Frequency domain ground penetrating radar emission source coding and receiving signal synthesis method and system

Abstract

The invention discloses a frequency domain ground penetrating radar transmitting source coding and receiving signal synthesis method and system. The method comprises the following steps: constructing a frequency domain coding continuous wave ground penetrating radar transmitting signal by extracting amplitude and phase information of multiple frequency points of a time domain ultra-wideband transmitting pulse; adopting a fast forward modeling method based on impulse response to realize forward modeling of a coding source emission signal of the typical geoelectric model; in-phase components and orthogonal components of all frequency points are extracted, frequency responses are synthesized into responses of quasi-time-domain transmitted pulses through an inverse Fourier transform method, the high resolution equal to that of time-domain ultra-wideband transmitted signals is obtained, and higher anti-noise performance is achieved. According to the invention, the amplitude phase coding continuous wave transmitting signal is adopted, so that the frequency spectrum shaping of the quasi-time domain pulse of the transmitting frequency spectrum is realized, the resolving power of the synthetic signal is improved, and a theoretical basis is laid for signal synthesis of frequency domain ground penetrating radar hardware design.

Description

Technical Field

[0001] The present invention belongs to the field of exploration geophysical theory and data processing, and in particular relates to a method and system for frequency domain ground penetrating radar emission source coding and received signal synthesis. Background Art

[0002] Ground penetrating radar is fast, non-destructive and efficient, and is widely used in near-surface physical surveys such as urban underground pipeline detection, road structure inspection, engineering inspection and environmental monitoring.

[0003] Currently, common ground-penetrating radar systems include time-domain pulse radar and frequency-domain continuous-wave radar. Time-domain pulse radar uses ultra-wideband pulses as its transmitting signal, offering high temporal resolution. While the transmitted signal possesses high instantaneous power, the short pulse duration and low average power result in poor noise immunity. Frequency-domain continuous-wave radar uses a continuous-wave or stepped-frequency signal as its transmitting source, offering excellent anti-interference capabilities. However, because the amplitude and phase of the transmitted signals at each frequency point are incoherent and lack a coding coordination relationship between the frequencies, the reconstructed image typically only synthesizes a one-dimensional range image. The coherent features between target echoes are not retained, reducing the ability to identify unusual targets.

[0004] Although the current frequency domain ground penetrating radar has a certain resolution capability, the amplitude and phase of the transmitted signal at each frequency point are not constrainedly encoded, and there is a lack of synthesis methods suitable for the echo response of the coded transmitted signal, which restricts the theoretical development and practical application of ground penetrating radar. Summary of the Invention

[0005] In view of the shortcomings of the prior art, one of the objectives of the present invention is to provide a frequency domain ground penetrating radar transmission source encoding and receiving signal synthesis method to improve the anti-noise performance of the ground penetrating radar and the ability to resolve the reflection signals of abnormal bodies.

[0006] A second object of the present invention is to provide a system for implementing the frequency domain ground penetrating radar transmission source encoding and receiving signal synthesis method.

[0007] The present invention provides a method for frequency domain ground penetrating radar transmission source coding and receiving signal synthesis, comprising the following steps:

[0008] S1. Based on a preset energy interception threshold, the effective bandwidth is intercepted, and the frequency step size is calculated using the target detection depth. Ultimately, the main frequency amplitude and phase of the ultra-wideband transmit pulse are calculated.

[0009] S2. Construct a multi-frequency coded sine wave transmission signal based on the main frequency amplitude and phase of the ultra-wideband transmit pulse obtained in step S1;

[0010] S3. Construct a typical geoelectric model for forward simulation based on the target detection depth and application scenario;

[0011] S4. Using the impulse signal as the emission source, the ground-penetrating radar signal is forward modeled on the geoelectric model obtained in step S3 to obtain an impulse response. Then, based on the multi-frequency coded sine wave emission signal and the impulse response obtained in step S2, the time domain forward modeling result is obtained;

[0012] S5. According to the time domain forward modeling result obtained in step S4, extract the in-phase component and the orthogonal component of the frequency response, and then synthesize the frequency domain response into the time domain equivalent signal based on the obtained in-phase component and the orthogonal component of the frequency response.

