corresponding to this ridge point, for the situation of two ridge points, Wavelet Ridge center yardstick is exactly the yardstick corresponding to mid point of these two Wavelet Ridge points.Other step is identical with one of embodiment one to four.
Embodiment six: one of present embodiment and embodiment one to five unlike: the detailed process calculating each moment underwater signal instantaneous frequency according to Wavelet Ridge center yardstick described in step 9 is:
Assuming that the Wavelet Ridge center yardstick of t interference signal is a c, so the instantaneous frequency f computing formula of underwater signal t is such as formula shown in (13), f in formula sfor the sampling rate of interference signal acquisition module
f=f a·f s/a c (13)
Wherein, f abeing the centre frequency of Morlet small echo, is a setting value.Other step is identical with one of embodiment one to five.
Experimental verification of the present invention is as follows:
For observing the characteristic distributions of Wavelet Ridge point, utilizing aforementioned homodyne interferometric method measuring system to carry out laser interference detection to the water surface sound wave that frequency is 2kHz, obtaining the interference signal by the modulation of water surface sound wave.In time-frequency domain, there is the parsing small echo of well focussed to carry out wavelet transformation as wavelet basis to this interference signal, obtain matrix of wavelet coefficients, calculate yardstick a corresponding to underwater signal frequency 2kHz according to the wavelet center frequency of setting and the time interval of signal sampling s=10.40.Figure 3 shows that two not wavelet module value in the same time with the distribution situation of dimensional variation, as seen from the figure, there are two kinds of distinct ridge features in the wavelet transformation of water surface sound wave laser interference detectable signal: Wavelet Ridge point or be positioned on yardstick corresponding to underwater signal frequency, or divide the both sides being listed in this yardstick, with theoretical analysis is consistent above.
For checking Wavelet Ridge method extracts the accuracy of underwater signal instantaneous frequency, the underwater signal that frequency linearly changes is detected, the frequency change rate of setting underwater signal is 8kHz/s, laser interference detection is carried out to this water surface sound wave, obtain interference signal and carry out the distribution of coefficient modulus value after wavelet transformation as shown in Figure 4, the local maximum place yardstick of wavelet module value changes along with the change of time as seen from the figure, and also namely the distributing position of Wavelet Ridge changes along with the change of water surface frequency of sound wave.As shown in Figure 5, the center of Wavelet Ridge point is that 7 to be reduced to yardstick be gradually 5 by yardstick to the distribution of Wavelet Ridge point, and this shows that Wavelet Ridge can the change of real-time follow-up water surface frequency of sound wave, and Wavelet Ridge place yardstick can reflect the instantaneous frequency of underwater signal.
According to the defining method of instantaneous frequency, calculate the instantaneous frequency in each moment in observation time, whether then matching frequency time straight line, calculate frequency change rate and match with actual value.Fitting result as shown in Figure 6, figure cathetus is frequency time change curve, the frequency change rate (i.e. slope) calculated is 8.12kHz/s, substantially match with theoretical value, its error is because the factors such as noise spot when frequency resolution and Wavelet Ridge extract cause, and this demonstrate that Wavelet Ridge method extracts the accuracy of underwater signal instantaneous frequency.
Technical scheme main line of the present invention is: 1) obtain wavelet conversion coefficient to signal wavelet transformation; 2) distributing position of each moment Wavelet Ridge point is obtained according to local model maximum value method; 3) the Wavelet Ridge center yardstick in each moment is calculated according to the distributing position of Wavelet Ridge point; 4) according to the instantaneous frequency in wavelet center yardstick each moment of reverse.The present invention be applicable to audible target audible frequency under water detection, liquid surface frequency of sound wave detection, small amplitude mechanical oscillation frequencies measurement.

Claims (6)

1., based on a underwater signal instantaneous frequency demodulation method for Wavelet Ridge, it is characterized in that said method comprising the steps of:
Step one, utilize Michelson laser interference system detect water surface;
Step 2, collection laser interference signal, described gatherer process is: interference signal by photoelectric detector, and is translated into electric signal, and this electric signal sends host computer to after being gathered by data collecting card;
Step 3, spectrum analysis is carried out to the interference signal collected;
Step 4, determine the observing result of wavelet transformation;
Step 5, wavelet transformation is carried out to interference signal;
Step 6, extract Wavelet Ridge according to the mould of wavelet conversion coefficient;
Step 7, filtering noise point;
Step 8, determine the Wavelet Ridge center yardstick in each moment;
Step 9, calculate each moment underwater signal instantaneous frequency according to Wavelet Ridge center yardstick.
2. the underwater signal instantaneous frequency demodulation method based on Wavelet Ridge according to claim 1, is characterized in that the spectrum analysis described in step 3, refers to and adopts fast fourier transform algorithm, i.e. fft algorithm to the interference signal collected.
3. the underwater signal instantaneous frequency demodulation method based on Wavelet Ridge according to claim 2, is characterized in that the detailed process of the wavelet transformation described in step 5 is:
Select Morlet small echo to be morther wavelet, its mathematical expression formula is
ψ ( t ) = exp ( - t 2 2 σ ) exp ( jω 0 t ) - - - ( 10 )
In formula, ω 0for the center angular frequency of morther wavelet, σ is Gaussian function parameter, and j is imaginary symbols, tfor the time, then as follows to the wavelet conversion coefficient computing formula of interference signal:
W f ( a , b ) = 1 a ∫ f ( t ) ψ ( t - b a ) dt - - - ( 12 )
In formula, be the family of functions that is morther wavelet with Morlet small echo, a is scale factor, and b is shift factor, namely by to the translation of wavelet mother function and the flexible family of functions obtained, the interference signal of f (t) for collecting, W f(a, b) is wavelet conversion coefficient.
4. the underwater signal instantaneous frequency demodulation method based on Wavelet Ridge according to claim 3, is characterized in that the detailed process of the extraction of the mould according to the wavelet conversion coefficient Wavelet Ridge described in step 6 is:
Wavelet conversion coefficient W is obtained according to wavelet conversion coefficient computing formula f(a, b), to wavelet conversion coefficient delivery value, then utilizes local model maximum value-based algorithm to calculate the distributing position (t that local model maximum value obtains Wavelet Ridge point 0, a 0), t here 0be exactly the Wavelet Ridge point place moment, a 0it is exactly the yardstick at Wavelet Ridge point place.
5. the underwater signal instantaneous frequency demodulation method based on Wavelet Ridge according to claim 4, is characterized in that the detailed process of the Wavelet Ridge center yardstick in each moment of determination described in step 8 is:
For the moment only having a ridge point, this ridge point place yardstick is Wavelet Ridge center yardstick;
For the moment having two ridge points, then the mid point place yardstick of these two ridge points is Wavelet Ridge center yardstick, and the frequency that Wavelet Ridge center yardstick is corresponding is the instantaneous frequency in this moment.
6. the underwater signal instantaneous frequency demodulation method based on Wavelet Ridge according to claim 5, is characterized in that the detailed process calculating each moment underwater signal instantaneous frequency according to Wavelet Ridge center yardstick described in step 9 is:
Assuming that the Wavelet Ridge center yardstick of t interference signal is a c, so the instantaneous frequency f computing formula of underwater signal t is such as formula shown in (13), f in formula sfor the sampling rate of interference signal acquisition module
f=f a·f s/a c (13)
Wherein, f abeing the centre frequency of Morlet small echo, is a setting value.
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