TI acquisition system joint error compensation method based on periodic time-varying filtering

Abstract

The invention discloses a TI acquisition system joint error compensation method based on periodic time-varying filtering, and the method comprises the steps: transmitting different excitation signals into a TI acquisition system, achieving the estimation of an FRM error of the TI acquisition system, and designing a periodic time-varying filter for FRM error compensation; compensating the error of the FRM, performing FRD error estimation, and designing a frequency response non-ideal error compensation filter for FRD error compensation; and finally, the periodic time-varying filter and the frequency response non-ideal error compensation filter are cascaded and then deployed in the FPGA, so that combined compensation of FRM and FRD errors of the input signal can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of TI acquisition systems, and more specifically, relates to a TI acquisition system joint error compensation method based on periodic time-varying filtering. Background Art

[0002] As the core unit that converts analog signals into digital signals, the data acquisition system is widely used in communications, nuclear physics,

[0003] It has a wide range of applications in deep space exploration, measuring instruments and other fields. With the advancement of science and technology, the signals in these fields are becoming more and more complex, with wider bandwidth and more significant transient characteristics, which puts higher performance requirements on the sampling rate of the data acquisition system. However, limited by the existing integrated circuit process, the monolithic analog to digital converter (ADC) chip is difficult to meet the indicators of the data acquisition system, especially the sampling rate indicator requirements. According to the Nyquist sampling theorem, the sampling clock frequency should be greater than 2 times the frequency of the signal in order to reconstruct the signal. For more complex waveforms, if the waveform details are to be better described, a higher sampling rate is required to obtain more sample points. Therefore, the time-interleaved (TI) acquisition architecture is proposed to achieve performance indicators that are several times higher than the sampling rate of the monolithic ADC.

[0004] The TI acquisition architecture was proposed by Black and Hodges in 1980. Its core principle is to use M slices with a sampling rate of f s ADC, increasing the sampling rate of the acquisition system to Mf s , which adjusts the sampling clock phase of the M-chip ADCs so that the ADCs sample the signals at fixed intervals in sequence, and finally splices the collected data, thereby increasing the sampling rate. In actual acquisition systems, since the physical parameters of the front-end analog circuits of different sampling paths cannot be guaranteed to be exactly the same, the TI architecture will inevitably produce sampling inconsistency errors, and as the bandwidth of the acquisition system increases, the error changes with frequency, which is called frequency response mismatch (FRM) error.

[0005] In addition, due to the non-ideality of the signal conditioning channel of the high-bandwidth acquisition system, the amplitude-frequency response in the acquisition system is not flat and the phase response is nonlinear. This frequency response distortion (FRD) error further increases the distortion of the broadband signal sampling result. The existence of these errors makes it impossible for the sampling result to accurately restore the original input signal. In order to reduce the difference between the sampling result and the input signal, these errors must be compensated so that the compensated signal is an accurate reconstruction of the original input.

[0006] At present, the compensation of TI acquisition system errors mostly adopts the divide-and-conquer method, that is, to compensate for FRM and FRD errors separately. Among them, FRD error compensation is divided into amplitude frequency compensation (Amplitude Frequency Compensation, AFC) and phase frequency compensation (Phase Frequency Compensation, PFC). Patent CN106209103A uses spectrum analysis to analyze the sampling data of each channel ADC and performs fixed mismatch error correction through the built-in correction unit of the ADC; Patent CN13114241A realizes the compensation of frequency response mismatch error in the time alternating architecture acquisition system; Patent CN108616277B obtains the error frequency response by sinusoidal frequency sweep to realize channel amplitude frequency compensation; Patent CN112084741A uses a digital all-pass filter based on a hybrid particle swarm algorithm to perform channel phase frequency compensation.

[0007] The advantages of this divide-and-conquer approach are precision, modularity, and simplification of the design of a single filter, but at the same time it leads to overlapping compensation resources, poor real-time performance, and consumes too many Field Programmable Gate Array (FPGA) resources.

[0008] In summary, there is currently no simple and universal method that can achieve the overall error compensation of the time-alternating architecture data acquisition system while ensuring that the compensation system consumes little resources, has a wide range of applications, and has high real-time performance. Therefore, it is extremely important to design a simpler and more universal TI acquisition system error compensation method that further saves hardware resource consumption. Summary of the invention

[0009] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a TI acquisition system joint error compensation method based on periodic time-varying filtering, which adopts an FRM / FRD joint correction method based on periodic time-varying filtering to achieve joint compensation of FRM and FRD errors.

