A high-precision amplitude-phase extraction method for GAFDEM signals

Abstract

The application is suitable for the technical field of ground-air frequency domain electromagnetic detection, and provides a GAFDEM signal high-precision amplitude and phase extraction method, which comprises the following steps: performing Fourier transform on a non-stationary multi-frequency GAFDEM signal to obtain a frequency spectrum representation of the signal; constructing a frequency domain mask according to a preset target frequency to eliminate interference components of adjacent frequency bands and retain narrowband spectrum information near the target frequency; performing inverse Fourier transform on the filtered frequency spectrum to reconstruct a narrowband time domain sub-signal corresponding to the target frequency; performing Hilbert transform on the narrowband time domain sub-signal to construct a complex analytic signal, and extracting an instantaneous amplitude and an instantaneous phase of the target frequency component from the complex analytic signal; and performing phase unwrapping processing on the instantaneous phase to obtain a continuous phase sequence. The application effectively suppresses spectrum aliasing and adjacent frequency interference, greatly simplifies the implementation of the algorithm, avoids the trouble of adjusting parameters in different noise environments, and is more adaptable.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ground-air frequency domain electromagnetic detection, and particularly relates to a high-precision amplitude and phase extraction method for GAFDEM signals. BACKGROUND

[0002] Ground-air frequency domain electromagnetic method (GAFDEM) is a semi-airborne electromagnetic exploration method for detecting large-depth underground structures. In this method, the ground transmitting system transmits single-frequency square waves or multi-frequency pseudo-random waves through a grounded long wire, and the air receiving system receives vertical magnetic field signals of different frequencies during flight. The received multi-frequency electromagnetic signals contain information about the electrical resistivity of the underground medium. By processing and analyzing the amplitudes and phases of signals of different frequencies, the characteristics of the underground structure can be inferred. The accuracy of amplitude and phase extraction directly affects the reliability of the subsequent geological structure results, so a high-precision signal processing method is needed.

[0003] Currently, the amplitude and phase extraction of GAFDEM non-stationary multi-frequency signals mainly uses traditional techniques such as frequency domain analysis and adaptive filtering, but there are obvious shortcomings. Typical methods include:

[0004] Orthogonal recursive least squares: This parameterized method estimates the amplitude and phase of each frequency component of the signal through recursive iteration. However, this method is highly dependent on parameter settings and initial conditions, and requires adjustment of parameters such as algorithm order and forgetting factor in different noise environments. Improper use may cause cumulative errors and result in extraction deviations. In addition, this method has high computational complexity, and its point-by-point iteration process requires matrix updating and a large number of multiplication operations for multi-frequency components. For signals with long length and many frequency components, the processing time increases dramatically, making it difficult to meet the real-time or high-efficiency requirements of electromagnetic exploration.

[0005] Fourier transform and short-time Fourier transform (STFT): Traditional Fourier transform assumes that the signal is stationary, and cannot be directly applied to non-stationary signals such as GAFDEM that change over time. The common improvement is short-time Fourier transform, which divides the long signal into a series of short-time approximately stationary segments by selecting a fixed-length window, and then performs frequency spectrum analysis on each segment. However, STFT has a built-in resolution compromise, i.e. a narrow window improves time resolution but lacks frequency resolution, and a wide window improves frequency resolution but violates the stationary segment assumption. Even with improved schemes such as adaptive window length adjustment, STFT essentially performs zero-order fitting on the signal in the time-frequency plane, making it difficult to capture the details of the time-varying spectrum. In particular, when the signal contains multiple similar frequency components, the fixed window length of STFT lacks spectral separation ability, and spectral aliasing and adjacent frequency interference phenomena easily occur, causing the extracted target component amplitude and phase to fluctuate or deviate significantly over time. This extraction instability caused by spectral ambiguity seriously affects the accuracy of underground resistivity inversion.

