A 5MHz / 30MHz dual-frequency focused ultrasound transceiver system and method based on FPGA

Abstract

This invention discloses a 5MHz / 30MHz dual-frequency focused ultrasound transceiver system and method based on FPGA. In the system, a host computer, an FPGA main control system, a pulse generation circuit, a switching circuit, and a dual-frequency focused ultrasound probe are sequentially connected to form a dual-frequency focused ultrasound transmitting system. An operational amplifier circuit is connected between an 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, along with the switching circuit, operational amplifier circuit, AD sampling circuit, FPGA main control system, and host computer, forms a closed-loop dual-frequency focused ultrasound receiving system. In this invention, the FPGA main control system and the pulse generation circuit work together to output a pulse width excitation signal with adjustable pulse width from 60ns to 400ns and an amplitude adjustable from 16V to 150V. Noise filtering and amplification of harmonic signals through the operational amplifier circuit reduces the difficulty of processing the sampled data by the FPGA main control system. The use of a nonlinear pulse compression method based on sector transform increases the signal-to-noise ratio and separates different harmonic components.

Description

Technical Field

[0001] This invention relates to the technical field of industrial testing, and in particular to a 5MHz / 30MHz dual-frequency focused ultrasonic transceiver system and method based on FPGA. Background Technology

[0002] When low-frequency ultrasonic array elements emit low-frequency ultrasound, the reflected ultrasound waves contain high-order or ultra-high-order harmonic components due to nonlinear effects. Ultrasonic harmonics refer to frequency components in the ultrasonic signal whose frequencies are integer multiples of the fundamental frequency. During the generation of ultrasound, a fundamental frequency (first harmonic), second harmonic, third harmonic, etc., are typically generated, and these second and third harmonics are integer multiples of the fundamental frequency. Specifically, if the fundamental frequency of the ultrasound is f0, then its second harmonic is 2f0, its 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. Utilizing nonlinear ultrasound to detect grain changes, track structural degradation, assess microscopic damage, and detect microcracks is a cutting-edge technique in nondestructive assessment. Research shows that material nonlinearity, dislocations, persistent slip bands, and precipitation characteristics lead to harmonic generation. Based on these theoretical studies, numerous experiments have been conducted to evaluate fatigue damage in different materials, such as structural steel and nickel-based superalloys. Besides fatigue damage, nonlinear ultrasound has also been used to detect other failure mechanisms, such as hardening, thermal aging, and radiation damage. However, due to the superposition of various harmonic signals, their small amplitude, and low energy content, the signal-to-noise ratio is poor, making it difficult to separate the individual harmonic signals. Furthermore, due to the inherent nature of electronic devices, it is impossible to generate pulse width excitation signals that meet the required pulse width, resulting in low resolution for receiving superharmonic signals. Moreover, current traditional ultrasonic transceiver systems can only receive the fundamental frequency ultrasonic signal that is reflected and match it, and cannot receive second or higher harmonic signals, thus preventing the utilization of harmonic defect signals generated by nonlinear effects. Summary of the Invention

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

[0004] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0005] A 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA includes 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 generation circuit, switching circuit and dual-frequency focused ultrasound probe are connected in sequence to form a dual-frequency focused ultrasound transmission system.

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

[0008] Furthermore, the FPGA main control system includes a transmission control module for transmitting pulse width excitation signals, a data acquisition module, a data down-conversion module, a pulse compression module, and a communication module.

[0009] The transmission control module is connected to the pulse generation circuit;

[0010] The data acquisition module, data down-conversion 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 transmitter interface, a receiver interface, a transmitter adapter electrical module, a receiver adapter electrical module, a 5MHz transmitter chip, a 30MHz receiver chip, and an acoustic insulating sheet;

[0012] Both the transmitter interface and the receiver interface are located on the top of the housing, and both are connected to the switching circuit.

[0013] The acoustic insulating sheet is located inside the outer shell, dividing the interior of the outer shell into a separate transmitting space and a receiving space.

[0014] Both the transmission adapter electrical module and the 5MHz transmission chip are located within the transmission space, with the transmission adapter electrical module connected between the transmitter interface and the 5MHz transmission chip.

[0015] Both the receiver adapter electrical module and the 30MHz receiver chip are located within the receiving space, with the receiver adapter electrical module connected between the receiver interface and the 30MHz receiver chip.