[0013] Step S1 includes the following steps:

[0014] Analyze the emission spectrum characteristics of pulse radar, intercept the effective bandwidth, and obtain ultra-wideband emission pulses;

[0015] Determine the time window length and frequency step size based on the preset target detection depth requirements;

[0016] Determine a number of frequency points with equal frequency differences according to the frequency step size;

[0017] The amplitude and phase coding of each frequency point are obtained according to the spectrum value of the ultra-wideband pulse.

[0018] Step S1 is specifically as follows:

[0019] Analyze the emission spectrum characteristics of the pulse radar and obtain the ultra-wideband emission pulse, which can be expressed using the following formula:

[0020]

[0021] Where x(t) is the time domain waveform of the ultra-wideband transmitted pulse; j is the imaginary unit; X(f) is the complex spectrum of x(t), and X(f) = |X(f)|e jφ(f) ; |X(f)| is the amplitude spectrum of the ultra-wideband transmitted pulse; φ(f) is the phase spectrum of the ultra-wideband transmitted pulse;

[0022] Cut off the frequency band where the main part of the energy is concentrated [f min ,f max ] as the effective bandwidth, where the frequency band [f min ,f max ]conform to Wherein, η is the preset energy interception threshold, which is adjusted according to the actual application scenario;

[0023] According to the preset target detection depth requirements, determine the time window length and frequency step size, and use the following calculation formula:

[0024]

[0025] Where T is the time window length; d max is the preset target detection depth requirement; Δf is the frequency step;

[0026] Determine a number of frequency points with equal frequency differences based on the frequency step size, and use the following formula to express it:

[0027] f i =f min +(i-1)·Δf,i=1,2,...,M

[0028] Where M is the total number of frequency points; f i is the i-th frequency point;

[0029] The amplitude code and phase code of each frequency point are obtained according to the spectrum value of the ultra-wideband pulse, which can be expressed using the following formula:

[0030] A(f i )=|X(f i )|

[0031] φ(f i )=arg(X(f i ))

[0032] Among them, A(f i ) is the amplitude of the ith frequency point; φ(f i ) is the phase code of the ith frequency point; arg() is the argument function.

[0033] Step S2 is specifically as follows: constructing a multi-frequency coded sinusoidal wave transmission signal based on the main frequency amplitude and phase of the ultra-wideband transmission pulse obtained in step S1, which is expressed by the following formula:

[0034] s i (t) = A(f i )cos(2πf i t+φ(f i ))

[0035] Among them, s i (t) is the coded sinusoidal wave transmitted signal at the i-th frequency point.

[0036] Step S4 is specifically as follows:

[0037] Using the impulse signal as the emission source, the ground penetrating radar signal is forward modeled on the geoelectric model obtained in step S3 to obtain the impulse response, which is expressed by the following formula:

[0038] h(t)=λ{δ(t)}

[0039] Where h(t) is the impulse response; λ is the forward operator of the geoelectric model; δ(t) is the impulse signal;

[0040] Then, a convolution operation is performed on the multi-frequency coded sinusoidal wave transmission signal obtained in step S2 and the impulse response to obtain the time domain forward modeling result, which is expressed by the following formula:

[0041] y i (t) = s i (t)*h(t)

[0042] Among them, y i (t) is the time domain forward modeling result of the continuous wave transmission signal at the i-th frequency point; s i (t) is the coded sinusoidal wave transmitted signal at the i-th frequency point.

[0043] Step S5 includes the following steps:

[0044] Performing a fast Fourier transform on the frequency point forward modeling results obtained in step S4 to convert the amplitude and phase values ​​of each frequency point into an in-phase component and a quadrature component;

[0045] The complex-valued response of each frequency point is mapped to a double-sided spectrum satisfying Hermitian symmetry, and a double-sided spectrum satisfying conjugate symmetry is obtained;

[0046] The constructed bilateral spectrum is inversely Fourier transformed to realize the synthesis of frequency domain response into time domain equivalent signal.