[0006] In summary, the prior art in GAFDEM signal processing is faced with the following difficulties: spectral aliasing and adjacent frequency interference lead to inaccurate target signal amplitude and phase estimation, parameter dependence and high computational overhead lead to unsatisfactory performance in complex environments or real-time applications. Therefore, there is an urgent need for a new amplitude and phase joint extraction method that does not require tedious parameter adjustment, can effectively suppress spectral aliasing, improve extraction accuracy and has high computational efficiency. SUMMARY

[0007] In view of the shortcomings of the prior art, the purpose of the present application is to provide a GAFDEM signal high-precision amplitude and phase extraction method for improving the amplitude and phase extraction accuracy of target frequency components in ground-air frequency domain electromagnetic (GAFDEM) signals, especially in multi-frequency non-stationary signal processing, which can effectively overcome problems such as spectral aliasing and adjacent frequency interference.

[0008] A GAFDEM signal high-precision amplitude and phase extraction method, the method comprising:

[0009] Step 1, Fourier transform the non-stationary multi-frequency GAFDEM signal to obtain the spectral representation of the signal;

[0010] Step 2, construct a frequency domain mask according to a preset target frequency to eliminate interference components in adjacent frequency bands and retain narrowband spectral information around the target frequency to suppress adjacent frequency interference;

[0011] eliminate interference components in adjacent frequency bands, and retain narrowband spectral information with the target frequency as the center and a mask bandwidth of , wherein , is the target frequency, is a relative bandwidth coefficient in the range of 0.02-0.1, is the minimum bandwidth lower limit;

[0012] Step 3, perform inverse Fourier transform on the filtered spectrum to reconstruct a narrowband time domain sub-signal corresponding to the target frequency;

[0013] Step 4, perform Hilbert transform on the narrowband time domain sub-signal to construct a complex analytic signal and extract the instantaneous amplitude and instantaneous phase of the target frequency component therefrom;

[0014] Step 5, perform phase unwrapping processing on the instantaneous phase to obtain a continuous phase sequence.

[0015] Preferably, in step 2, the dynamic bandwidth adjustment mechanism of the frequency domain mask can effectively suppress adjacent frequency interference, wherein a wider mask bandwidth is used for high frequency signals to enhance frequency drift tolerance, and a narrower mask bandwidth is used for low frequency signals to maintain frequency resolution.

[0016] wherein the high frequency signal refers to a signal with a frequency variable greater than 512 Hz, the low frequency signal refers to a signal with a frequency variable less than 128 Hz, and the mask bandwidth is determined according to The high frequency signal takes The low frequency signal takes .

[0017] Preferably, the frequency domain mask is a binary function, with a value of 1 for a predetermined frequency band in which the target frequency is located, and a value of 0 for frequencies outside the predetermined frequency band, so as to only retain narrowband spectral information centered on the target frequency with a mask bandwidth of and filter out other frequency components.

[0018] The present application has the following beneficial effects:

[0019] The present application effectively suppresses spectral aliasing and adjacent frequency interference through the frequency domain mask technology, and can accurately extract the instantaneous amplitude and phase of the target frequency component in the multi-frequency GAFDEM signal.

[0020] The present application adopts the frequency domain mask filtering and Hilbert transform scheme without the need for presetting a complex window function or adjusting parameters, greatly simplifies the implementation of the algorithm, avoids the trouble of adjusting parameters in different noise environments, has stronger adaptability, and is particularly suitable for application in complex environments. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a flowchart of a GAFDEM signal high-precision amplitude and phase extraction method. DETAILED DESCRIPTION

[0022] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0023] Please refer to Figure 1 The embodiments of the present application provide a GAFDEM signal high-precision amplitude and phase extraction method, which comprises the following steps:

[0024] Step 1, performing Fourier transform on a non-stationary multi-frequency GAFDEM signal to obtain a spectral representation of the signal;

[0025] Step 2, constructing a frequency domain mask according to a preset target frequency, eliminating interference components of adjacent frequency bands and retaining narrowband spectral information near the target frequency, so as to suppress adjacent frequency interference;

[0026] eliminate interference components of adjacent frequency bands and retain narrow-band spectrum information centered on the target frequency with a mask bandwidth of , , , , , ,

[0027] Step 3, performing inverse Fourier transform on the filtered spectrum to reconstruct a narrow-band time-domain sub-signal corresponding to the target frequency;

[0028] Step 4, performing Hilbert transform on the narrow-band time-domain sub-signal to construct a complex analytic signal and extract the instantaneous amplitude and instantaneous phase of the target frequency component therefrom;

[0029] Step 5, performing phase unwrapping on the instantaneous phase to obtain a continuous phase sequence.

