5MHz / 30MHz double-frequency focused ultrasound transmitting and receiving system and method based on FPGA (Field Programmable Gate Array)

Abstract

The invention discloses a 5MHz / 30MHz double-frequency focused ultrasound transmitting and receiving system and method based on an FPGA (Field Programmable Gate Array), in the system, an upper computer, an FPGA main control system, a pulse generating circuit, a switching circuit and a double-frequency focused ultrasound probe are sequentially connected to form a double-frequency focused ultrasound transmitting system; the operational amplifier circuit is connected between the AD sampling circuit and the switching circuit, and the AD sampling circuit is connected with the FPGA main control system; the double-frequency focused ultrasound probe is matched with the switching circuit, the operational amplifier circuit, the AD sampling circuit, the FPGA master control system and the upper computer to form a closed-loop double-frequency focused ultrasound receiving system with the double-frequency focused ultrasound transmitting system. According to the invention, the FPGA master control system is matched with the pulse generation circuit, and pulse width excitation signals with adjustable pulse width of 60 ns-400 ns and adjustable amplitude of 16 V-150 V can be output. And noise filtering and amplification are carried out on the harmonic signals through the operational amplifier circuit, so that the difficulty of processing the sampled data by the FPGA main control system can be reduced. By adopting the non-linear pulse compression method based on fan-shaped transformation, the signal-to-noise ratio can be increased, and different harmonic components can be separated.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial detection, and in particular to a 5MHz / 30MHz dual-frequency focused ultrasound transceiver system and method based on FPGA. Background Art

[0002] When low-frequency ultrasonic array elements emit low-frequency ultrasound, due to nonlinear effects, the reflected ultrasound will contain high-order or ultra-high-order harmonic components. Among them, ultrasonic harmonics refer to frequency components in ultrasonic signals whose frequencies are integer multiples of the fundamental frequency. In the process of ultrasonic generation, the fundamental frequency (first harmonic), second harmonic, third harmonic, etc. are usually generated, and the second harmonic, third harmonic, etc. are integer multiples of the fundamental frequency. Specifically, if the fundamental frequency of the ultrasound is f0, then its second harmonic is 2f0, the third harmonic is 3f0, and so on. These harmonic frequencies have important applications in ultrasonic technology because they can provide higher frequency resolution or finer signal characteristics than the fundamental frequency. Using nonlinear ultrasound to detect grain changes, track structural degradation, evaluate microscopic damage, and detect microcracks is a cutting-edge technology in non-destructive evaluation. Studies have shown that material nonlinearity, dislocations, persistent slip bands, and precipitation characteristics can lead to harmonic generation. Based on these theoretical studies, a large number of experiments have been conducted to evaluate fatigue damage in different materials, such as structural steels and nickel-based high-temperature alloys. In addition to fatigue damage, nonlinear ultrasound is also used to detect other failure mechanisms such as hardening, thermal aging, and radiation damage. However, since the various harmonic signals generated are superimposed on each other and have small amplitudes and low energy content of harmonics, the signal-to-noise ratio is poor, resulting in high difficulty in separating the harmonic signals. In addition, due to the nature of the electronic devices themselves, it is impossible to generate a pulse width excitation signal that satisfies the small pulse width, resulting in low resolution of received superharmonic signals. Moreover, the current traditional ultrasonic transceiver system can only receive the fundamental frequency ultrasonic signal that matches the reflection, and cannot receive the second or higher harmonic signals, which in turn makes it impossible to utilize the harmonic defect signals generated by the nonlinear effect. Summary of the invention

[0003] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA.

[0004] To achieve the above purpose, the technical solution provided by the present invention is:

[0005] A 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA, including a host computer, an FPGA main control system, a pulse generation circuit, a switching circuit, a dual-frequency focused ultrasound probe, an operational amplifier circuit, and an AD sampling circuit;

[0006] The host computer, FPGA main control system, pulse generating circuit, switching circuit, and dual-frequency focused ultrasound probe are connected in sequence to form a dual-frequency focused ultrasound transmitting system;

[0007] The operational amplifier circuit is connected between the AD sampling circuit and the switching circuit, and the AD sampling circuit is connected to the FPGA main control system; the dual-frequency focused ultrasound probe cooperates with the switching circuit, the operational amplifier circuit, the AD sampling circuit, the FPGA main control system, and the host computer to form a dual-frequency focused ultrasound receiving system that forms a closed loop with the dual-frequency focused ultrasound transmitting system.

