Ship radiated noise envelope spectrum estimation method based on spectrum whitening

Abstract

This invention discloses a method for estimating the envelope spectrum of ship radiated noise based on spectral whitening, belonging to the field of underwater acoustic signal processing. The method first determines the main frequency band containing the modulation characteristics of the target signal through cyclic modulation spectrum analysis; then, it processes the background noise spectrum within the main frequency band using smoothing, and calculates a spectral shaping factor based on the median of the smoothed spectrum to construct a conjugate symmetric whitening filter; finally, it performs weighted shaping of the target signal spectrum in the frequency domain, and restores the whitened spectrum to the time domain for amplitude demodulation and power spectrum analysis. This invention effectively improves the signal-to-noise ratio (SNR) of broadband envelope spectrum estimation by introducing a spectral whitening mechanism, providing a reliable guarantee for accurately extracting physical characteristics such as the number and rotational speed of ship propellers. Experiments show that this method can improve the average SNR of the envelope spectrum by approximately 7 dB, demonstrating strong engineering practical value.

Description

Technical Field

[0001] This application belongs to the field of underwater acoustic target detection and target signal parameter estimation. Specifically, it relates to a method for estimating the envelope spectrum of ship radiated noise based on spectral whitening. Background Technology

[0002] In the field of underwater acoustic target detection, envelope spectrum analysis is a core method for extracting the physical features of targets. By analyzing the envelope frequency of radiated noise, key information such as the number of propeller blades and the rotational speed of the shaft can be effectively extracted, which is of great significance for target classification and identification. The signal-to-noise ratio (SNR) of the envelope spectrum directly affects the accuracy of feature extraction; therefore, obtaining envelope spectrum estimation results with high SNR has always been a research focus in this field.

[0003] Traditional envelope spectrum estimation methods typically employ bandpass filters to extract the frequency band containing modulation information, followed by demodulation and power spectrum analysis. To improve performance, existing technologies also include methods that extract and fuse features from multiple sub-bands, or utilize the correlation of envelope spectra between sub-bands to enhance the signal-to-noise ratio.

[0004] However, in real-world marine environments, the spectrum of ship-radiated noise is non-flat, resulting in significant spectral attenuation of background noise when using wide-bandwidth demodulation. The energy distribution of background noise varies significantly across different frequencies, leading to a masking effect of strong low-frequency noise on high-frequency intensity characteristics when using wideband envelope spectrum estimation. This reduces the signal-to-noise ratio (SNR) of traditional envelope spectrum estimation methods. Therefore, effectively suppressing the spectral non-flatness of wideband background noise and improving the SNR of wideband envelope spectrum estimation when the background noise spectrum is non-flat is a crucial technical problem that urgently needs to be solved in the field of underwater acoustic signal processing. Summary of the Invention

[0005] This application aims to address the issue of decreased signal-to-noise ratio in the envelope spectrum obtained by broadband demodulation when traditional envelope spectrum estimation methods suffer from significant variations in the spectral levels of the background noise spectrum. A method for estimating the envelope spectrum of ship radiated noise based on spectral whitening is provided.

[0006] The technical solution adopted in this application to solve the above-mentioned technical problems is: a method for estimating the envelope spectrum of ship radiated noise based on spectral whitening, which includes the following steps:

[0007] Step 1: Perform cyclic modulation spectrum analysis on the target signal and calculate its signal-to-noise ratio (SNR). Based on the SNR distribution results, determine the main frequency band where the modulation characteristics of the target signal are located.

[0008] Step 2: Perform a Fast Fourier Transform on the background noise to obtain its spectrum. The specific process is as follows:

[0009] The collected background noise has a length of sequence ,in Index of time sampling points Perform a Fourier transform on the sequence to obtain the spectrum of the background noise. The expression is:

[0010] ,

[0011] In the formula It is a frequency index;

[0012] Step 3: Within the main frequency band, extract the envelope of the background noise spectrum and smooth it to obtain the smoothed noise spectrum;

[0013] Step 4: Based on the smoothed noise spectrum, calculate the spectral shaping factor of each frequency point in the main frequency band, and construct the response function of the whitening filter accordingly.

