Very low frequency modulation feature extraction method based on double Hilbert transform

Abstract

A very low frequency modulation feature extraction method based on double Hilbert transform belongs to the field of underwater acoustic signal processing, and comprises the following steps: performing Hilbert transform on a received signal to obtain an analytic signal of the received signal; the absolute value of the obtained analysis signal is obtained, and an envelope signal of the received signal is obtained; performing detrending processing on the obtained envelope signal to remove the influence of the amplitude of the direct wave; performing Hilbert transform on the obtained signal again to obtain an enveloped analysis signal; the absolute value of the obtained analysis signal of the envelope is obtained, and an envelope signal of the envelope is obtained; fourier transform is carried out on the obtained envelope signal of the envelope, and an envelope spectrum of the envelope is obtained; and reading the modulation frequency and the demodulation depth from the obtained envelope spectrum of the envelope. According to the method, direct wave suppression is not needed, the modulation characteristics of the received signals can be directly extracted, the modulation frequency can be accurately obtained, and the demodulation depth can be directly obtained. The calculation method is simple, and the calculation result is accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic signal processing, and in particular relates to a very low frequency modulation feature extraction method based on double Hilbert transform. Background Art

[0002] With the development of vibration reduction and noise reduction technology, it is becoming increasingly difficult to detect underwater targets through the radiation noise, and the frequency of underwater acoustic detection is gradually becoming very low frequency. When a moving body is sailing underwater, it will produce extremely low-frequency periodic motion, thereby exciting the fluid medium around the moving body to produce water gravity waves of the same frequency. Wang Huan et al. (Wang H, Fang E, Wu M, et al. Ultra Low Frequency Wave Produced by Underwater Oscillating Sphere and Its Measurement [J]. Journal of Marine Science and Engineering, 2021, 9 (12): 1317.) verified the existence of very low frequency water gravity waves from both theoretical and experimental aspects. Water gravity waves will couple with the low-frequency sound emitted by the active sound source to produce forward scattered sound signals carrying modulation characteristics (Semenov A G. Ultra low frequency fields of moving bodies [M]. 2017: 1-240.). The modulation characteristics are often related to the tonnage, depth and speed of the moving body, so the target can be distinguished by the modulation characteristics.

[0003] The application of very low frequency oscillation of underwater moving bodies will become one of the effective ways to improve the detection distance of underwater targets. So far, the research on underwater very low frequency modulated acoustic scattering has focused more on the generation mechanism, and there is very little research on the extraction of very low frequency modulation features. There is no detailed introduction to the modulation feature extraction method in the relevant Russian experiments and literature, but it only explains that the modulation is obtained by observing the envelope of the received signal for a long time. When using dual-base sonar to detect underwater moving bodies, the relative movement of the target and the receiving transducer will inevitably cause Doppler frequency shift, and Doppler frequency shift and very low frequency modulation are very likely to appear in the scattered signal at the same time. The method of removing the influence of Doppler frequency by de-skewing and then extracting modulation features requires the target forward scattered signal to be processed on the basis of completely suppressing the direct wave, but it is very difficult to completely suppress the direct wave. Summary of the invention

[0004] In order to solve the technical problems existing in the prior art, the present invention provides a very low frequency modulation feature extraction method based on double Hilbert transform. The purpose of the present invention is to extract the modulation features carried in the received signal with direct wave interference and Doppler frequency shift interference, including modulation frequency and demodulation depth. Based on special scenarios and previous theoretical and methodological research, the present invention uses two Hilbert transforms to directly extract the envelope spectrum of the envelope of the received signal containing the direct wave and the forward scattered signal, thereby realizing the extraction of very low frequency modulation features.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] The very low frequency modulation feature extraction method based on double Hilbert transform provided by the present invention specifically comprises the following steps:

[0007] (a) performing Hilbert transform on the received signal to obtain an analytical signal of the received signal;

[0008] (b) taking the absolute value of the analytical signal obtained in step (a) to obtain an envelope signal of the received signal;

[0009] (c) performing detrending processing on the envelope signal obtained in step (b) to remove the influence of the direct wave amplitude;

[0010] (d) performing Hilbert transform again on the signal obtained in step (c) to obtain an analytical signal of the envelope;

[0011] (e) taking an absolute value of the analytical signal of the envelope obtained in step (d) to obtain an envelope signal of the envelope;

[0012] (f) performing Fourier transform on the envelope signal of the envelope obtained in step (e) to obtain an envelope spectrum of the envelope;

[0013] (g) Read the modulation frequency and demodulation depth from the envelope spectrum of the envelope obtained in step (f).