[0030] The method of the present application effectively separates the target frequency component through frequency domain masking, avoiding the spectral aliasing problem in traditional signal processing methods. The application of Hilbert transform further simplifies the extraction process of amplitude and phase, avoiding the window function selection problem in traditional methods, and enabling accurate instantaneous features to be directly extracted from the signal. This method not only improves the accuracy of signal processing, but also improves the computational efficiency, and is particularly suitable for real-time signal processing in complex environments.

[0031] In addition, for the case of low signal-to-noise ratio or multi-frequency interference, the present application provides a dynamic bandwidth adjustment mechanism for frequency domain masking, which can automatically adjust the bandwidth of the mask according to the signal characteristics of different frequencies, thereby further enhancing the robustness of the system in a multi-interference environment.

[0032] In this embodiment, the step of performing Fourier transform on the non-stationary multi-frequency GAFDEM signal to obtain the spectral representation of the signal includes:

[0033] performing fast Fourier transform on the received non-stationary multi-frequency GAFDEM signal to obtain the spectral representation of the signal in the frequency domain ; the Fourier transform converts the non-stationary multi-frequency GAFDEM signal to the frequency domain and represents it as a weighted superposition of different frequency components:

[0034] performing Fourier transform on the received non-stationary multi-frequency GAFDEM signal to obtain the spectral representation of the signal in the frequency domain , and represents it as a weighted superposition of different frequency components:

[0035] ;

[0036] wherein, is the input non-stationary multi-frequency GAFDEM signal; is the spectral representation of the signal in the frequency domain, containing the superposition of different frequency components; is the frequency variable; is the Fourier basis, representing the projection of a sinusoidal wave with the time signal.

[0037] In step 2 of the embodiment, the dynamic bandwidth adjustment mechanism of the frequency domain mask can effectively suppress adjacent frequency interference, wherein the high frequency signal adopts a wider mask bandwidth to enhance the frequency drift tolerance, and the low frequency signal adopts a narrower mask bandwidth to maintain the frequency resolution.

[0038] wherein the high frequency signal refers to the signal with a frequency variable greater than 512 Hz, and the low frequency signal refers to the signal with a frequency variable less than 128 Hz, and the mask bandwidth is determined according to , the high frequency signal takes , and the low frequency signal takes .

[0039] In the embodiment, the frequency domain mask is a binary function, assigning a value of 1 to the predetermined frequency band where the target frequency is located, and a value of 0 to the frequencies outside the predetermined frequency band, thereby retaining only the narrowband spectral components near the target frequency and filtering out other frequency components.

[0040] thereby retaining only the narrowband spectral information centered on the target frequency with a mask bandwidth of and filtering out other frequency components.

[0041] In the embodiment, in step 2, the frequency domain mask is constructed according to the preset target frequency, eliminating the interference components of adjacent frequency bands and retaining the narrowband spectral information centered on the target frequency with a mask bandwidth of to suppress adjacent frequency interference, the steps comprising:

[0042] To suppress adjacent frequency interference and focus on the target frequency, a frequency domain mask is constructed, the mask function being a binary function with a value of 1 in the frequency band centered on the target frequency with a mask bandwidth of and a value of 0 in the remaining frequency band, the mask bandwidth controlling the spectral width around the target frequency, the formula being:

[0043] ;

[0044] wherein, is the target frequency, is the mask bandwidth, and if the adjacent transmission frequency interval is , the mask bandwidth needs to meet In order to realize the adaptability of bandwidth selection, the mask bandwidth Determined as follows:

[0045] ;

[0046] In the formula, The relative bandwidth coefficient proportional to the target frequency is usually in the range of 0.02-0.1; The minimum bandwidth lower limit prevents the energy loss caused by the narrow mask in the low frequency band; by multiplying And The filtered frequency spectrum , expressed as:

[0047] .