[0047] Step S5 is specifically as follows:

[0048] Perform fast Fourier transform on the frequency point forward modeling result obtained in step S4 and express it using the following formula:

[0049] Y i (f) = FFT{y i (t)}

[0050] Where, FFT{} is fast Fourier transform; Y i (f) is y i (t), and Y i (f i )=H(f i )=I(f i )+jQ(f i ); H(f i ) is the complex value response of the ith frequency point; I(f i ) is the in-phase component of the i-th frequency point; Q(f i ) is the orthogonal component of the i-th frequency point; j is the imaginary unit;

[0051] According to the sampling interval Δt of the time domain signal to be synthesized, the system bandwidth B is calculated using the following formula:

[0052]

[0053] Where Δt is the time domain signal sampling interval; B is the system bandwidth;

[0054] The complex-valued response at each frequency point is mapped to a double-sided spectrum that satisfies Hermitian symmetry, which can be expressed using the following formula:

[0055]

[0056] Among them, H synth (f k ) is the double-sided spectrum; f k For interval Frequency points evenly distributed with Δf as interval; H * (-f i ) is the complex-valued response H(f i ) is the conjugate symmetry value of .

[0057] The bilateral spectrum is subjected to inverse Fourier transform to realize the synthesis of the frequency domain response into the time domain equivalent signal, which is expressed by the following formula:

[0058] S synth (t) = IFFT{H synth (f)}

[0059] Among them, S synth (t) is the final synthesized signal; IFFT{} is the inverse Fourier transform.

[0060] The present invention also provides a system for implementing the frequency domain ground penetrating radar transmission source coding and receiving signal synthesis method, comprising an ultra-wideband transmission pulse calculation module, a multi-frequency point coded sinusoidal wave transmission signal construction module, a typical geoelectric model construction module, a ground penetrating radar signal forward modeling module, and a signal synthesis module;

[0061] The ultra-wideband transmit pulse calculation module intercepts the effective bandwidth based on the preset energy interception threshold, and then calculates the frequency step size using the target detection depth. It finally calculates the main frequency amplitude and phase of the ultra-wideband transmit pulse and uploads the data to the multi-frequency point coded sine wave transmit signal construction module.

[0062] The multi-frequency point coded sine wave transmission signal construction module constructs a multi-frequency point coded sine wave transmission signal according to the received data, and uploads the data to the ground penetrating radar signal forward modeling module;

[0063] The typical geoelectric model construction module constructs a typical geoelectric model for forward simulation based on the target detection depth and application scenario, and uploads the data to the ground penetrating radar signal forward modeling module;

[0064] The GPR signal forward modeling module performs GPR signal forward modeling on the geoelectric model based on the received data and uses the impulse signal as the emission source to obtain the impulse response. It then obtains the time domain forward modeling result based on the multi-frequency coded sine wave emission signal and the impulse response, and uploads the data to the signal synthesis module.

[0065] The signal synthesis module extracts the in-phase component and the orthogonal component of the frequency response according to the received data and the time domain forward modeling results, and then realizes the synthesis of the frequency domain response into the time domain equivalent signal based on the obtained in-phase component and the orthogonal component of the frequency response.

[0066] The present invention discloses a method and system for frequency-domain ground-penetrating radar (GPR) source coding and received signal synthesis. Compared to the short-duration pulse transmission signals of conventional time-domain pulse radars, the frequency-domain coded continuous wave (FDCW) signal employed in the present invention significantly increases the average transmission power. Compared to the conventional stepped-frequency radar's constant-amplitude, in-phase continuous wave transmission signals at each frequency point, the amplitude-phase coded continuous wave (APCW) signal employed in the present invention achieves spectral shaping of the transmission spectrum similar to a time-domain pulse, improving the resolution of the synthesized signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Schematic diagram of the process of the present invention;

[0068] Figure 2 Schematic diagram of the structure of the system of the present invention;

[0069] Figure 3 The ricker wavelet with a center frequency of 900 MHz and its spectrum characteristic diagram in the embodiment of the present invention are shown in FIG. Figure 3 a is the time domain waveform of Ricker wavelet; Figure 3 b is the characteristic diagram of the Ricker wavelet amplitude spectrum; Figure 3 c is the characteristic diagram of Ricker wavelet phase spectrum;

[0070] Figure 4 is an amplitude-phase coding diagram of the main frequency band of the quasi-ricker wavelet in an embodiment of the present invention; wherein, Figure 4 a is the amplitude diagram of the main frequency band of the quasi-ricker wavelet; Figure 4 b is the main frequency band phase diagram of the quasi-ricker wavelet;