[0014] Step 5: Perform a Fast Fourier Transform on the target signal to obtain the target signal spectrum, and use the response function of the whitening filter to perform weighted shaping on the target signal spectrum to obtain the whitened spectrum;

[0015] Step 6: Perform an inverse Fourier transform on the whitened spectrum to obtain the whitened time-domain signal, perform amplitude demodulation on the whitened time-domain signal to extract the envelope signal, and perform power spectrum analysis on the envelope signal to obtain the envelope spectrum estimation result.

[0016] Furthermore, the specific process of determining the main frequency band in step one is as follows:

[0017] The target signal is of length sequence ,in Index of time sampling points ;

[0018] First, the target signal sequence The time-frequency spectrum is obtained by performing a short-time Fourier transform, where the window function of the transform is... Window length points correspond , For the index of sampling points within the window, ;

[0019] Moving between adjacent windows If the number of points is [number], then the total number of time windows is [number]. ,in This indicates the floor function, which yields the time spectrum. The expression is:

[0020] ,

[0021] in, It is a time window index; Using the frequency index of the spectrum, a Fourier transform is performed along the time axis on the time spectrum to obtain the cyclic modulation spectrum. :

[0022] ,

[0023] in This is the frequency index for the envelope spectrum.

[0024] Calculate the signal-to-noise ratio (SNR) of the cyclic modulation spectrum at each frequency, and confirm the main frequency band of the target modulation feature based on the SNR distribution results.

[0025] Furthermore, before calculating the signal-to-noise ratio, a bidirectional filter is used to filter the cyclic modulation spectrum. Background estimation is performed at each spectral frequency along the direction of the envelope spectral frequency. The specific process is as follows:

[0026] Background estimation results Take the positive smoothing result and reverse smoothing results The mean, specifically expressed as:

[0027] ,

[0028] Both the forward smoothing and the reverse smoothing are implemented using first-order recursive formulas, specifically:

[0029] ,

[0030] In the formula This is a smoothing coefficient, with a range of values. This is used to control the weight between the current background value and historical values, with the following initial conditions:

[0031] ,

[0032] Calculate the signal-to-noise ratio of the cyclic modulation spectrum based on the background value. for:

[0033] .

[0034] Furthermore, the specific process for obtaining the smoothed noise spectrum in step three is as follows:

[0035] Based on the main frequency band range determined in step one Extract the envelope information of the spectrum from the background noise spectrum obtained in step two. ,in This indicates a modulo operation; the main frequency band includes... There are discrete frequency points, and the frequency index of each frequency point is denoted as . ,in It is the frequency sequence number;

[0036] noise spectrum envelope within the main frequency band Smoothing is performed to obtain the smoothed noise spectrum. The smoothing process is achieved through the following recursive formula:

[0037] ,

[0038] In the formula This is the smoothing coefficient, and its value range is... The initial value of the smoothing process is .

[0039] Furthermore, based on the smoothed noise spectrum obtained in step three, the spectral shaping factor of each frequency point within the modulation main frequency band is calculated, and the response function of the whitening filter is constructed accordingly. The specific process is as follows:

[0040] Based on the smoothed noise spectrum obtained in step three Calculate the spectral shaping factor at each frequency point. First, calculate the noise spectrum. The median is denoted as The spectral shaping factor is defined as the ratio of the baseline amplitude to the smoothed spectrum:

[0041] ,

[0042] in It is a preset constant scaling factor, median The value retrieval method is defined as follows:

[0043] Let the spectrum The finite set of numbers formed is Arranging all elements in the logarithm set in ascending order of their values ​​yields an ordered sequence.

[0044]

[0045] in It is the first There are several ordinal statistics. The median is... Defined as

[0046]

[0047] Furthermore, based on Construct the amplitude-frequency response function of the whitening filter. The specific process is as follows:

[0048] Within the main frequency band, the amplitude-frequency response is equal to the spectral shaping factor at the corresponding frequency point; outside the main frequency band, the response value is set to 1. Represented as:

[0049] ;

[0050] right The final response function is obtained by performing symmetry processing to satisfy the conjugate symmetry condition required for the real signal. The process is as follows:

[0051] ,

[0052] In the formula, It is the response function ultimately used for whitening the target signal.