[0008] Furthermore, the FPGA main control system is provided with a transmission control module, a data acquisition module, a data frequency reduction module, a pulse compression module and a communication module for transmitting a pulse width excitation signal;

[0009] The emission control module is connected to the pulse generating circuit;

[0010] The data acquisition module, data frequency reduction module, pulse compression module, communication module and host computer are connected in sequence.

[0011] Furthermore, the dual-frequency focused ultrasound probe includes a housing, a transmitting end interface, a receiving end interface, a transmitting adaptor electrical module, a receiving adaptor electrical module, a 5MHz transmitting chip, a 30MHz receiving chip, and an acoustic insulating sheet;

[0012] The transmitting end interface and the receiving end interface are both arranged on the top of the housing, and both are connected to the switching circuit;

[0013] The acoustic insulation sheet is arranged in the shell, dividing the inside of the shell into a transmitting space and a receiving space which are separated;

[0014] The transmitting adapting electrical module and the 5 MHz transmitting chip are both arranged in the transmitting space, and the transmitting adapting electrical module is connected between the transmitting end interface and the 5 MHz transmitting chip;

[0015] The receiving adapter electrical module and the 30MHz receiving chip are both arranged in the receiving space, and the receiving adapter electrical module is connected between the receiving end interface and the 30MHz receiving chip.

[0016] Furthermore, the 5 MHz transmitting chip is a lead magnesium niobate 5 MHz transmitting chip.

[0017] Furthermore, the 30 MHz receiving chip is a polyvinylidene fluoride 30 MHz receiving chip.

[0018] To achieve the above object, the present invention further provides a 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA, which is implemented by the above-mentioned 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA, including:

[0019] Signal transmission phase:

[0020] Place the dual-frequency focused ultrasonic probe on the workpiece to be inspected, and set the parameters and the type of pulse width excitation signal on the host computer;

[0021] The FPGA main control system transmits a pulse width excitation signal with adjustable frequency f and adjustable amplitude;

[0022] The pulse generating circuit amplifies the amplitude of the pulse width excitation signal;

[0023] The switching circuit performs path switching to transmit the amplified pulse width excitation signal to the dual-frequency focused ultrasound probe;

[0024] The dual-frequency focused ultrasound probe converts the amplified pulse width excitation signal into pulsed ultrasound waves;

[0025] Signal receiving stage:

[0026] The workpiece to be inspected generates a harmonic signal with a frequency of nf under the action of the pulse ultrasonic signal, where n is 1 / 2, 1, 2, 3, ...;

[0027] The dual-frequency focused ultrasound probe receives the harmonic signal and converts the harmonic signal into an electrical signal;

[0028] The switching circuit performs path switching and transmits the electrical signal to the operational amplifier circuit;

[0029] The operational amplifier circuit performs noise filtering and amplification on the electrical signal;

[0030] The AD sampling circuit samples the electrical signal after noise filtering and amplification;

[0031] The FPGA main control system processes the sampled data to increase the signal-to-noise ratio and separate different harmonic components;

[0032] The host computer displays the data processed by the FPGA main control system.

[0033] Furthermore, the FPGA main control system processes the sampled data by down-converting the data and adopting nonlinear pulse compression based on sector transformation.