[0010] To achieve the above-mentioned object of the invention, the present invention provides a TI acquisition system joint error compensation method based on periodic time-varying filtering, which is characterized by comprising the following steps:

[0011] (1) Assume that the number of channels of the TI acquisition system to be compensated is M, and the sampling rate of the ADC in each channel is f s The total sampling rate of the TI acquisition system is Mf s , bandwidth is f c ;

[0012] (2) In the passband range 0~f c The sine sweep signal is input into the TI acquisition system to be compensated in sequence with a fixed step Δf, and the waveform data at each frequency point is obtained through TIADC sampling; the waveform data at each frequency point is uploaded to the host computer, and the frequency response U of each channel is fitted through MATLAB. m (jω), m = 0, 1, 2, ..., M-1, j represents the imaginary part, ω is the angular frequency;

[0013] (3) Design of periodic time-varying filter

[0014] (3.1) Calculate the ideal frequency response of the TI acquisition system to be compensated

[0015]

[0016] (3.2) Design of periodic time-varying filter for FRM error compensation

[0017]

[0018] (4) Calculate the passband amplitude-frequency response |T(jω)| of the TI acquisition system to be compensated;

[0019] (4.1) Synchronously pass the waveform data collected at each frequency point in step (2) through a periodic time-varying filter Filter compensation, obtain the sinusoidal waveform data after compensating the FRM error at each frequency point;

[0020] (4.2) Use the sine fitting algorithm to fit the sine waveform data to obtain the amplitude M(jω);

[0021] (4.3) Taking the signal amplitude M(jω0) of the first frequency point ω0 in the sine waveform data as the reference amplitude, calculate the passband amplitude-frequency response |T(jω)| of the TI acquisition system to be compensated;

[0022]

[0023] (5) Calculate the group delay error of the TI acquisition system to be compensated;

[0024] (5.1) Input the fast edge signal to the reference TI acquisition system to obtain reference sampling data; input the same fast edge signal to the TI acquisition system to be compensated multiple times to obtain multiple groups of sampling data to be compensated, and pass through a periodic time-varying filter Filter compensation to obtain multiple groups of compensated sampling data; the total number of sampling points is an integer multiple of the fast edge signal period;

[0025] (5.2) After averaging multiple sets of compensated sampling data, align them with the edge of the reference sampling data, and then perform FFT operations to obtain the spectrum Y ref (jω) and Y dut (jω);

[0026] (5.3) Use the angle function in MATLAB to calculate the spectrum Y ref (jω) and Y dut (jω) for each frequency point ω l Calculate the phase-frequency response and obtain the phase-frequency response at each frequency point, which is recorded as and ω l is the lth frequency point of the fast edge signal;

[0027] (5.4) Calculate the phase-frequency response error at each frequency point of the TI acquisition system to be compensated

[0028]

[0029] (5.5) Calculate the discrete group delay error τ of the TI acquisition system to be compensated comp (ω l ):

[0030]

[0031] (5.6), and τ comp (ω l ) is fitted to obtain the group delay error τ of the TI acquisition system to be compensated error (ω);

[0032] (6) Design a frequency response non-ideal error compensation filter;

[0033] (6.1) According to the passband amplitude-frequency response |T(jω)|, the amplitude-frequency compensation linear phase FIR filter is designed using the amplitude-frequency compensation filter design method. Its frequency domain coefficient H AFC (jω) satisfies:

[0034]

[0035] (6.2), according to the group delay error τ of the TI acquisition system to be compensated error (ω), the phase-frequency compensation IIR all-pass filter is designed by using the second-order section diagram method, so that its group delay τ PFC Satisfy: τ PFC +τ error (ω) = 0, thus obtaining the frequency domain coefficient H of the phase-frequency compensation IIR all-pass filter PFC (jω);

[0036] (6.3), the frequency domain coefficient H of the amplitude-frequency compensation linear phase FIR filter AFC (jω) and the frequency domain coefficient H of the phase-frequency compensation IIR all-pass filter PFC (jω) are cascaded to obtain the frequency response non-ideal error compensation filter coefficient C(jω);

[0037] C(jω)=H AFC (jω)H PFC (jω)

[0038] (7) The periodic time-varying filter and frequency response non-ideal error compensation filter coefficient C(jω) cascade;

[0039] (7.1), the frequency response non-ideal error compensation filter coefficient C(jω) is regarded as a periodic time-varying filter with the same M channel coefficients Cascade to obtain a cascade filter

[0040]

[0041] (7.2), the cascade filter Multiplying by the delay factor, we get the joint compensation filter

[0042]

[0043] (8) A joint compensation filter is deployed in the FPGA. The input signal is sampled by the TIADC and then input into the joint compensation filter for filtering and compensation to obtain an error-compensated signal.