[0053] Furthermore, the specific process of weighted shaping of the target signal spectrum in step five is as follows:

[0054] For target signal Perform a Fast Fourier Transform to obtain the corresponding spectrum. :

[0055]

[0056] The response function obtained in step four is used for whitening the target signal. The whitened spectrum is obtained by weighted shaping of the target signal spectrum in the frequency domain. Specifically:

[0057] .

[0058] Furthermore, the whitened spectrum obtained in step five is subjected to an inverse Fourier transform to obtain the corresponding time-domain signal, and the envelope spectrum is estimated using the time-domain signal. The specific process is as follows:

[0059] Based on the whitened spectrum of the target signal obtained in step five Perform an inverse Fourier transform on it to restore it to the time domain, and obtain the whitened time-domain signal. The inverse Fourier transform process is specifically represented as follows:

[0060] ,

[0061] In the formula The whitened time-domain signal is obtained by taking the real part of the corresponding inverse Fourier transform result of the spectrum. ;

[0062] Based on the main frequency band determined in step one, design a corresponding bandpass filter to extract the target signal in that frequency band. Let the unit impulse response of the bandpass filter be... ,in This is the filter delay index, and the filter length is... The whitened signal is filtered to obtain the filtered signal. :

[0063] ,

[0064] In the formula This is a convolution operation.

[0065] Furthermore, in step six, the filtered signal... The specific process of obtaining the envelope signal by amplitude demodulation is as follows:

[0066] ,

[0067] Extract using a low-pass filter Low-frequency components The envelope signal is used for subsequent envelope spectrum analysis.

[0068] Furthermore, in step six, the envelope signal... Perform power spectrum analysis to obtain envelope spectrum estimation results. The specific process is as follows:

[0069] ,

[0070] In the formula, It is the frequency index of the envelope spectrum.

[0071] This invention reshapes the target signal spectrum by constructing a whitening filter, effectively eliminating the impact of background noise non-flatness on broadband envelope spectrum estimation and solving the problem of high-frequency modulation features being masked under broadband demodulation. Through spectral whitening, the signal-to-noise ratio of the envelope spectrum is significantly improved, enhancing the extractability of target features and achieving overall enhancement of the main frequency band modulation features. Furthermore, when constructing the whitening filter, the median of the smoothed noise spectrum is preferably used as the reference amplitude. Simultaneously, conjugate symmetry processing is introduced during filter construction to ensure that the signal after frequency domain shaping remains a real signal after being restored back to the time domain, meeting the physical requirements for engineering implementation and possessing high engineering practicality and physical feasibility. The algorithm of this invention has a clear flow and moderate computational complexity, making it well-suited to the processing needs of existing underwater acoustic target detection systems. Attached Figure Description

[0072] Figure 1 This is a flowchart of a method for estimating the envelope spectrum of ship radiated noise based on spectral whitening.

[0073] Figure 2 It is the normalized power spectrum of the target signal and background noise before whitening;

[0074] Figure 3 It is the normalized power spectrum of the whitened target signal;

[0075] Figure 4 This is a comparison of the signal-to-noise ratio of the envelope spectrum before and after albinoing. Detailed Implementation

[0076] The following will describe the method for estimating the envelope spectrum of ship radiated noise based on spectral whitening, with reference to specific embodiments. Specific Implementation Example 1:

[0078] In this embodiment, the sampling frequency is 30kHz, and the total signal duration is 50s. The modulation main frequency band for simulating ship radiated noise is 200 Hz–4 kHz, and the fundamental frequency of the target signal's envelope spectrum modulation is 3 Hz. The background noise is non-flat noise, with the spectrum attenuating at a rate of -6 dB / oct from 200 Hz upwards. The 1.5 kHz–2.5 kHz sub-band has relatively strong modulation energy, with an input spectral level signal-to-noise ratio of 0 dB. The remaining range of the main frequency band corresponds to -10 dB, simulating the uneven distribution of modulation energy at different frequencies in a real marine environment. The frequency resolution of the demodulated envelope spectrum is 0.2 Hz. Figure 1 The method involves processing the target signal and background noise before whitening, calculating their power spectra, and combining this with... Figure 2 It can be observed that the modulation energy of the target signal is mainly concentrated in 1.5–2.5 kHz, and the cyclic modulation spectrum analysis shows that the modulation energy is distributed in the range of 200 Hz–4 kHz.