[0034] Furthermore, nonlinear pulse compression based on sector transformation is adopted, including:

[0035] Define the FCT transform kernel:

[0036] The generated n-th order harmonic components have similar phase parameters as the FCT kernel; for any given chirp rate, the FCT achieves the best compression including all harmonics of the FCT of interest, as follows:

[0037] Generate a linear frequency modulated real signal:

[0038]

[0039] in,

[0040] Where A(t) is the amplitude modulation function, f0 is the center frequency, f0 = 5 MHz, B is the -20-dB bandwidth containing 99% of the total signal energy, T is the signal duration, and σ = B / T is the chirp rate;

[0041] The FCT transform of the modulated real signal s(t), centered at the origin and with a signal duration of T, is output as:

[0042]

[0043] in,

[0044] Where t is time, f is frequency, is a phase function controlled by the normalized chirp rate (σ / f); is expressed as the frequency-normalized phase function associated with a linear frequency chirp of the same slope as defined in (1.1); when f = f0, = θ(t) / f, the best match for the transformation kernel f = nf0 will be a new chirp rate with a center frequency and slope that are n times the original;

[0045] Generate a series of harmonic modulation signals, expressed as:

[0046]

[0047] That

[0048] Among them, f n is the nth-order harmonic frequency, n=1, 2, 3, ...;

[0049] The received ultrasonic echo signal F(t) is combined with each harmonic modulation signal S n (f n ,σ) are multiplied one by one:

[0050] F(f n ,σ)=F(t)·S n [(f n ,σ)] (1.4)

[0051] Inverse FCT transform:

[0052] Separation between spectrally overlapping harmonics is achieved by applying the inverse FCT transform to all individual harmonics:

[0053]

[0054] Compared with the prior art, the principles and advantages of this technical solution are as follows:

[0055] 1. The FPGA main control system and the pulse generating circuit cooperate to output a pulse width excitation signal with adjustable pulse width of 60ns to 400ns and adjustable amplitude of 16V to 150V.

[0056] 2. By filtering and amplifying the harmonic signal through the operational amplifier circuit, the difficulty of the FPGA main control system in processing the sampled data can be reduced.

[0057] 3. The use of nonlinear pulse compression method based on fan chirp transform (FCT) can increase the signal-to-noise ratio and separate different harmonic components. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the services required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0059] Figure 1 This is a connection block diagram of a 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA of the present invention;

[0060] Figure 2 A stereoscopic diagram of a dual-frequency focused ultrasound probe in a 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA of the present invention;

[0061] Figure 3 This is an internal schematic diagram of a dual-frequency focused ultrasound probe in a 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA of the present invention (A is a workpiece to be inspected);

[0062] Figure 4 The present invention is a principle flow chart of a 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA.

[0063] Reference numerals:

[0064] 1-host computer; 2-FPGA main control system; 3-pulse generating circuit; 4-switching circuit; 5-dual-frequency focused ultrasound probe; 6-operational amplifier circuit; 7-AD sampling circuit; 8-transmission control module; 9-data acquisition module; 10-data frequency reduction module; 11-pulse compression module; 12-communication module; 13-housing; 14-transmitter interface; 15-receiver interface; 16-transmitter adapter electrical module; 17-receiver adapter electrical module; 18-5MHz transmitter chip; 19-30MHz receiver chip; 20-acoustic insulation sheet. DETAILED DESCRIPTION

[0065] The present invention will be further described below in conjunction with specific embodiments:

[0066] like Figure 1 As shown, the 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA described in this embodiment includes a host computer 1, an FPGA main control system 2, a pulse generating circuit 3, a switching circuit 4, a dual-frequency focused ultrasound probe 5, an operational amplifier circuit 6, and an AD sampling circuit 7;

[0067] The host computer 1, the FPGA main control system 2, the pulse generating circuit 3, the switching circuit 4, and the dual-frequency focused ultrasound probe 5 are sequentially connected to form a dual-frequency focused ultrasound transmitting system;

[0068] The operational amplifier circuit 6 is connected between the AD sampling circuit 7 and the switching circuit 4, and the AD sampling circuit 7 is connected to the FPGA main control system 2; the dual-frequency focused ultrasound probe 5 cooperates with the switching circuit 4, the operational amplifier circuit 6, the AD sampling circuit 7, the FPGA main control system 2, and the host computer 1 to form a dual-frequency focused ultrasound receiving system that forms a closed loop with the dual-frequency focused ultrasound transmitting system.