[0071] Figure 5 is a schematic diagram of a typical geoelectric model in an embodiment of the present invention;

[0072] Figure 6 Graph showing the rapid simulation results of the coded continuous wave transmission signal response according to an embodiment of the present invention;

[0073] Figure 7 3 is a comparison diagram of the synthetic signal of the frequency domain response and the time domain response in an embodiment of the present invention. DETAILED DESCRIPTION

[0074] The present invention provides a method for frequency domain ground penetrating radar source coding and receiving signal synthesis, the flow chart of which is as follows: Figure 1 As shown, the following steps are included:

[0075] S1. Based on a preset energy interception threshold, the effective bandwidth is intercepted, and the frequency step size is calculated using the target detection depth. Ultimately, the main frequency amplitude and phase of the ultra-wideband transmit pulse are calculated.

[0076] Step S1 is specifically as follows:

[0077] Analyze the emission spectrum characteristics of the pulse radar and obtain the ultra-wideband emission pulse, which can be expressed using the following formula:

[0078]

[0079] Where x(t) is the time domain waveform of the ultra-wideband transmitted pulse; j is the imaginary unit; X(f) is the complex spectrum of x(t), and X(f) = |X(f)|e jφ(f) ; |X(f)| is the amplitude spectrum of the ultra-wideband transmitted pulse; φ(f) is the phase spectrum of the ultra-wideband transmitted pulse;

[0080] Cut off the frequency band where the main part of the energy is concentrated [f min ,f max ] as the effective bandwidth, where the frequency band [f min ,f max ]conform to Wherein, η is the preset energy interception threshold, which is adjusted according to the actual application scenario;

[0081] According to the preset target detection depth requirements, determine the time window length and frequency step size, and use the following calculation formula:

[0082]

[0083] Where T is the time window length; d max is the preset target detection depth requirement; Δf is the frequency step;

[0084] Determine a number of frequency points with equal frequency differences based on the frequency step size, and use the following formula to express it:

[0085] f i =f min+(i-1)·Δf,i=1,2,...,M

[0086] Where M is the total number of frequency points; f i is the i-th frequency point;

[0087] The amplitude and phase encoding of each frequency point are obtained based on the spectrum value of the ultra-wideband pulse, and are expressed using the following formula:

[0088] A(f i )=|X(f i )|

[0089] φ(f i )=arg(X(f i ))

[0090] Among them, A(f i ) is the amplitude of the ith frequency point; φ(f i ) is the phase code of the ith frequency point; arg() is the argument function.

[0091] S2. Construct a multi-frequency coded sine wave transmission signal based on the main frequency amplitude and phase of the ultra-wideband transmit pulse obtained in step S1;

[0092] Step S2 is specifically as follows: constructing a multi-frequency coded sinusoidal wave transmission signal based on the main frequency amplitude and phase of the ultra-wideband transmission pulse obtained in step S1, which is expressed by the following formula:

[0093] s i (t) = A(f i )cos(2πf i t+φ(f i ))

[0094] Among them, s i (t) is the coded sinusoidal wave transmitted signal at the i-th frequency point.

[0095] S3. Construct a typical geoelectric model for forward simulation based on the target detection depth and application scenario;

[0096] S4. Using the impulse signal as the emission source, the ground penetrating radar signal is forward modeled on the geoelectric model obtained in step S3 to obtain an impulse response. Then, based on the multi-frequency coded sine wave emission signal and the impulse response obtained in step S2, the time domain forward modeling result is obtained;

[0097] Step S4 is specifically as follows:

[0098] Using the impulse signal as the emission source, the ground penetrating radar signal is forward modeled on the geoelectric model obtained in step S3 to obtain the impulse response, which is expressed by the following formula:

[0099] h(t)=λ{δ(t)}

[0100] Where h(t) is the impulse response; λ is the forward operator of the geoelectric model; δ(t) is the impulse signal;

[0101] Then, a convolution operation is performed on the multi-frequency coded sinusoidal wave transmission signal obtained in step S2 and the impulse response to obtain the time domain forward modeling result, which is expressed by the following formula:

[0102] y i (t) = s i (t)*h(t)

[0103] Among them, y i (t) is the time domain forward modeling result of the continuous wave transmission signal at the i-th frequency point; s i (t) is the coded sinusoidal wave transmitted signal at the i-th frequency point.