[0044] The object of the invention of the present invention is achieved in this way:

[0045] The present invention is based on a TI acquisition system joint error compensation method of periodic time-varying filtering. Different excitation signals are sent into the TI acquisition system to estimate the FRM error of the TI acquisition system, and a periodic time-varying filter for FRM error compensation is designed; then, the FRM error is compensated and then the FRD error is estimated, and a frequency response non-ideal error compensation filter for FRD error compensation is designed; finally, the periodic time-varying filter and the frequency response non-ideal error compensation filter are cascaded and deployed in an FPGA, thereby realizing joint compensation of the FRM and FRD errors of the input signal.

[0046] At the same time, the TI acquisition system joint error compensation method based on periodic time-varying filtering of the present invention also has the following beneficial effects:

[0047] (1) The present invention realizes the joint compensation of the frequency response mismatch error and the frequency response distortion error of the TI acquisition system by cascading multiple filters, simplifies the compensation structure, reduces resource consumption, and has great research value and significance.

[0048] (2) With the increase of sampling rate and bandwidth of TI acquisition system, its error becomes more complex, so the order of compensation filter becomes higher and higher. When the order of filter is the same, frequency domain filtering consumes less resources in FPGA than time domain filtering. The traditional compensation architecture adopts divide-and-conquer method, sampling inconsistency error compensation is realized by frequency domain multiplication filtering, and frequency response non-ideal error is realized by time domain convolution. However, the present invention realizes all compensation filtering processes in frequency domain, so it is more suitable for TI acquisition system with higher bandwidth and higher sampling rate; in addition, the same filter design consumes less resources, or a filter with higher order and better performance can be designed under the same resource consumption.

[0049] (3) The present invention abandons the multi-stage filtering in the traditional compensation architecture and implements all compensation processes in one frequency domain filtering, which greatly reduces the compensation process and greatly improves the real-time performance of the system.

[0050] (4) Due to the simple structure of the present invention, the design, generation and simulation of the filter correlation coefficients can be realized by software such as MATLAB, and the coefficients can be imported into the FPGA. Therefore, for the errors of different acquisition systems, it is only necessary to change the imported filter coefficients. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the TI acquisition system joint error compensation method based on periodic time-varying filtering of the present invention.

[0052] Figure 2 1 is a comparison diagram between the filter compensation architecture of the present invention and the traditional compensation architecture, (a) is the traditional architecture, and (b) is the architecture of the present invention.

[0053] Figure 3 This is a diagram of the FPGA compensation architecture of the present invention.

[0054] Figure 4 It is the process of data flow and data selection of the present invention. DETAILED DESCRIPTION

[0055] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0056] Example

[0057] In this embodiment, if Figure 1 As shown, the present invention provides a TI acquisition system joint error compensation method based on periodic time-varying filtering, comprising the following steps:

[0058] (1) Assume that the number of channels of the TI acquisition system to be compensated is 4, the sampling rate of the ADC in each channel is 5 GSPS, the total sampling rate of the TI acquisition system is 20 GSPS, and the bandwidth is 4 GHz;

[0059] (2) Input the sine frequency sweep signal to the TI acquisition system to be compensated in a fixed step of 100 MHz within the passband range of 0 to 4 GHz, and obtain the waveform data at each frequency point through TIADC sampling; upload the waveform data at each frequency point to the host computer, and use MATLAB to fit the frequency response U of each channel. m (jω), m = 0, 1, 2, 3, j represents the imaginary part, ω is the angular frequency;

[0060] (3) Design of periodic time-varying filter

[0061] (3.1) Calculate the ideal frequency response of the TI acquisition system to be compensated

[0062]

[0063] (3.2) Design of periodic time-varying filter for FRM error compensation

[0064]

[0065] (4) Calculate the passband amplitude-frequency response |T(jω)| of the TI acquisition system to be compensated;

[0066] (4.1) Synchronously pass the waveform data collected at each frequency point in step (2) through a periodic time-varying filter Filter compensation, obtain the sinusoidal waveform data after compensating the FRM error at each frequency point;

[0067] (4.2) Use the sine fitting algorithm to fit the sine waveform data to obtain the amplitude M(jω);