[0069] Specifically, in this embodiment, the FPGA main control system 2 is provided with a transmission control module 8, a data acquisition module 9, a data frequency reduction module 10, a pulse compression module 11 and a communication module 12 for transmitting a pulse width excitation signal; the transmission control module 8 is connected to the pulse generating circuit 3; the data acquisition module 9, the data frequency reduction module 10, the pulse compression module 11, the communication module 12, and the host computer 1 are connected in sequence.

[0070] like Figure 2 and Figure 3As shown, the dual-frequency focused ultrasound probe 5 includes a shell 13, a transmitting end interface 14, a receiving end interface 15, a transmitting adapter electrical module 16, a receiving adapter electrical module 17, a 5MHz transmitting chip 18, a 30MHz receiving chip 19, and an acoustic insulating sheet 20; the transmitting end interface 14 and the receiving end interface 15 are both arranged at the top of the shell 13, and both are connected to the switching circuit 4; the acoustic insulating sheet 20 is arranged in the shell 13, dividing the inside of the shell 13 into a separated transmitting space and a receiving space; the transmitting adapter electrical module 16 and the 5MHz transmitting chip 18 are both arranged in the transmitting space, and the transmitting adapter electrical module 16 is connected between the transmitting end interface 14 and the 5MHz transmitting chip 18; the receiving adapter electrical module 17 and the 30MHz receiving chip 19 are both arranged in the receiving space, and the receiving adapter electrical module 17 is connected between the receiving end interface 15 and the 30MHz receiving chip 19.

[0071] Specifically, in this embodiment, the dual-frequency focused ultrasonic probe 5 is a dual-frequency focused ultrasonic transducer with 5MHz transmission and 30MHz reception, and its transmission center frequency is 5MHz, -6dB bandwidth is 80%, and its reception center frequency is 30MHz, -6dB bandwidth is 65%. The dual-frequency focused ultrasonic probe 5 uses lead magnesium niobate (PMN-PT) single crystal as the transmission material, which has the characteristics of high piezoelectric constant, large electromechanical coupling coefficient, high dielectric constant and low loss. In particular, the piezoelectric performance is about 10 times higher than that of ordinary piezoelectric materials, so that it can be used in a wider range of applications than traditional PZT piezoelectric ceramics, and the ultrasonic transducer made of it has lower input power loss; in addition, PVDF (polyvinylidene fluoride) is used as the receiving material. It is a high molecular piezoelectric polymer with small elastic stiffness and large mechanical damping, which is easy to obtain better matching. At the same time, its low permittivity is also easy to match with the electrical output circuit, and there are few tail waves when receiving.

[0072] like Figure 4 As shown, the working principle of this embodiment is as follows:

[0073] Signal transmission phase:

[0074] Place the dual-frequency focused ultrasonic probe 5 on the workpiece to be detected, and set the parameters (frequency, amplitude, duty cycle, etc.) and the type of pulse width excitation signal (square wave, sine wave, triangle wave, spike wave, etc.) on the host computer 1;

[0075] The FPGA main control system 2 transmits a pulse width excitation signal with adjustable frequency f (1-5MHz) and adjustable amplitude (0-10V);

[0076] The pulse generating circuit 3 amplifies the amplitude of the pulse width excitation signal, and the amplitude can be adjusted to 16-150V;

[0077] The switching circuit 4 performs path switching and transmits the amplified pulse width excitation signal to the dual-frequency focused ultrasound probe 5;

[0078] The dual-frequency focused ultrasound probe 5 converts the amplified pulse width excitation signal into pulsed ultrasound waves;

[0079] Signal receiving stage:

[0080] The workpiece to be inspected generates a harmonic signal with a frequency of nf under the action of the pulse ultrasonic signal, where n is 1 / 2, 1, 2, 3, ...;

[0081] The dual-frequency focused ultrasound probe 5 receives the harmonic signal and converts the harmonic signal into an electrical signal;

[0082] The switching circuit 4 performs path switching and transmits the electrical signal to the operational amplifier circuit 6;

[0083] The operational amplifier circuit 6 performs noise filtering and amplification on the electrical signal;

[0084] The AD sampling circuit 7 samples the electrical signal after noise filtering and amplification;

[0085] The FPGA main control system 2 processes the sampled data to increase the signal-to-noise ratio and separate different harmonic components;

[0086] The host computer 1 displays the data processed by the FPGA main control system 2.