[0048] In this embodiment, the step of performing inverse Fourier transform on the filtered frequency spectrum to reconstruct the time domain signal corresponding to the target frequency component includes:

[0049] Performing inverse Fourier transform on the filtered frequency spectrum Reconstructing the time domain signal of the target frequency component of the target frequency component , expressed as:

[0050] .

[0051] In this embodiment, the step of performing Hilbert transform on the narrowband time domain sub-signal to construct a complex analytic signal and extracting the instantaneous amplitude and instantaneous phase of the target frequency component from the complex analytic signal includes:

[0052] Performing Hilbert transform on the reconstructed time domain signal of the target frequency component To get the imaginary part signal orthogonal to the original signal, the Hilbert transform is a process of converting a signal into its orthogonal component, and the formula is as follows:

[0053] ;

[0054] In the formula, The principal value integral;

[0055] By combining the reconstructed time domain signal of the target frequency component With the imaginary part signal obtained by Hilbert transform, a complex analytic signal is constructed, expressed as:

[0056] ;

[0057] wherein, is a complex unit;

[0058] complex analytic signal instantaneous amplitude is obtained from the modulus of the complex signal, formula:

[0059] ;

[0060] complex analytic signal instantaneous phase is obtained from the argument of the complex signal, formula:

[0061] .

[0062] In this embodiment, the step of performing phase unwrapping processing on the instantaneous phase to obtain a continuous phase sequence includes:

[0063] When extracting the instantaneous phase, since the phase function may have a 2π jump in the range , phase unwrapping is required, and the final phase is written as:

[0064] ;

[0065] wherein, is a rounding function.

[0066] Through the above detailed formula derivation and step explanation, this embodiment shows how to extract the instantaneous amplitude and phase of the target frequency by combining frequency domain masking and Hilbert transform. These steps provide a complete signal processing scheme suitable for complex electromagnetic detection environments.

[0067] The method described in the application is applied to the ground-air detection process of a ground-air frequency domain electromagnetic detection (GAFDEM) system, including the following steps: transmitting a multi-frequency electromagnetic detection signal using a grounded long wire source; acquiring the returned multi-frequency non-stationary GAFDEM signal through an airborne receiving platform; performing steps 1-5 above on the received signal in turn to extract the amplitude and phase of each target frequency component for imaging or inversion analysis of the underground electrical structure.

[0068] The above is only a preferred embodiment of the application, and does not limit the patent scope of the application, and any equivalent structure or equivalent process transformation made by the application specification, or direct or indirect application in other related technical fields, is also included in the patent protection scope of the application.

Claims

1. A method for high-precision amplitude and phase extraction of a GAFDEM signal, characterized in that, The method comprises: Step 1, Fourier transform is performed on the non-stationary multi-frequency GAFDEM signal to obtain a spectral representation of the signal; Step 2, a frequency domain mask is constructed according to a preset target frequency, interference components in adjacent frequency bands are eliminated, and narrowband spectral information near the target frequency is retained to suppress adjacent frequency interference; eliminate interference components of adjacent frequency bands and retain narrow-band spectrum information centered on the target frequency with a mask bandwidth of , , , , ; Step 3, inverse Fourier transform is performed on the filtered spectrum to reconstruct a narrowband time domain sub-signal corresponding to the target frequency; Step 4, Hilbert transform is performed on the narrowband time domain sub-signal to construct a complex analytic signal, and instantaneous amplitude and instantaneous phase of the target frequency component are extracted from the complex analytic signal; Step 5, phase unwrapping is performed on the instantaneous phase to obtain a continuous phase sequence; In step 2, a frequency domain mask is constructed according to the preset target frequency, to eliminate interference components of adjacent frequency bands and retain narrowband spectrum information centered on the target frequency with a mask bandwidth of The step of suppressing adjacent frequency interference includes: Constructing frequency domain mask The mask function is a binary function, with the target frequency center and mask bandwidth as The value in the frequency band of the target frequency center is 1, and the value in the other frequency bands is 0. The mask bandwidth controls the spectral width around the target frequency, and the formula is: ； In the formula, is the target frequency, is the mask bandwidth, if the interval between adjacent transmission frequencies is , the mask bandwidth needs to satisfy In order to realize the adaptability of bandwidth selection, the mask bandwidth is determined according to the following formula: ； wherein is a relative bandwidth factor proportional to the target frequency; is a minimum bandwidth lower limit; by multiplying with adjacent frequency interference signals are filtered out and the filtered spectrum is represented as: 。 2. The method according to claim 1, wherein, In step 1, the step of Fourier transforming the non-stationary multi-frequency GAFDEM signal to obtain a spectral representation of the signal comprises: The received non-stationary multi-frequency GAFDEM signal is subjected to a Fourier transform to obtain a spectral representation of the signal in the frequency domain The Fourier transform converts the non-stationary multi-frequency GAFDEM signal into the frequency domain and represents it as a weighted superposition of different frequency components for a received non-stationary multi-frequency GAFDEM signal performing a Fourier transform to obtain a spectral representation of the signal in the frequency domain and represented as a weighted superposition of different frequency components: ； wherein is the input non-stationary multi-frequency GAFDEM signal; is the spectral representation of the signal in the frequency domain, containing the superposition of different frequency components; is the frequency variable; is the Fourier basis, representing the projection of a sinusoidal wave with the time signal.