[0104] S5. According to the time domain forward modeling result obtained in step S4, extract the in-phase component and the orthogonal component of the frequency response, and then synthesize the frequency domain response into the time domain equivalent signal based on the obtained in-phase component and the orthogonal component of the frequency response.

[0105] Step S5 is specifically as follows:

[0106] Perform fast Fourier transform on the frequency point forward modeling result obtained in step S4 and express it using the following formula:

[0107] Y i (f) = FFT{y i (t)}

[0108] Where, FFT{} is fast Fourier transform; Y i (f) is y i (t), and Y i (f i )=H(f i )=I(f i )+jQ(f i ); H(f i ) is the complex value response of the ith frequency point; I(f i ) is the in-phase component of the i-th frequency point; Q(f i ) is the orthogonal component of the i-th frequency point; j is the imaginary unit;

[0109] According to the sampling interval Δt of the time domain signal to be synthesized, the system bandwidth B is calculated using the following formula:

[0110]

[0111] Where Δt is the time domain signal sampling interval; B is the system bandwidth;

[0112] The complex-valued response at each frequency point is mapped to a double-sided spectrum that satisfies Hermitian symmetry, which can be expressed using the following formula:

[0113]

[0114] Among them, H synth (f k ) is the double-sided spectrum; f k For interval Frequency points evenly distributed with Δf as interval; H * (-f i ) is the complex-valued response H(f i ) is the conjugate symmetry value of .

[0115] The bilateral spectrum is subjected to inverse Fourier transform to realize the synthesis of the frequency domain response into the time domain equivalent signal, which is expressed by the following formula:

[0116] S synth (t) = IFFT{H synth (f)}

[0117] Among them, S synth (t) is the final synthesized signal; IFFT{} is the inverse Fourier transform.

[0118] The present invention also provides a system for realizing the frequency domain ground penetrating radar transmission source coding and receiving signal synthesis method, the structural diagram of which is shown as follows: Figure 2 As shown, it includes an ultra-wideband transmission pulse calculation module, a multi-frequency point coded sinusoidal wave transmission signal construction module, a typical geoelectric model construction module, a ground penetrating radar signal forward modeling module, and a signal synthesis module;

[0119] The ultra-wideband transmit pulse calculation module intercepts the effective bandwidth based on the preset energy interception threshold, and then calculates the frequency step size using the target detection depth. It finally calculates the main frequency amplitude and phase of the ultra-wideband transmit pulse and uploads the data to the multi-frequency point coded sine wave transmit signal construction module.

[0120] The multi-frequency point coded sine wave transmission signal construction module constructs a multi-frequency point coded sine wave transmission signal according to the received data, and uploads the data to the ground penetrating radar signal forward modeling module;

[0121] The typical geoelectric model construction module constructs a typical geoelectric model for forward simulation based on the target detection depth and application scenario, and uploads the data to the ground penetrating radar signal forward modeling module;

[0122] The GPR signal forward modeling module performs GPR signal forward modeling on the geoelectric model based on the received data and uses the impulse signal as the emission source to obtain the impulse response. It then obtains the time domain forward modeling result based on the multi-frequency coded sine wave emission signal and the impulse response, and uploads the data to the signal synthesis module.

[0123] The signal synthesis module extracts the in-phase component and the orthogonal component of the frequency response according to the received data and the time domain forward modeling results, and then realizes the synthesis of the frequency domain response into the time domain equivalent signal based on the obtained in-phase component and the orthogonal component of the frequency response.

[0124] The method of the present invention is further described below with reference to an embodiment:

[0125] In this embodiment, the amplitude-phase coded frequency signals in the frequency band where the main energy of the Ricker wavelet of the typical time-domain ground penetrating radar transmission signal is concentrated are used as the stepped frequency continuous wave transmission signal. The in-phase component I(f i ) and the quadrature component Q(f i ). The complex response of each frequency point I(f i )+jQ(f i ), and the frequency domain synthetic response of the quasi-ricker wavelet is obtained by inverse Fourier transform.