[0087] In the above, the FPGA main control system 2 processes the sampled data by performing data frequency reduction through the data frequency reduction module 10 and adopting a nonlinear pulse compression method based on sector transformation through the pulse compression module 11 .

[0088] Adopt nonlinear pulse compression based on sector transformation, including:

[0089] Define the FCT transform kernel:

[0090] The generated n-th order harmonic components have similar phase parameters as the FCT kernel; for any given chirp rate, the FCT achieves the best compression including all harmonics of the FCT of interest, as follows:

[0091] Generate a linear frequency modulated real signal:

[0092]

[0093] That

[0094] Where A(t) is the amplitude modulation function, f0 is the center frequency, f0 = 5 MHz, B is the -20-dB bandwidth containing 99% of the total signal energy, T is the signal duration, and σ = B / T is the chirp rate;

[0095] The FCT transform of the modulated real signal s(t), centered at the origin and with a signal duration of T, is output as:

[0096]

[0097] in,

[0098] Where t is time, f is frequency, is a phase function controlled by the normalized chirp rate (σ / f); is expressed as the frequency-normalized phase function associated with a linear frequency chirp of the same slope as defined in (1.1); when f = f0, = θ(t) / f, the best match for the transformation kernel f = nf0 will be a new chirp rate with a center frequency and slope that are n times the original;

[0099] Generate a series of harmonic modulation signals, expressed as:

[0100]

[0101] sweet

[0102] Among them, f n is the nth-order harmonic frequency, n=1, 2, 3, ...;

[0103] The received ultrasonic echo signal F(t) is combined with each harmonic modulation signal S n (f n ,σ) are multiplied one by one:

[0104] F(f n ,σ)=F(t)·S n [(f n ,σ)] (1.4)

[0105] (This process helps to enhance or extract signal components associated with specific harmonic frequencies)

[0106] Inverse FCT transform:

[0107] Separation between spectrally overlapping harmonics is achieved by applying the inverse FCT transform to all individual harmonics:

[0108]

[0109] In this embodiment,

[0110] 1) The FPGA main control system 2 and the pulse generating circuit 3 cooperate to output a pulse width excitation signal with an adjustable pulse width of 60ns to 400ns and an adjustable amplitude of 16V to 150V.

[0111] 2) By filtering and amplifying the noise of the harmonic signal through the operational amplifier circuit 6, the difficulty of the FPGA main control system 2 in processing the sampled data can be reduced.

[0112] 3) The nonlinear pulse compression method based on fan chirp transform (FCT) can increase the signal-to-noise ratio and separate different harmonic components. The nonlinear pulse compression algorithm is used to obtain narrow pulses during reception to improve the resolution, which better solves the problem of unclear pulse width characteristics of the received superharmonic signal.

[0113] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, all changes made according to the shape and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA, characterized in that: It includes a host computer, FPGA main control system, pulse generation circuit, switching circuit, dual-frequency focused ultrasound probe, operational amplifier circuit, and AD sampling circuit; The host computer, FPGA main control system, pulse generating circuit, switching circuit, and dual-frequency focused ultrasound probe are connected in sequence to form a dual-frequency focused ultrasound transmitting system; The operational amplifier circuit is connected between the AD sampling circuit and the switching circuit, and the AD sampling circuit is connected to the FPGA main control system; the dual-frequency focused ultrasound probe cooperates with the switching circuit, the operational amplifier circuit, the AD sampling circuit, the FPGA main control system, and the host computer to form a dual-frequency focused ultrasound receiving system that forms a closed loop with the dual-frequency focused ultrasound transmitting system.

2. The 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA according to claim 1, characterized in that: The FPGA main control system is provided with a transmission control module, a data acquisition module, a data frequency reduction module, a pulse compression module and a communication module for transmitting a pulse width excitation signal; The emission control module is connected to the pulse generating circuit; The data acquisition module, data frequency reduction module, pulse compression module, communication module and host computer are connected in sequence.