3. The method of claim 1, wherein the GAFDEM signal is a GAFDEM signal of a digital television signal, and the GAFDEM signal is a GAFDEM signal of a digital television signal. In step 2, the dynamic bandwidth adjustment mechanism of the frequency domain mask suppresses adjacent frequency interference, wherein a high-frequency signal adopts a wider mask bandwidth to enhance frequency drift tolerance, and a low-frequency signal adopts a narrower mask bandwidth to maintain frequency resolution; Wherein, the high frequency signal refers to the signal with frequency variable greater than 512Hz, the low frequency signal refers to the signal with frequency variable less than 128Hz, the mask bandwidth is according to Determination, the high frequency signal takes , the low frequency signal takes .

4. The method of claim 1, wherein the GAFDEM signal high-precision amplitude and phase extraction method is characterized by, The frequency domain mask is a binary function, and a predetermined frequency band where the target frequency is located is assigned a value of 1, and a frequency outside the predetermined frequency band is assigned a value of 0, so that only narrowband spectral components near the target frequency are retained and other frequency components are filtered out; Thus only and preserve narrow band spectrum information centered at the target frequency with a mask bandwidth of and filter out other frequency components.

5. The method of claim 2, wherein the GAFDEM signal high-precision amplitude and phase extraction method is characterized by, The step of performing inverse Fourier transform on the filtered spectrum to reconstruct a time domain signal corresponding to the target frequency component comprises: the filtered frequency spectrum performing an inverse Fourier transform to reconstruct a time domain signal of the target frequency component is expressed as: 。 6. The method of claim 1, wherein the GAFDEM signal high-precision amplitude and phase extraction method is characterized by, The step of performing Hilbert transform on the narrowband time domain sub-signal to construct a complex analytic signal and extracting instantaneous amplitude and instantaneous phase of the target frequency component from the complex analytic signal comprises: a time domain signal of the reconstructed target frequency component performing a Hilbert transform to obtain a quadrature signal orthogonal to the original signal The Hilbert transform is a process that transforms a signal into its quadrature component, and is given by the formula: ； wherein is the principal value integral; By convolving the reconstructed time-domain signal of the target frequency component with the imaginary part signal obtained by the Hilbert transform in combination, a complex analytic signal is constructed is represented as ； In the formulae, is the complex unit; complex analytic signal instantaneous amplitude from the modulus of the complex signal, given by ； complex analytic signal whose instantaneous phase is given by the argument of the complex signal 。 7. The method of claim 6, wherein the GAFDEM signal high-precision amplitude and phase extraction method is characterized by, The step of performing phase unwrapping on the instantaneous phase to obtain a continuous phase sequence comprises: In extracting the instantaneous phase, phase unwrapping is performed, and the final phase is written as: ； In the formula, is a rounding function.

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