[0126] In this embodiment, the Ricker wavelet with a center frequency of 900 MHz is taken as an example (eg Figure 3 shown). Figure 3 (a) shows the time domain waveform of the Ricker wavelet. The amplitude spectrum is obtained by Fourier transforming the Ricker wavelet (e.g. Figure 3 (b)) and phase spectrum (as shown in Figure 3 (c)). Figure 3 (b) It can be seen that the amplitude spectrum of this Ricker wavelet has the largest amplitude near the center frequency of 900 MHz, which means that the energy at this frequency point is the strongest; the amplitude values ​​of frequencies greater than 3 GHz approach 0, and the energy is negligible. Therefore, it is determined that the passband of the Ricker wavelet with a center frequency of 900 MHz is 0-3 GHz.

[0127] The amplitude spectrum of the Ricker wavelet is obtained in the passband range of 0-3GHz with a frequency step of 20MHz ( Figure 3 (b)) and phase spectrum ( Figure 3 (c)) is discretized to obtain the amplitude values ​​of 150 frequency points ( Figure 4 (a)) and phase value ( Figure 4 (b)), and use this as the amplitude A(f i ) and phase φ(f iThe amplitude and phase of each frequency point code are used to construct the coded sine (cosine) wave transmission signal s i (t) = A(f i )cos(2πf i t+φ(f i )), serves as the source signal for the subsequent geoelectric model forward modeling.

[0128] In order to obtain the geoelectric response of the continuous wave transmission signal, a typical simple model (such as Figure 5 The model is 3m*2.1m in size and consists of three layers of dielectric material: air, dielectric material with a small dielectric constant, and dielectric material with a large dielectric constant. Two circular anomalies are placed at the interface between the lower two dielectric layers.

[0129] The encoded signal s i (t) is used as a continuous wave emission source, and the open source ground penetrating radar simulation software gprMax is used to perform forward modeling on the above model. Figure 6 is the geoelectric model response of the continuous wave emission at 900MHz with the observation point located at the center of the model air layer medium, and the response y at other frequencies i (t) can be obtained by the same method. In order to improve the efficiency of forward calculation, this example adopts the method of convolving the transmission signal based on the impulse response of the model. It only needs to set the transmission signal as the impulse signal and use the gprMax software to forward the model once to obtain the impulse response of the geoelectric model. The encoded transmission signal s at each frequency point is converted into i (t) Perform convolution operation with the impulse response one by one to quickly obtain the forward modeling results y of each frequency point i (t).

[0130] The response y of each frequency point i (t) The in-phase component I(f) of each frequency response is obtained by Fourier transform. i ) and the quadrature component Q(f i ), combined into the complex response I(f i )+jQ(f i ). The complex response I(f i )+jQ(f i ) inverse Fourier transform to obtain the quasi-ricker wavelet response of the frequency domain coding source, that is, Figure 7 The data1 composite signal marked with "+" in the figure. Figure 7 Data2, marked with "----," is the forward modeling result of the geoelectric model using a time-domain Ricker wavelet with a center frequency of 900 MHz as the transmission signal. Comparing the synthesized signal data1 (frequency-domain coded source response) with the forward modeling result using the time-domain Ricker wavelet, the two are almost identical.

[0131] The above results show that by performing Ricker-like wavelet spectrum shaping on the spectrum of the frequency domain continuous wave ground penetrating radar transmission signal, the amplitude and phase encoding of each frequency point of the quasi-ricker wavelet can be obtained. The model response of the encoded frequency domain ground penetrating radar transmission signal is accurately synthesized into a quasi-ricker wavelet response through inverse Fourier transform. The present invention provides an effective frequency domain ground penetrating radar emission source coding scheme and realizes the synthesis of multi-frequency point frequency domain ground penetrating radar signals. This scheme can be extended to other coding schemes for frequency domain ground penetrating radar transmission signals, such as quasi-Gaussian waveform coding, quasi-Gaussian derivative waveform coding of various orders, and various custom coding, laying a theoretical foundation for the development of frequency domain ground penetrating radar hardware.