[0079] Step 1: Perform cyclic modulation spectrum analysis on the target signal and calculate its signal-to-noise ratio (SNR). Based on the SNR distribution results, determine the main frequency band where the modulation characteristics of the target signal are located.

[0080] First, the received target signal Process it.

[0081] Preferably, a window function is used. Obtain the time spectrum by performing a short-time Fourier transform on the signal. The cyclic modulation spectrum is obtained by performing a Fourier transform along the time axis. .

[0082] Furthermore, in order to obtain the signal-to-noise ratio estimation results, a bidirectional filter is used. Background estimation is performed at each spectral frequency along the direction of the envelope spectral frequency to obtain the background value. .

[0083] Background estimation results Take the positive smoothing result and reverse smoothing results The mean, specifically expressed as:

[0084] ,

[0085] Both the forward smoothing and the reverse smoothing are implemented using first-order recursive formulas, specifically:

[0086] ,

[0087] In the formula This is a smoothing coefficient, with a range of values. This is used to control the weight between the current background value and historical values, with the following initial conditions:

[0088] ,

[0089] Calculate the signal-to-noise ratio of the cyclic modulation spectrum based on the background value. for:

[0090] ,

[0091] In this embodiment, the modulation frequency band for simulating ship radiated noise is 200Hz–4kHz.

[0092] Step 2: Perform a Fast Fourier Transform on the background noise to obtain the background noise spectrum.

[0093] For the collected background noise sequence Perform a Fourier transform to obtain the spectrum of the background noise. The expression is:

[0094] ,

[0095] In the formula It is a frequency index;

[0096] Step 3: Within the main frequency band, extract the envelope of the background noise spectrum and smooth it to obtain the smoothed noise spectrum.

[0097] Preferably, the spectral envelope is extracted within the defined 200Hz-4kHz main frequency band. The smoothed noise spectrum is obtained. The smoothing process is achieved through the following recursive formula:

[0098] ,

[0099] In the formula This is the smoothing coefficient, and its value range is... The initial value of the smoothing process is .

[0100] Preferably, a filter capable of compensating for background unevenness is constructed based on the smoothed noise spectrum. Specifically:

[0101] Based on the smoothed noise spectrum Calculate the spectral shaping factor at each frequency point. First, calculate the noise spectrum. The median is denoted as The spectral shaping factor is defined as the ratio of the baseline amplitude to the smoothed spectrum:

[0102] ,

[0103] in It is a preset constant scaling factor, median The value retrieval method is defined as follows:

[0104] Let the spectrum The finite set of numbers formed is Arranging all elements in the logarithm set in ascending order of their values ​​yields an ordered sequence.

[0105] ,

[0106] in It is the first There are several ordinal statistics. The median is... Defined as

[0107] ,

[0108] Step 4: Based on the smoothed noise spectrum, calculate the spectral shaping factor of each frequency point in the main frequency band, and construct the response function of the whitening filter accordingly.

[0109] Furthermore, based on Construct the amplitude-frequency response function of the whitening filter. In the main frequency band, make it equal to Outside the main frequency band, its value is set to 1. To ensure physical feasibility, for The final response function is obtained by performing symmetry processing to satisfy the conjugate symmetry condition required for the real signal. :

[0110] ,

[0111] Step 5: Perform a Fast Fourier Transform on the target signal to obtain the target signal spectrum, and use the response function of the whitening filter to perform weighted shaping on the target signal spectrum to obtain the whitened spectrum.

[0112] Preferably, the specific process of weighted shaping of the target signal spectrum is as follows:

[0113] For target signal Perform a Fast Fourier Transform to obtain the corresponding spectrum. :

[0114]

[0115] Combination Figure 3 This explains the use of the response function to the whitening process of the target signal. The whitened spectrum is obtained after weighted shaping of the target signal spectrum in the frequency domain:

[0116] The response function obtained in step four is used for whitening the target signal. The whitened spectrum is obtained by weighted shaping of the target signal spectrum in the frequency domain. :

[0117] .

[0118] This step enhances the modulation characteristics of the main frequency band while suppressing the masking effect of strong low-frequency background noise on high-frequency modulation components.