[0068] (4.3) Taking the signal amplitude M(jω0) of the first frequency point ω0 in the sine waveform data as the reference amplitude, calculate the passband amplitude-frequency response |T(jω)| of the TI acquisition system to be compensated;

[0069]

[0070] (5) Calculate the group delay error of the TI acquisition system to be compensated;

[0071] (5.1) Input the fast edge signal to the reference TI acquisition system to obtain reference sampling data; input the same fast edge signal to the TI acquisition system to be compensated multiple times to obtain multiple groups of sampling data to be compensated, and pass through a periodic time-varying filter Filter compensation to obtain multiple groups of compensated sampling data; the total number of sampling points is an integer multiple of the fast edge signal period;

[0072] (5.2) After averaging multiple sets of compensated sampling data, align them with the edge of the reference sampling data, and then perform FFT operations to obtain the spectrum Y ref (jω) and Y dut (jω);

[0073] (5.3) Use the angle function in MATLAB to calculate the spectrum Y ref (jω) and Y dut (jω) for each frequency point ω l Calculate the phase-frequency response and obtain the phase-frequency response at each frequency point, which is recorded as and ω l is the lth frequency point of the fast edge signal;

[0074] (5.4) Calculate the phase-frequency response error at each frequency point of the TI acquisition system to be compensated

[0075]

[0076] (5.5) Calculate the discrete group delay error τ of the TI acquisition system to be compensated comp (ω l ):

[0077]

[0078] (5.6), and τ comp (ω l ) is fitted to obtain the group delay error τ of the TI acquisition system to be compensated error (ω);

[0079] (6) Design a frequency response non-ideal error compensation filter;

[0080] (6.1) According to the passband amplitude-frequency response |T(jω)|, the amplitude-frequency compensation linear phase FIR filter is designed using the amplitude-frequency compensation filter design method. Its frequency domain coefficient H AFC (jω) satisfies:

[0081]

[0082] (6.2), according to the group delay error τ of the TI acquisition system to be compensated error (ω), the phase-frequency compensation IIR all-pass filter is designed by using the second-order section diagram method, so that its group delay is τ PFC Satisfy: τ PFC +τ error (ω) = 0, thus obtaining the frequency domain coefficient H of the phase-frequency compensation IIR all-pass filter PFC (jω);

[0083] (6.3), the frequency domain coefficient H of the amplitude-frequency compensation linear phase FIR filter AFC (jω) and the frequency domain coefficient H of the phase-frequency compensation IIR all-pass filter PFC (jω) are cascaded to obtain the frequency response non-ideal error compensation filter coefficient C(jω);

[0084] C(jω)=H AFC (jω)H PFC (jω)

[0085] (7) The periodic time-varying filter and frequency response non-ideal error compensation filter coefficient C(jω) cascade;

[0086] (7.1), such as Figure 2 As shown, (a) is a traditional error compensation architecture, and (b) is an error compensation architecture of the present invention; the present invention combines FRM error compensation and FRD error compensation into one filter, and regards the frequency response non-ideal error compensation filter coefficient C(jω) as a periodic time-varying filter with the same four channel coefficients Cascade to obtain a cascade filter

[0087]

[0088] (7.2), the cascade filter Multiplying by the delay factor, we get the joint compensation filter

[0089]

[0090] (8) A joint compensation filter is deployed in the FPGA. The input signal is sampled by the TIADC and then input into the joint compensation filter for filtering and compensation to obtain an error-compensated signal.

[0091] In this embodiment, if Figure 3 As shown in the figure, the structure of the deployed joint compensation filter includes a main path, a slave path and a data selector at the output end of the main and slave paths; wherein the main path includes a 1024-point FFT unit, a parallel complex multiplier, a parallel spectrum folding unit, a parallel 256-point IFFT unit and a data selector; the structure of the slave path is basically similar to that of the main path, except that a data loss point module is added at the front end of the main path.

[0092] Next we combine Figure 3 The process of filtering and compensating the TIADC sampling data by the joint compensation filter is specifically described, which specifically includes the following steps:

[0093] (3.1) The data sampled by TIADC is y[n], and the sampled data y[n] is input to the master path and the slave path respectively; wherein n represents the number of the sampling point, n=0, 1, 2, ..., 10239, the number of data points in a single frame is 1024, that is, the length of FFT, and the number of data frames is 10;

[0094] (3.2) Process the sampled data y[n] through the main path;

[0095] (3.2.1) Divide the sampled data y[n] into 10 frames, each frame contains 1024 data points, and then input each frame of sampled data into a 1024-point FFT unit;