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

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

[0018] To achieve the above objectives, the present invention further provides a 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA, implemented using the aforementioned 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA, comprising:

[0019] Signal transmission phase:

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

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

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

[0023] The switching circuit performs path switching, transmitting 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 reception stage:

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

[0027] The dual-frequency focused ultrasound probe receives harmonic signals and converts them into electrical signals.

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

[0029] Operational amplifier circuits filter noise and amplify electrical signals;

[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, including data down-frequency reduction and nonlinear pulse compression based on sector transform.

[0034] Furthermore, nonlinear pulse compression based on sector transform is employed, including:

[0035] Define the FCT transform kernel:

[0036] The generated nth-order harmonic components have phase parameters similar to those of the FCT kernel; for any given chirp rate, the FCT achieves optimal 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 = 5MHz, B is the bandwidth containing 99% of the total signal energy in -20 dB, T is the signal duration, and σ = B / T is the chirp rate.

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

[0042]

[0043] in,

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

[0045] A series of harmonic modulation signals are generated, represented as:

[0046]

[0047] That

[0048] Among them, f n Let n be the nth harmonic frequency, where n = 1, 2, 3, ...;

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

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

[0051] Inverse FCT transform:

[0052] By applying the inverse FCT transform to process all individual harmonics, separation between spectrally overlapping harmonics is achieved.

[0053]

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

[0055] 1. The FPGA main control system and pulse generation circuit work together to output pulse width excitation signals with adjustable pulse width from 60ns to 400ns and adjustable amplitude from 16V to 150V.

[0056] 2. By using operational amplifier circuits to filter and amplify harmonic signals, the difficulty of processing the sampled data by the FPGA main control system can be reduced.

[0057] 3. The nonlinear pulse compression method based on fan chirp transform (FCT) can increase the signal-to-noise ratio and separate different harmonic components. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the services required in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

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

[0060] Figure 2 This is a three-dimensional view of the dual-frequency focused ultrasound probe in a 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA according to the present invention.

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

[0062] Figure 4 This is a flowchart illustrating the principle of a 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA according to the present invention.

[0063] Figure label:

[0064] 1-Host computer; 2-FPGA main control system; 3-Pulse generation circuit; 4-Switching circuit; 5-Dual-frequency focusing ultrasonic probe; 6-Operational amplifier circuit; 7-AD sampling circuit; 8-Transmission control module; 9-Data acquisition module; 10-Data down-conversion module; 11-Pulse compression module; 12-Communication module; 13-Housing shell; 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 Implementation

[0065] The present invention will be further described below with reference to specific embodiments:

[0066] like Figure 1 As shown in the figure, 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 generation 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, FPGA main control system 2, pulse generation circuit 3, switching circuit 4, and dual-frequency focused ultrasound probe 5 are connected in sequence to form a dual-frequency focused ultrasound transmission system.

[0068] Operational amplifier circuit 6 is connected between AD sampling circuit 7 and switching circuit 4, while AD sampling circuit 7 is connected to FPGA main control system 2; dual-frequency focused ultrasound probe 5, together with switching circuit 4, operational amplifier circuit 6, AD sampling circuit 7, FPGA main control system 2, and host computer 1, form a closed-loop dual-frequency focused ultrasound receiving system with 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 for transmitting pulse width excitation signals, a data acquisition module 9, a data down-conversion module 10, a pulse compression module 11, and a communication module 12; the transmission control module 8 is connected to the pulse generation circuit 3; the data acquisition module 9, the data down-conversion 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 housing 13, a transmitter interface 14, a receiver interface 15, a transmitter adapter electrical module 16, a receiver adapter electrical module 17, a 5MHz transmitter chip 18, a 30MHz receiver chip 19, and an acoustic insulating sheet 20. The transmitter interface 14 and the receiver interface 15 are both located on the top of the housing 13 and are both connected to the switching circuit 4. The acoustic insulating sheet 20 is located inside the housing 13, dividing the interior of the housing 13 into a separate transmitter space and a receiver space. The transmitter adapter electrical module 16 and the 5MHz transmitter chip 18 are both located in the transmitter space, with the transmitter adapter electrical module 16 connected between the transmitter interface 14 and the 5MHz transmitter chip 18. The receiver adapter electrical module 17 and the 30MHz receiver chip 19 are both located in the receiver space, with the receiver adapter electrical module 17 connected between the receiver interface 15 and the 30MHz receiver chip 19.