[0119] Preferably, for Perform an inverse Fourier transform and take the real part to restore it to the time domain, thus obtaining the whitened time-domain signal. Specifically:

[0120] ,

[0121] In the formula The whitened time-domain signal is obtained by taking the real part of the corresponding inverse Fourier transform result of the spectrum. .

[0122] Furthermore, based on the 200Hz-4kHz main frequency band determined in step 1, a corresponding bandpass filter is designed to extract the target signal in this frequency band. Let the unit impulse response of the bandpass filter be... ,in This is the filter coefficient delay index, and the filter length is... ,right Filtering is performed to obtain the filtered signal. To accurately extract target modulation information within this frequency band:

[0123] ,

[0124] In the formula This is a convolution operation.

[0125] Step 6: Perform an inverse Fourier transform on the whitened spectrum to obtain the whitened time-domain signal, perform amplitude demodulation on the whitened time-domain signal to extract the envelope signal, and perform power spectrum analysis on the envelope signal to obtain the envelope spectrum estimation result.

[0126] Preferably, the filtered signal The specific process of obtaining the preliminary envelope signal by amplitude demodulation is as follows:

[0127] ,

[0128] Extract using a low-pass filter Low-frequency components The envelope signal is used for subsequent envelope spectrum analysis.

[0129] For envelope signal Perform power spectrum analysis to obtain envelope spectrum estimation results. The specific process is as follows:

[0130] ,

[0131] In the formula, It is the frequency index of the envelope spectrum.

[0132] Combination Figure 4 The final envelope spectrum signal-to-noise ratio estimation results were used to verify the implementation effect. In the simulated environment of this embodiment, the background noise gradually attenuated with increasing frequency, exhibiting non-flat characteristics. The experimental results show that after the spectrum whitening process described in this invention, the signal-to-noise ratio of the multi-order envelope spectrum is improved by an average of about 7dB compared with that before whitening. This proves that the method can effectively enhance the envelope spectrum characteristics in ship radiated noise, providing a high-quality data foundation for the accurate extraction of the number of propeller blades and the rotational speed of the shaft.

[0133] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0134] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for estimating the envelope spectrum of ship radiated noise based on spectral whitening, characterized in that, Includes the following steps: Step 1: Perform cyclic modulation spectrum analysis on the target signal and calculate its signal-to-noise ratio (SNR). Based on the SNR distribution results, determine the main frequency band where the modulation characteristics of the target signal are located. Step 2: Perform a Fast Fourier Transform on the background noise to obtain its spectrum. The specific process is as follows: The collected background noise has a length of sequence ,in Index of time sampling points Perform a Fourier transform on the sequence to obtain the spectrum of the background noise. The expression is: ， In the formula It is a frequency index; Step 3: Within the main frequency band, extract the envelope of the background noise spectrum and smooth it to obtain the smoothed noise spectrum; Step 4: Based on the smoothed noise spectrum, calculate the spectral shaping factor of each frequency point in the main frequency band, and construct the response function of the whitening filter accordingly. Step 5: Perform a Fast Fourier Transform on the target signal to obtain the target signal spectrum, and use the response function of the whitening filter to perform weighted shaping on the target signal spectrum to obtain the whitened spectrum; Step 6: Perform an inverse Fourier transform on the whitened spectrum to obtain the whitened time-domain signal, perform amplitude demodulation on the whitened time-domain signal to extract the envelope signal, and perform power spectrum analysis on the envelope signal to obtain the envelope spectrum estimation result.

2. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 1, characterized in that, The specific process for determining the main frequency band in step one is as follows: The target signal is of length sequence ,in Index of time sampling points ; First, the target signal sequence The time-frequency spectrum is obtained by performing a short-time Fourier transform, where the window function of the transform is... Window length points correspond , For the index of sampling points within the window, ; Moving between adjacent windows If the number of points is [number], then the total number of time windows is [number]. ,in This indicates the floor function, which yields the time spectrum. The expression is: ， in, It is a time window index; Using the frequency index of the spectrum, a Fourier transform is performed along the time axis on the time spectrum to obtain the cyclic modulation spectrum. : ， in For envelope spectrum frequency index' Calculate the signal-to-noise ratio (SNR) of the cyclic modulation spectrum at each frequency, and confirm the main frequency band of the target modulation feature based on the SNR distribution results.

3. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 2, characterized in that, Before calculating the signal-to-noise ratio, a bidirectional filter is used to analyze the cyclic modulation spectrum. Background estimation is performed at each spectral frequency along the direction of the envelope spectral frequency. The specific process is as follows: Background estimation results Take the positive smoothing result and reverse smoothing results The mean, specifically expressed as: ， Both the forward smoothing and the reverse smoothing are implemented using first-order recursive formulas, specifically: ， In the formula This is a smoothing coefficient, with a range of values. This is used to control the weight between the current background value and historical values, with the following initial conditions: ， Calculate the signal-to-noise ratio of the cyclic modulation spectrum based on the background value. for: 。 4. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 1, characterized in that, The specific process for obtaining the smoothed noise spectrum in step three is as follows: Based on the main frequency band range determined in step one Extract the envelope information of the spectrum from the background noise spectrum obtained in step two. ,in This indicates a modulo operation; the main frequency band includes... There are discrete frequency points, and the frequency index of each frequency point is denoted as . ,in It is the frequency sequence number; noise spectrum envelope within the main frequency band Smoothing is performed to obtain the smoothed noise spectrum. The smoothing process is achieved through the following recursive formula: ， In the formula This is the smoothing coefficient, and its value range is... The initial value of the smoothing process is .

5. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 1, characterized in that, Based on the smoothed noise spectrum obtained in step three, the spectral shaping factor of each frequency point within the modulation main frequency band is calculated, and the response function of the whitening filter is constructed accordingly. The specific process is as follows: Based on the smoothed noise spectrum obtained in step three Calculate the spectral shaping factor at each frequency point. First, calculate the noise spectrum. The median is denoted as The spectral shaping factor is defined as the ratio of the baseline amplitude to the smoothed spectrum: ， in It is a preset constant scaling factor, median The value retrieval method is defined as follows: Let the spectrum The finite set of numbers formed is Arranging all elements in the logarithm set in ascending order of their values ​​yields an ordered sequence. in It is the first There are several ordinal statistics. The median is... Defined as 6. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 5, characterized in that, based on Construct the amplitude-frequency response function of the whitening filter. The specific process is as follows: Within the main frequency band, the amplitude-frequency response is equal to the spectral shaping factor at the corresponding frequency point; outside the main frequency band, the response value is set to 1. Represented as: ； right The final response function is obtained by performing symmetry processing to satisfy the conjugate symmetry condition required for the real signal. The process is as follows: ， In the formula, It is the response function ultimately used for whitening the target signal.

7. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 1, characterized in that, The specific process of weighted shaping of the target signal spectrum in step five is as follows: For target signal Perform a Fast Fourier Transform to obtain the corresponding spectrum. : The response function obtained in step four is used for whitening the target signal. The whitened spectrum is obtained by weighted shaping of the target signal spectrum in the frequency domain. Specifically: 。 8. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 1, characterized in that, The whitened spectrum obtained in step five is subjected to an inverse Fourier transform to obtain the corresponding time-domain signal, and the envelope spectrum is estimated using the time-domain signal. The specific process is as follows: Based on the whitened spectrum of the target signal obtained in step five Perform an inverse Fourier transform on it to restore it to the time domain, and obtain the whitened time-domain signal. The inverse Fourier transform process is specifically represented as follows: ， In the formula The whitened time-domain signal is obtained by taking the real part of the corresponding inverse Fourier transform result of the spectrum. ; Based on the main frequency band determined in step one, design a corresponding bandpass filter to extract the target signal in that frequency band. Let the unit impulse response of the bandpass filter be... ,in This is the filter delay index, and the filter length is... The whitened signal is filtered to obtain the filtered signal. : ， In the formula This is a convolution operation.

9. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 8, characterized in that, Step six involves processing the filtered signal. The specific process of obtaining the envelope signal by amplitude demodulation is as follows: ， Extract using a low-pass filter Low-frequency components The envelope signal is used for subsequent envelope spectrum analysis.

10. The method for estimating the envelope spectrum of ship radiated noise based on spectral whitening according to claim 9, characterized in that, Step six involves the envelope signal. Perform power spectrum analysis to obtain envelope spectrum estimation results. The specific process is as follows: ， In the formula, It is the frequency index of the envelope spectrum.

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