Claims

1. A method for frequency domain ground penetrating radar source coding and received signal synthesis, characterized in that: The following steps are involved: S1. Based on a preset energy interception threshold, the effective bandwidth is intercepted, and the frequency step size is calculated using the target detection depth. Ultimately, the main frequency amplitude and phase of the ultra-wideband transmit pulse are calculated. S2. Construct a multi-frequency coded sine wave transmission signal based on the main frequency amplitude and phase of the ultra-wideband transmit pulse obtained in step S1; S3. Construct a typical geoelectric model for forward simulation based on the target detection depth and application scenario; S4. Using the impulse signal as the emission source, the ground penetrating radar signal is forward modeled on the geoelectric model obtained in step S3 to obtain an impulse response. Then, based on the multi-frequency coded sine wave emission signal and the impulse response obtained in step S2, the time domain forward modeling result is obtained; S5. According to the time domain forward modeling result obtained in step S4, extract the in-phase component and the orthogonal component of the frequency response, and then synthesize the frequency domain response into the time domain equivalent signal based on the obtained in-phase component and the orthogonal component of the frequency response.

2. The frequency domain ground penetrating radar transmission source coding and received signal synthesis method according to claim 1, characterized in that: Step S1 includes the following steps: Analyze the emission spectrum characteristics of pulse radar, intercept the effective bandwidth, and obtain ultra-wideband emission pulses; Determine the time window length and frequency step size based on the preset target detection depth requirements; Determine a number of frequency points with equal frequency differences according to the frequency step size; The amplitude and phase coding of each frequency point are obtained according to the spectrum value of the ultra-wideband pulse.

3. The frequency domain ground penetrating radar transmission source coding and received signal synthesis method according to claim 2, characterized in that: Step S1 is specifically as follows: Analyze the emission spectrum characteristics of the pulse radar and obtain the ultra-wideband emission pulse, which can be expressed using the following formula: Where x(t) is the time domain waveform of the ultra-wideband transmitted pulse; j is the imaginary unit; X(f) is the complex spectrum of x(t), and X(f) = |X(f)|e jφ(f) ; |X(f)| is the amplitude spectrum of the ultra-wideband transmitted pulse; φ(f) is the phase spectrum of the ultra-wideband transmitted pulse; Cut off the frequency band where the main part of the energy is concentrated [f min ,f max ] as the effective bandwidth, where the frequency band [f min ,f max ]conform to Wherein, η is the preset energy interception threshold, which is adjusted according to the actual application scenario; According to the preset target detection depth requirements, determine the time window length and frequency step size, and use the following calculation formula: Where T is the time window length; d max is the preset target detection depth requirement; Δf is the frequency step; Determine a number of frequency points with equal frequency differences based on the frequency step size, and use the following formula to express it: f i =f min +(i-1)·Δf,i=1,2,...,M Where M is the total number of frequency points; f i is the i-th frequency point; The amplitude code and phase code of each frequency point are obtained according to the spectrum value of the ultra-wideband pulse, which can be expressed using the following formula: A(f i )=|X(f i )| φ(f i )=arg(X(f i )) Among them, A(f i ) is the amplitude code of the i-th frequency point; φ(f i ) is the phase code of the ith frequency point; arg() is the argument function.

4. The frequency domain ground penetrating radar transmission source coding and received signal synthesis method according to claim 1, characterized in that: Step S2 is specifically as follows: constructing a multi-frequency coded sinusoidal wave transmission signal based on the main frequency amplitude and phase of the ultra-wideband transmission pulse obtained in step S1, which is expressed by the following formula: s i (t)=A(f i )cos(2πf i t+φ(f i )) Among them, s i (t) is the coded sinusoidal wave transmitted signal at the i-th frequency point; A(f i ) is the amplitude of the ith frequency point; φ(f i ) is the phase code of the i-th frequency point; f i is the ith frequency point.

5. The frequency domain ground penetrating radar transmission source coding and received signal synthesis method according to claim 1, characterized in that: Step S4 is specifically as follows: Using the impulse signal as the emission source, the ground penetrating radar signal is forward modeled on the geoelectric model obtained in step S3 to obtain the impulse response, which is expressed by the following formula: h(t)=λ{δ(t)} Where h(t) is the impulse response; λ is the forward operator of the geoelectric model; δ(t) is the impulse signal; Then, a convolution operation is performed on the multi-frequency coded sinusoidal wave transmission signal obtained in step S2 and the impulse response to obtain the time domain forward modeling result, which is expressed by the following formula: y i (t)=s i (t)*h(t) Among them, y i (t) is the time domain forward modeling result of the continuous wave transmission signal at the i-th frequency point; s i (t) is the coded sinusoidal wave transmitted signal at the i-th frequency point.