[0071] Specifically, in this embodiment, the dual-frequency focused ultrasonic probe 5 is a dual-frequency focused ultrasonic transducer with a 5MHz transmitter and a 30MHz receiver. Its transmitter center frequency is 5MHz with a -6dB bandwidth of 80%, and its receiver center frequency is 30MHz with a -6dB bandwidth of 65%. The dual-frequency focused ultrasonic probe 5 uses lead magnesium niobate (PMN-PT) single crystal as the transmitting material. This material has the characteristics of high piezoelectric constant, large electromechanical coupling coefficient, high dielectric constant, and low loss. In particular, its piezoelectric performance is about 10 times higher than that of ordinary piezoelectric materials, which allows it to have a wider range of applications than traditional PZT piezoelectric ceramics. The ultrasonic transducer made with 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 low elastic stiffness and high mechanical damping, which makes it easy to obtain good matching. At the same time, its low permittivity makes it easy to match with the electrical output circuit, resulting in less wake wave during reception.

[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 tested, and set the parameters (frequency, amplitude and 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 an adjustable frequency f (1-5MHz) and adjustable amplitude (0-10V);

[0076] The pulse generation circuit 3 amplifies the amplitude of the pulse width excitation signal, and the amplitude is adjustable from 16-150V;

[0077] The switching circuit 4 performs path switching, transmitting 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 reception stage:

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

[0081] The dual-frequency focused ultrasound probe 5 receives harmonic signals and converts them into electrical signals.

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

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

[0084] 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 down-frequency reduction through the data down-frequency module 10 and by using a nonlinear pulse compression method based on sector transformation through the pulse compression module 11.

[0088] The nonlinear pulse compression based on sector transform is employed, including:

[0089] Define the FCT transform kernel:

[0090] The generated nth-order harmonic components have phase parameters similar to those of the FCT kernel; for any given chirp rate, the FCT achieves optimal 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 = 5MHz, B is the bandwidth containing 99% of the total signal energy in -20 dB, T is the signal duration, and σ = B / T is the chirp rate.

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

[0096]

[0097] in,

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

[0099] A series of harmonic modulation signals are generated, represented as:

[0100]

[0101] sweet

[0102] Among them, f n Let n be the nth harmonic frequency, where n = 1, 2, 3, ...;

[0103] The received ultrasonic echo signal F(t) is combined with each harmonic modulation signal S n (f n Multiply by σ 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 related to specific harmonic frequencies)

[0106] Inverse FCT transform:

[0107] By applying the inverse FCT transform to process all individual harmonics, separation between spectrally overlapping harmonics is achieved.

[0108]

[0109] In this embodiment,

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

[0111] 2) By using the operational amplifier circuit 6 to filter and amplify the harmonic signal, the difficulty of the FPGA main control system 2 in processing the sampled data can be reduced.

[0112] 3) Employing a nonlinear pulse compression method based on fan-chip transform (FCT) can increase the signal-to-noise ratio and separate different harmonic components. During reception, a nonlinear pulse compression algorithm is used to obtain narrow pulses, thereby improving resolution and effectively solving the problem of unclear pulse width characteristics in the received superharmonic signals.