[0096] (3.2.2), initialize k = 1; perform a 1024-point FFT transformation on the k-th frame sampling data, and then use a parallel complex multiplier to convert the spectrum after FFT transformation into the joint compensation filter coefficients corresponding to each channel. Multiply them separately to get the discrete spectrum Y after filtering of each channel m,k [l1], l1 = 0, 1, 2, ..., 1023;

[0097] (3.2.3), the discrete spectrum Y m,k [l1] is input to the corresponding spectrum folding unit for M-fold extraction to obtain the spectrum

[0098]

[0099] (3.2.4), the spectrum Input to the 256-point IFFT module, and take the real part after inverse FFT to get the data y m,k [l2];

[0100] (3.2.5) In the data selector, the kth frame data {y 0,k [l2],y 1,k [l2],…,y m,k [l2],…,y M-1,k [l2]} According to the time alternating sampling data, select and combine to obtain the k-th frame output data y k [l1];

[0101] (3.2.6) Traverse each frame of sampling data and obtain 10 frames of output data {y0[l1], y1[l1], …, y8[l1], y9[l1]} according to steps (3.2.2) to (3.25);

[0102] (3.3), by processing the sampled data y[n] from the path;

[0103] (3.3.1) Input the sampled data y[n] into the data point dropping module, discard the first and last 512 data points, and then divide the remaining data points into 9 frames, each frame contains 1024 data points, and then input each frame of sampled data into the 1024-point FFT unit;

[0104] (3.3.2), follow steps (3.2.2) to (3.25) to obtain 9 frames of output data, recorded as

[0105] (3.4) Master-slave path data selection and splicing, the splicing process is as follows Figure 4 As shown,

[0106] With a period of 512, alternate from {y0[l1],y1[l1],…,y k [l1],…,y9[l1]} and Select the middle 512 data points from each frame of data, and then combine the selected data points to form the final correction output y c [n];

[0107]

[0108] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A TI acquisition system joint error compensation method based on periodic time-varying filtering, characterized in that: The following steps are involved: (1) Assume that the number of channels of the TI acquisition system to be compensated is M, and the sampling rate of the ADC in each channel is f s The total sampling rate of the TI acquisition system is Mf s , bandwidth is f c ; (2) In the passband range 0~f c The sine sweep signal is input into the TI acquisition system to be compensated in sequence with a fixed step Δf, and the waveform data at each frequency point is obtained through TIADC sampling; the waveform data at each frequency point is uploaded to the host computer, and the frequency response U of each channel is fitted through MATLAB. m (jω), m = 0, 1, 2, ..., M-1, j represents the imaginary part, ω is the angular frequency; (3) Design of periodic time-varying filter (3.1) Calculate the ideal frequency response of the TI acquisition system to be compensated (3.2) Design of periodic time-varying filter for FRM error compensation (4) Calculate the passband amplitude-frequency response |T(jω)| of the TI acquisition system to be compensated; (4.1) Synchronously pass the waveform data collected at each frequency point in step (2) through a periodic time-varying filter Filter compensation, obtain the sinusoidal waveform data after compensating the FRM error at each frequency point; (4.2) Use the sine fitting algorithm to fit the sine waveform data to obtain the amplitude M(jω); (4.3) Taking the signal amplitude M(jω0) of the first frequency point ω0 in the sine waveform data as the reference amplitude, calculate the passband amplitude-frequency response |T(jω)| of the TI acquisition system to be compensated; (5) Calculate the group delay error of the TI acquisition system to be compensated; (5.1) Input the fast edge signal to the reference TI acquisition system to obtain reference sampling data; input the same fast edge signal to the TI acquisition system to be compensated multiple times to obtain multiple groups of sampling data to be compensated, and pass through a periodic time-varying filter Filter compensation to obtain multiple groups of compensated sampling data; the total number of sampling points is an integer multiple of the fast edge signal period; (5.2) After averaging multiple sets of compensated sampling data, align them with the edge of the reference sampling data, and then perform FFT operations to obtain the spectrum Y ref (jω) and Y dut (jω); (5.3) Use the angle function in MATLAB to calculate the spectrum Y ref (jω) and Y dut (jω) for each frequency point ω l Calculate the phase-frequency response and obtain the phase-frequency response at each frequency point, which is recorded as and ω l is the lth frequency point of the fast edge signal; (5.4) Calculate the phase-frequency response error at each frequency point of the TI acquisition system to be compensated (5.5) Calculate the discrete group delay error τ of the TI acquisition system to be compensated comp (ω l ): (5.6), and τ comp (ω l ) is fitted to obtain the group delay error τ of the TI acquisition system to be compensated error (ω); (6) Design a frequency response non-ideal error compensation filter; (6.1) According to the passband amplitude-frequency response |T(jω)|, the amplitude-frequency compensation linear phase FIR filter is designed using the amplitude-frequency compensation filter design method. Its frequency domain coefficient H AFC (jω) satisfies: (6.2), according to the group delay error τ of the TI acquisition system to be compensated error (ω), the phase-frequency compensation IIR all-pass filter is designed by using the second-order section diagram method, so that its group delay τ PFC Satisfy: τ PFC +τ error (ω) = 0, thus obtaining the frequency domain coefficient H of the phase-frequency compensation IIR all-pass filter PFC (jω); (6.3), the frequency domain coefficient H of the amplitude-frequency compensation linear phase FIR filter AFC (jω) and the frequency domain coefficient H of the phase-frequency compensation IIR all-pass filter PFC (jω) are cascaded to obtain the frequency response non-ideal error compensation filter coefficient C(jω); C(jω)=H AFC (jω)H PFC (jω) (7) The periodic time-varying filter and frequency response non-ideal error compensation filter coefficient C(jω) cascade; (7.1), the frequency response non-ideal error compensation filter coefficient C(jω) is regarded as a periodic time-varying filter with the same M channel coefficients Cascade to obtain a cascade filter (7.2), the cascade filter Multiplying by the delay factor, we get the joint compensation filter (8) A joint compensation filter is deployed in the FPGA. The input signal is sampled by the TIADC and then input into the joint compensation filter for filtering and compensation to obtain an error-compensated signal.