6. The frequency domain ground penetrating radar transmission source coding and received signal synthesis method according to claim 1, characterized in that: Step S5 includes the following steps: Performing a fast Fourier transform on the frequency point forward modeling results obtained in step S4 to convert the amplitude and phase values ​​of each frequency point into an in-phase component and a quadrature component; The complex-valued response of each frequency point is mapped to a double-sided spectrum satisfying Hermitian symmetry, and a double-sided spectrum satisfying conjugate symmetry is obtained; The constructed bilateral spectrum is inversely Fourier transformed to realize the synthesis of frequency domain response into time domain equivalent signal.

7. The frequency domain ground penetrating radar transmission source coding and received signal synthesis method according to claim 6, characterized in that: Step S5 is specifically as follows: Perform fast Fourier transform on the frequency point forward modeling result obtained in step S4 and express it using the following formula: Y i (f)=FFT{y i (t)} Where, FFT{} is fast Fourier transform; y i (t) is the time domain forward modeling result of the continuous wave transmission signal at the i-th frequency point; Y i (f) is y i (t), and Y i (f i )=H(f i )=I(f i )+jQ(f i ); H(f i ) is the complex value response of the ith frequency point; j is the imaginary unit; I(f i ) is the in-phase component of the i-th frequency point; Q(f i ) is the orthogonal component of the i-th frequency point; f i is the i-th frequency point; According to the sampling interval Δt of the time domain signal to be synthesized, the system bandwidth B is calculated using the following formula: Where Δt is the time domain signal sampling interval, and B is the system bandwidth; The complex-valued response at each frequency point is mapped to a double-sided spectrum that satisfies Hermitian symmetry, which can be expressed using the following formula: Among them, H synth (f k ) is the double-sided spectrum; f k For interval Frequency points evenly distributed with Δf as interval; H * (-f i ) is the complex-valued response H(f i )’s conjugate symmetry value; The bilateral spectrum is subjected to inverse Fourier transform to realize the synthesis of the frequency domain response into the time domain equivalent signal, which is expressed by the following formula: S synth (t)=IFFT{H synth (f)} Among them, S synth (t) is the final synthesized signal; IFFT{} is the inverse Fourier transform.

8. A system for implementing the frequency domain ground penetrating radar transmission source coding and received signal synthesis method according to any one of claims 1 to 7, characterized in that: It includes ultra-wideband transmission pulse calculation module, multi-frequency coded sine wave transmission signal construction module, typical geoelectric model construction module, ground penetrating radar signal forward modeling module, and signal synthesis module; The ultra-wideband transmit pulse calculation module intercepts the effective bandwidth based on the preset energy interception threshold, and then calculates the frequency step size using the target detection depth. It finally calculates the main frequency amplitude and phase of the ultra-wideband transmit pulse and uploads the data to the multi-frequency point coded sine wave transmit signal construction module. The multi-frequency point coded sine wave transmission signal construction module constructs a multi-frequency point coded sine wave transmission signal according to the received data, and uploads the data to the ground penetrating radar signal forward modeling module; The typical geoelectric model construction module constructs a typical geoelectric model for forward simulation based on the target detection depth and application scenario, and uploads the data to the ground penetrating radar signal forward modeling module; The GPR signal forward modeling module performs GPR signal forward modeling on the geoelectric model based on the received data and uses the impulse signal as the emission source to obtain the impulse response. It then obtains the time domain forward modeling result based on the multi-frequency coded sine wave emission signal and the impulse response, and uploads the data to the signal synthesis module. The signal synthesis module extracts the in-phase component and the orthogonal component of the frequency response according to the received data and the time domain forward modeling results, and then realizes the synthesis of the frequency domain response into the time domain equivalent signal based on the obtained in-phase component and the orthogonal component of the frequency response.

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