[0113] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA, characterized in that, Includes host computer, FPGA main control system, pulse generation circuit, switching circuit, dual-frequency focusing ultrasound probe, operational amplifier circuit, and AD sampling circuit; The host computer, FPGA main control system, pulse generation circuit, switching circuit and dual-frequency focused ultrasound probe are connected in sequence to form a dual-frequency focused ultrasound transmission system. The operational amplifier circuit is connected between the AD sampling circuit and the switching circuit, while the AD sampling circuit is connected to the FPGA main control system; the dual-frequency focused ultrasound probe, together with the switching circuit, operational amplifier circuit, AD sampling circuit, FPGA main control system, and host computer, forms a closed-loop dual-frequency focused ultrasound receiving system with the dual-frequency focused ultrasound transmitting system; The FPGA main control system includes a transmission control module for transmitting pulse width excitation signals, a data acquisition module, a data down-conversion module, a pulse compression module, and a communication module. The transmission control module is connected to the pulse generation circuit; The data acquisition module, data down-conversion module, pulse compression module, communication module, and host computer are connected in sequence. The dual-frequency focused ultrasound probe includes a housing, a transmitter interface, a receiver interface, a transmitter adapter electrical module, a receiver adapter electrical module, a 5MHz transmitter chip, a 30MHz receiver chip, and an acoustic insulating sheet. Both the transmitter interface and the receiver interface are located on the top of the housing, and both are connected to the switching circuit. The acoustic insulating sheet is located inside the outer shell, dividing the interior of the outer shell into a separate transmitting space and a receiving space. Both the transmission adapter electrical module and the 5MHz transmission chip are located within the transmission space, with the transmission adapter electrical module connected between the transmitter interface and the 5MHz transmission chip. Both the receiver adapter electrical module and the 30MHz receiver chip are located within the receiving space, with the receiver adapter electrical module connected between the receiver interface and the 30MHz receiver chip.

2. The FPGA-based 5MHz / 30MHz dual-frequency focused ultrasound transceiver system according to claim 1, characterized in that, The 5MHz transmitter chip is a lead magnesium niobate 5MHz transmitter chip.

3. The FPGA-based 5MHz / 30MHz dual-frequency focused ultrasound transceiver system according to claim 1, characterized in that, The 30MHz receiver chip is a polyvinylidene fluoride 30MHz receiver chip.

4. A 5MHz / 30MHz dual-frequency focused ultrasound transceiver method based on FPGA, implemented using the 5MHz / 30MHz dual-frequency focused ultrasound transceiver system based on FPGA as described in any one of claims 1-3, characterized in that, include: Signal transmission phase: Place the dual-frequency focused ultrasonic probe on the workpiece to be tested, and set the parameters and the type of pulse width excitation signal on the host computer. The FPGA main control system transmits pulse width excitation signals with adjustable frequency f and adjustable amplitude; The pulse generation circuit amplifies the amplitude of the pulse width excitation signal; The switching circuit performs path switching, transmitting 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 reception stage: The workpiece to be inspected generates a harmonic signal with a frequency of nf under the action of a pulsed ultrasonic signal, where n is 1 / 2, 1, 2, 3, ...; The dual-frequency focused ultrasound probe receives harmonic signals and converts them into electrical signals. The switching circuit performs path switching and sends the electrical signal to the operational amplifier circuit; Operational amplifier circuits filter noise and amplify electrical signals; 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; The FPGA main control system processes the sampled data, including data down-frequency reduction and nonlinear pulse compression based on sector transform.

5. The FPGA-based 5MHz / 30MHz dual-frequency focused ultrasound transceiver method according to claim 4, characterized in that, The nonlinear pulse compression based on sector transform is employed, including: Define the FCT transform kernel: The generated nth-order harmonic components have phase parameters similar to those of the FCT kernel; for any given chirp rate, the FCT achieves optimal compression including all harmonics of the FCT of interest, as follows: Generate a linear frequency modulated real signal: in, Where A(t) is the amplitude modulation function, f0 is the center frequency, f0 = 5MHz, B is the bandwidth containing 99% of the total signal energy in -20dB, T is the signal duration, and σ = B / T is the chirp rate. The FCT transform of a modulated real signal s(t), centered at the origin and with duration T, is output as: in, Where t is time and f is frequency. The phase function is controlled by the normalized chirp rate (σ / f); It is expressed as a frequency-normalized phase function associated with a linear frequency chirp with the same slope defined in (1.1); when f = f0, It is equal to θ(t) / f. In order to achieve the best match between the transform kernel and the signal, the center frequency and the chirp rate are both n times the original signal parameters f0 and σ. A series of harmonic modulation signals are generated, represented as: in, Among them, f n Let n be the nth harmonic frequency, where n is 1 / 2, 1, 2, 3, ...; The received ultrasonic echo signal F(t) is combined with each harmonic modulation signal S n (f n Multiply by σ one by one: F(f n ,σ)=F(t)·S n [(f n ,σ)] (1.4) Inverse FCT transform: By applying the inverse FCT transform to process all individual harmonics, separation between spectrally overlapping harmonics is achieved.

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