2. The TI acquisition system joint error compensation method based on periodic time-varying filtering according to claim 1 is characterized in that: The deployment structure of the joint compensation filter is: The joint compensation filter includes a main path, a slave path and a data selector at the output ends of the main and slave paths; wherein the main path includes an L-point FFT unit, a parallel complex multiplier, a parallel spectrum folding unit, a parallel L / M-point IFFT unit and a data selector; the structure of the slave path is basically similar to that of the main path, except that a data loss point module is added at the front end of the main path.

3. The TI acquisition system joint error compensation method based on periodic time-varying filtering according to claim 1 is characterized in that: The method of filtering and compensating the TIADC sampling data by the joint compensation filter is as follows: (3.1) The data sampled by TIADC is y[n], and the sampled data y[n] is input to the master path and the slave path respectively; wherein n represents the number of the sampling point, n=0, 1, 2, ..., L*K-1, L is the number of data points in a single frame, that is, the length of FFT, and K is the number of data frames; (3.2) Process the sampled data y[n] through the main path; (3.2.1) Divide the sampled data y[n] into K frames, each frame contains L data points, and then input each frame of sampled data into the FFT unit of L points; (3.2.2), initialize k = 1; perform L-point FFT transformation on the k-th frame sampling data, and then use the parallel complex multiplier to convert the spectrum after FFT transformation into the joint compensation filter coefficients corresponding to each channel. Multiply them separately to get the discrete spectrum Y after filtering of each channel m,k [l1],l1=0,1,2,…,L-1 (3.2.3), the discrete spectrum Y m,k [l1] is input to the corresponding spectrum folding unit for M-fold extraction to obtain the spectrum (3.2.4), the spectrum Input to the IFFT module at point L / M, and take the real part after inverse FFT transformation to get the data y m,k [l2]; (3.2.5) In the data selector, the kth frame data {y 0,k [l2],y 1,k [l2],…,y m,k [l2],…,y M-1,k [l2]} According to the time alternating sampling data, select and combine to obtain the k-th frame output data y k [l1]; (3.2.6) Traverse each frame of sampling data and obtain K frames of output data {y0[l1],y1[l1],…,y k [l1],…,y K-1 [l1]}; (3.3), by processing the sampled data y[n] from the path; (3.3.1) Input the sampled data y[n] to the data point dropping module, discard the first and last L / 2 data points, and then divide the remaining data points into K-1 frames, each frame contains L data points, and then input each frame of sampled data to the L-point FFT unit; (3.3.2) According to steps (3.2.2) to (3.25), we get K-1 frames of output data, which is recorded as (3.4) Master-slave path data selection and splicing; With a period of L / 2, alternately from {y0[l1],y1[l1],…,y k [l1],…,y K-1 [l1]} and Select the middle L / 2 data points from each frame of data, and then combine the selected data points to form the final correction output y c [n];

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