[0014] Furthermore, within a certain time range, the Doppler frequency shift is approximately regarded as linear frequency modulation, and the frequency modulation range of the linear frequency modulation pulse is f l -f h , f l is the lower frequency limit, f h is the upper frequency limit, then its linear frequency modulation slope is k.

[0015] Further, in step (a), the received signal is simplified to:

[0016]

[0017] Where D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, and m is the modulation depth. is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

[0018] Furthermore, in step (a), the analytical signal obtained by Hilbert transform is:

[0019]

[0020] Among them, j 2 =-1, D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

[0021] Furthermore, in step (b), the calculation formula of the envelope signal of the received signal is:

[0022]

[0023] Among them, || represents the absolute value operation, j 2 =-1, D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

[0024] Furthermore, in step (c), after detrending, we obtain:

[0025]

[0026] Among them, a 11 (t) is the envelope signal after detrending, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

[0027] Furthermore, in step (d), by performing a second Hilbert transform on the detrended envelope, the complex envelope signal obtained is:

[0028]

[0029] Where S is the amplitude of the forward scattered signal, f is the transmitted signal frequency, f0 is the modulation frequency, and m is the modulation depth. is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

[0030] Furthermore, in step (e), the calculation formula of the envelope signal of the envelope is:

[0031]

[0032] Where S is the amplitude of the forward scattered signal, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, and t is the time.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) The present invention does not require direct wave suppression and can directly extract modulation features from received signals;

[0035] (2) The present invention can accurately obtain the modulation frequency;

[0036] (3) The present invention can directly obtain the demodulation depth;

[0037] (4) The calculation method of the present invention is simple and the calculation result is accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 The present invention provides a flow chart of a very low frequency modulation feature extraction method based on double Hilbert transform.

[0039] Figure 2 is the LOFAR spectrum of the received signal.

[0040] Figure 3 is the envelope of the received signal.

[0041] Figure 4 is the envelope of the received signal after detrending.

[0042] Figure 5is the envelope spectrum of the envelope of the received signal.

[0043] Figure 6 It is the envelope spectrum of the envelope under different modulation depths. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0045] See also Figure 1 To illustrate, the present invention provides a very low frequency modulation feature extraction method based on double Hilbert transform, and its specific implementation process is as follows:

[0046] (a) performing Hilbert transform on the received signal to obtain an analytical signal of the received signal;

[0047] Within a certain time range, Doppler frequency shift can be approximately regarded as linear frequency modulation. The frequency modulation range of the linear frequency modulation pulse is f l -f h , f l is the lower frequency limit, f h If the upper frequency limit is , the linear frequency modulation slope is k. Without considering the influence of channel multipath and noise, the received signal can be simplified as:

[0048]

[0049] Where D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, and m is the modulation depth. is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, and t is the time.

[0050] The analytical signal obtained after Hilbert transform is:

[0051]

[0052] Among them, j 2 =-1.

[0053] (b) taking the absolute value of the analytical signal obtained in step (a) to obtain the envelope of the received signal; wherein the envelope of the received signal is specifically:

[0054]

[0055] Here, || represents the absolute value operation.

[0056] (c) Detrending the signal obtained in step (b) to remove the influence of the direct wave amplitude; after detrending, we get:

[0057]

[0058] Among them, a 11 (t) is the envelope signal after detrending.

[0059] (d) performing Hilbert transform again on the signal obtained in step (c) to obtain an envelope complex signal;

[0060] By performing a second Hilbert transform on the detrended envelope, the complex envelope signal obtained is:

[0061]

[0062] (e) taking an absolute value of the complex envelope signal obtained in step (d) to obtain an envelope signal of the envelope; wherein the envelope signal of the envelope is specifically:

[0063]

[0064] (f) performing Fourier transform on the envelope signal of the envelope obtained in step (e) to obtain an envelope spectrum of the envelope;

[0065] (g) Read the modulation frequency and demodulation depth from the envelope spectrum of the envelope obtained in step (f).

