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 includes: performing Hilbert transform on the received signal to obtain the analytical signal of the received signal; taking the absolute value of the obtained analytical signal to obtain the envelope signal of the received signal; performing detrending processing on the obtained envelope signal to remove the influence of the direct wave amplitude; performing Hilbert transform on the obtained signal again to obtain the analytical signal of the envelope; taking the absolute value of the analytical signal of the envelope to obtain the envelope signal of the envelope; performing Fourier transform on the obtained envelope signal to obtain the envelope spectrum of the envelope; and reading the modulation frequency and demodulation depth from the envelope spectrum of the envelope. The present invention does not require direct wave suppression and can directly extract the modulation features of the received signal, accurately obtain the modulation frequency, and directly obtain the demodulation depth. The calculation method of the present invention is simple and the calculation results are 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 navigates 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 oscillations (VLF) from underwater moving objects will be an effective way to increase the detection range of underwater targets. To date, research on underwater VLF modulated acoustic scattering has focused primarily on its generation mechanism, with very little research on VLF modulation feature extraction. Russian experiments and literature do not provide detailed descriptions of modulation feature extraction methods, stating only that modulation is derived from long-term observations of the received signal envelope. When using bistatic sonar to detect underwater moving objects, the relative motion between the target and the receiving transducer inevitably introduces Doppler shift, which is highly likely to occur simultaneously with VLF modulation in the scattered signal. Extracting modulation features by removing the influence of Doppler frequency through de-skewing requires performing a forward-scattered signal on the target while completely suppressing the direct wave, but this is extremely difficult. Summary of the Invention

[0004] To address the technical problems inherent in the prior art, the present invention provides a very low frequency (VLF) modulation feature extraction method based on a double Hilbert transform. The purpose of this invention is to extract modulation features, including modulation frequency and demodulation depth, from received signals in the presence of direct wave interference and Doppler shift interference. Based on specific scenarios and previous theoretical and methodological research, the present invention utilizes two Hilbert transforms to directly extract the envelope spectrum of the received signal containing the direct wave and forward scattered signals, thereby extracting the VLF modulation features.

[0005] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0006] The present invention provides a very low frequency modulation feature extraction method based on double Hilbert transform, which specifically includes the following steps:

[0007] (a) Performing Hilbert transform on the received signal to obtain the 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 the 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 can be 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] Furthermore, 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 frequency of the transmitted signal, 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 lower frequency 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 frequency of the transmitted 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, t is the time, f l is the lower frequency 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 frequency of the transmitted 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, t is the time, f l is the lower frequency 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 frequency of the transmitted 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, t is the time, f l is the lower frequency 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 frequency of the transmitted signal, 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 lower frequency limit, and k is the linear frequency modulation slope of the linear frequency modulation pulse.

[0030] Furthermore, in step (e), the envelope signal of the envelope is calculated as follows:

[0031]

[0032] Where S is the amplitude of the forward scattered signal, 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.

[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 the modulation characteristics of the received signal;

[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 results are accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 The present invention provides a flowchart 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 will be described in further detail below with reference to 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 the 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 frequency is the upper limit, then the linear frequency modulation slope is k. Without considering the influence of channel multipath and noise, the received signal can be simplified as follows:

[0048]

[0049] Where D is the amplitude of the direct wave signal, S is the amplitude of the forward scattered signal, f is the frequency of the transmitted signal, 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) Detrend 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 the absolute value of the envelope complex 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 between direct waves and Doppler frequency shift by extracting the envelope spectrum of the envelope of the received signal, and accurately obtains the 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 embodiments described 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 efforts 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 is convolved with the channel to generate the received 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 graph 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 as follows 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 in the figure, the amplitudes of the envelope spectra at different modulation depths are almost the same at the DC component, but there are obvious differences in the amplitudes 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 principles of the present invention. These improvements and modifications should also be regarded as within 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) Perform Hilbert transform on the received signal to obtain the analytical signal of the received signal; (b) taking the absolute value of the analytical signal obtained in step (a) to obtain the envelope signal of the received signal; (c) Detrending the envelope signal obtained in step (b) to remove the influence of the direct wave amplitude; In step (c), after detrending, we get: ； in, (t) is the envelope signal after detrending, is the amplitude of the forward scattered signal, is the frequency of the transmitted signal, is the modulation frequency, 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, For time, is the lower frequency limit, is the linear frequency modulation slope of the linear frequency modulation pulse; (d) performing Hilbert transform again on the signal obtained in step (c) to obtain an analytical signal of the envelope; (e) taking the 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 obtained in step (f).

2. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1, 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 , is the lower frequency limit, As the upper frequency limit, the linear frequency modulation slope is .

3. The very low frequency modulation feature extraction method based on double Hilbert transform according to claim 1, characterized in that: In step (a), the received signal is simplified to: ； in, is the amplitude of the direct wave signal, is the amplitude of the forward scattered signal, is the frequency of the transmitted signal, is the modulation frequency, 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, For time, is the lower frequency limit, 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, characterized in that: In step (a), the analytical signal obtained after Hilbert transform is: ； in, , is the amplitude of the direct wave signal, is the amplitude of the forward scattered signal, is the frequency of the transmitted signal, is the modulation frequency, 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, For time, is the lower frequency limit, 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: ； in, represents the absolute value operation, , is the amplitude of the direct wave signal, is the amplitude of the forward scattered signal, is the frequency of the transmitted signal, is the modulation frequency, 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, For time, is the lower frequency limit, 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 (d), the envelope complex signal obtained by performing a second Hilbert transform on the detrended envelope is: ； in, is the amplitude of the forward scattered signal, is the frequency of the transmitted signal, is the modulation frequency, 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, For time, is the lower frequency limit, 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 (e), the envelope signal of the envelope is calculated as follows: ； in, is the amplitude of the forward scattered signal, is the modulation frequency, 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, For time.

Images