3. The 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA according to claim 1, characterized in that: The dual-frequency focused ultrasound probe includes a housing, a transmitting end interface, a receiving end interface, a transmitting adapting electrical module, a receiving adapting electrical module, a 5MHz transmitting chip, a 30MHz receiving chip, and an acoustic insulating sheet; The transmitting end interface and the receiving end interface are both arranged on the top of the housing, and both are connected to the switching circuit; The acoustic insulation sheet is arranged in the shell, dividing the inside of the shell into a transmitting space and a receiving space which are separated; The transmitting adapting electrical module and the 5 MHz transmitting chip are both arranged in the transmitting space, and the transmitting adapting electrical module is connected between the transmitting end interface and the 5 MHz transmitting chip; The receiving adapter electrical module and the 30MHz receiving chip are both arranged in the receiving space, and the receiving adapter electrical module is connected between the receiving end interface and the 30MHz receiving chip.

4. The 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA according to claim 3, characterized in that: The 5 MHz transmitting chip is a lead magnesium niobate 5 MHz transmitting chip.

5. The 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA according to claim 3, characterized in that: The 30 MHz receiving chip is a polyvinylidene fluoride 30 MHz receiving chip.

6. A 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA, implemented by the 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA according to any one of claims 1 to 5, characterized in that: include: Signal transmission phase: Place the dual-frequency focused ultrasonic probe on the workpiece to be inspected, and set the parameters and the type of pulse width excitation signal on the host computer; The FPGA main control system transmits a pulse width excitation signal with adjustable frequency f and adjustable amplitude; The pulse generating circuit amplifies the amplitude of the pulse width excitation signal; The switching circuit performs path switching to transmit the amplified pulse width excitation signal to the dual-frequency focused ultrasound probe; The dual-frequency focused ultrasound probe converts the amplified pulse width excitation signal into pulsed ultrasound waves; Signal receiving stage: The workpiece to be inspected generates a harmonic signal with a frequency of nf under the action of the pulse ultrasonic signal, where n is 1 / 2, 1, 2, 3, ...; The dual-frequency focused ultrasound probe receives the harmonic signal and converts the harmonic signal into an electrical signal; The switching circuit performs path switching and transmits the electrical signal to the operational amplifier circuit; The operational amplifier circuit performs noise filtering and amplification on the electrical signal; The AD sampling circuit samples the electrical signal after noise filtering and amplification; The FPGA main control system processes the sampled data to increase the signal-to-noise ratio and separate different harmonic components; The host computer displays the data processed by the FPGA main control system.

7. The 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA according to claim 6, characterized in that: The FPGA main control system processes the sampled data including data frequency reduction and nonlinear pulse compression based on sector transformation.

8. The 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA according to claim 7, characterized in that: Adopt nonlinear pulse compression based on sector transformation, including: Define the FCT transform kernel: The generated n-th order harmonic components have similar phase parameters as the FCT kernel; for any given chirp rate, the FCT achieves the best compression including all harmonics of the FCT of interest, as follows: Generate a linear frequency modulated real signal: Sweet Where A(t) is the amplitude modulation function, f0 is the center frequency, f0 = 5 MHz, B is the -20-dB bandwidth containing 99% of the total signal energy, T is the signal duration, and σ = B / T is the chirp rate; The FCT transform of the modulated real signal s(t), centered at the origin and with a signal duration of T, is output as: in, Where t is time, f is frequency, is a phase function controlled by the normalized chirp rate (σ / f); is expressed as the frequency-normalized phase function associated with a linear frequency chirp of the same slope as defined in (1.1); when f = f0, = θ(t) / f, the best match for the transformation kernel f = nf0 will be a new chirp rate with a center frequency and slope that are n times the original; Generate a series of harmonic modulation signals, expressed as: in, Among them, f n is the nth-order harmonic frequency, n=1, 2, 3, ...; The received ultrasonic echo signal F(t) is combined with each harmonic modulation signal S n (f n ,σ) are multiplied one by one: F(f n ,σ)=F(t)·S n [(f n ,σ)] (1.4) Inverse FCT transform: Separation between spectrally overlapping harmonics is achieved by applying the inverse FCT transform to all individual harmonics:

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