[0066] The present invention discloses a very low frequency modulation feature extraction method based on double Hilbert transform, which eliminates interference of direct wave and Doppler frequency shift by extracting envelope spectrum of the envelope of received signal, and accurately obtains modulation frequency and demodulation depth.

[0067] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0068] The example parameter settings are as follows: the transmission signal frequency is 500Hz, the modulation frequency is 0.2Hz, the modulation depth is 0.2, and the transmission signal and the channel are convolved to generate the receiving signal. The modulation frequency and demodulation depth are accurately obtained by using a very low frequency modulation feature extraction method based on double Hilbert transform of the present invention. Figure 2 The LOFAR diagram of the received signal is given by Figure 2 It can be seen that the received signal is consistent with the simplified signal form given in step (a).

[0069] The envelope of the received signal is Figure 3 As shown, the required information cannot be obtained from it and further processing is required.

[0070] The envelope of the received signal after detrending is as follows: Figure 4 As shown, the modulation frequency and other information cannot be directly read from the time domain diagram. It is necessary to perform Fourier transform on it to obtain the frequency domain information and then extract the required features.

[0071] The envelope spectrum of the received signal envelope is as follows Figure 5 As shown, the modulation frequency can be clearly read from the envelope spectrum as 0.2 Hz.

[0072] The envelope spectrum of the envelope at different modulation depths is as follows: Figure 6 As shown, the amplitude of the envelope spectrum at different modulation depths is almost the same at the DC component, and there is a significant difference in the amplitude at the modulation component, and the trend of the size change is consistent with the modulation depth.

[0073] The error analysis table of modulation depth and demodulation depth is shown in Table 1. From the data in Table 1, it can be seen that the error of demodulation depth is within 17%, which is relatively accurate.

[0074] Table 1

[0075] Modulation Depth Demodulation Depth error 0.1 0.084 15.87％ 0.2 0.167 16.42％ 0.3 0.260 13.28％ 0.4 0.343 14.31％ 0.5 0.459 8.25％ 0.6 0.521 13.20％ 0.7 0.612 12.58％ 0.8 0.725 9.34％

[0076] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A very low frequency modulation feature extraction method based on double Hilbert transform, characterized in that: The following steps are involved: (a) performing Hilbert transform on the received signal to obtain an analytical signal of the received signal; (b) taking the absolute value of the analytical signal obtained in step (a) to obtain an envelope signal of the received signal; (c) performing detrending processing on the envelope signal obtained in step (b) to remove the influence of the direct wave amplitude; (d) performing Hilbert transform again on the signal obtained in step (c) to obtain an analytical signal of the envelope; (e) taking an absolute value of the analytical signal of the envelope obtained in step (d) to obtain an envelope signal of the envelope; (f) performing Fourier transform on the envelope signal of the envelope obtained in step (e) to obtain an envelope spectrum of the envelope; (g) Read the modulation frequency and demodulation depth from the envelope spectrum of the envelope obtained in step (f).

2. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1 is characterized in that: Within a certain time range, the Doppler frequency shift is approximately regarded as linear frequency modulation, and the frequency modulation range of the linear frequency modulation pulse is f l -f h , f l is the lower frequency limit, f h is the upper frequency limit, then its linear frequency modulation slope is k.

3. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1 is characterized in that: In step (a), the received signal is simplified to: Where D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, and m is the modulation depth. is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

4. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1 is characterized in that: In step (a), the analytical signal obtained after Hilbert transform is: Among them, j 2 =-1, D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

5. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1, characterized in that: In step (b), the calculation formula of the envelope signal of the received signal is: Among them, || represents absolute value operation, j 2 =-1, D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

6. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1, characterized in that: In step (c), after detrending, we get: Among them, a 11 (t) is the envelope signal after detrending, S is the amplitude of the forward scattered signal, f is the transmission signal frequency, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

7. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1, characterized in that: In step (d), by performing a second Hilbert transform on the detrended envelope, the complex envelope signal obtained is: Where S is the amplitude of the forward scattered signal, f is the transmit signal frequency, f0 is the modulation frequency, and m is the modulation depth. is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, t is the time, f l is the frequency lower limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

8. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1, characterized in that: In step (e), the calculation formula of the envelope signal of the envelope is: Where S is the amplitude of the forward scattered signal, f0 is the modulation frequency, m is the modulation depth, is the phase difference between the scattered signal and the direct wave signal, is the initial phase of the modulation signal, and t is the time.

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