Digital correction method for dynamic range expansion of multiple ADCs

Abstract

A digital correction method for dynamic range expansion of multiple ADCs includes: obtaining gain and offset correction values of other channels relative to a standard channel CH.sub.1 based on iterative computations through positive and negative amplitude auxiliary values and positive and negative base values, then performing gain-offset error correction on the other channels, and then calculating phase differences of the other channels relative to the standard channel CH.sub.1 and constructing fractional delay filters with a Farrow structure corresponding to the channels, correcting sampling data X.sub.2, . . . , X.sub.M after performing the gain-offset error correction. Digital correction of sampling data collected from multiple channels in a multi-ADC system is realized while ensuring that respective dynamic ranges of the sampling data with different gains output by the multiple channels are not lost.

Claims

1. A digital correction method for dynamic range expansion of multiple analog-to-digital converters (ADCs), wherein a number of channels of the multiple ADCs is M; and the digital correction method comprises the following steps: step 1, obtaining a gain correction value A.sub.m, 1mM1 and an offset correction value B.sub.m, 1mM1 of each channel in target channels of the M channels by iterative computations, and performing gain-offset error correction on each of the target channels based on the gain correction value A.sub.m and the offset correction value B.sub.m; wherein the M channels have different gains and different offset errors, and the M channels are denoted as CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M; sampling data of the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M are respectively denoted as X.sub.1, X.sub.2, . . . , X.sub.M; the channel CH.sub.1 of the M channels is determined as a reference channel, and the gain-offset error correction is performed on the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M, as the target channels, of the M channels according to gain correction values A.sub.1, A.sub.2, . . . , A.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 and offset correction values B.sub.1, B.sub.2, . . . , B.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 by the following formula: $\{\begin{array}{c}{X}_2=A_1{X}_2+B_1\\ X_3=A_2{X}_3+B_2\\ .Math.\\ X_M=A_{M-1}{X}_M+B_{M-1}\end{array};$ wherein the gain correction values A.sub.1, A.sub.2, . . . , A.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 and the offset correction values B.sub.1, B.sub.2, . . . , B.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 are obtained by performing the iterative computations on bipolar signals of the sampling data of two channels of the M channels; and the obtaining the gain correction value A.sub.m and the offset correction value B.sub.m comprises the following steps: step 1.1, selecting a first sampling data segment with a length L from the sampling data of the channel CH.sub.1 and a second sampling data segment with the length L from the sampling data of the channel CH.sub.m+1, denoting the first sampling data segment corresponding to the channel CH.sub.1 as X.sub.1(0), X.sub.1(1), . . . , X.sub.1(L1) and denoting the second sampling data segment corresponding to the channel CH.sub.m+1 as X.sub.m+1(0), X.sub.m+1(1), . . . , X.sub.m+1(L1); initializing a number of the iterative computations i=1, initializing a positive amplitude auxiliary value P(0)=X.sub.1(0), initializing a negative amplitude auxiliary value N(0)=X.sub.1(0), initializing the gain correction value A.sub.m(0)=1, and initializing the offset correction value B.sub.m(0)=0; step 1.2, calculating a positive amplitude auxiliary value P(i) of an i.sup.th iterative computation and a negative amplitude auxiliary value N(i) of the i.sup.th iterative computation according to the following formula: $P\left(i\right)=P\left(i-1\right)+$ $\left[X_1\left(i-1\right)+\left(X_{\mathrm{PMax}}-X_{m+1}\left(i-1\right)\right)A_m\left(i-1\right)+B_m\left(i-1\right)-P\left(i-1\right)\right]D^{};$ $N\left(i\right)=N\left(i-1\right)+$ $\left[X_1\left(i-1\right)+\left(X_{\mathrm{NMax}}-X_{m+1}\left(i-1\right)\right)A_m\left(i-1\right)+B_m\left(i-1\right)-N\left(i-1\right)\right]D^{};$ wherein X.sub.PMax represents a positive base value and is determined as a positive maximum value of a higher gain channel between the channel CH.sub.1 and the channel CH.sub.m+1; X.sub.NMax represents a negative base value and is determined as a negative maximum value of the higher gain channel between the channel CH.sub.1 and the channel CH.sub.m+1; A.sub.m(i1) represents a gain correction value of an (i1).sup.th iterative computation; B.sub.m(i1) represents an offset correction value of the (i1).sup.th iterative computation; and D represents an iteration speed; step 1.3, calculating a gain correction value A.sub.m(i) of the i.sup.th iterative computation and an offset correction value B.sub.m(i) of the i.sup.th iterative computation according to the following formula: $A_m\left(i\right)=\frac{P\left(i\right)-N\left(i\right)}{X_{\mathrm{PMax}}-X_{\mathrm{NMax}}};B_m\left(i\right)=\frac{X_{\mathrm{PMax}}N\left(i\right)-X_{\mathrm{NMax}}P\left(i\right)}{2\left(X_{\mathrm{PMax}}-X_{\mathrm{NMax}}\right)};$ step 1.4, calculating an error .sub.m(i) of the i.sup.th iterative computation according to the following formula: ${}_m\left(i\right)=X_1\left(i\right)-\left[A_m\left(i\right)X_{m+1}\left(i\right)+B_m\left(i\right)\right];$ and step 1.5, determining whether the error .sub.m(i) is less than a set iteration precision; when the error .sub.m(i) is less than the set iteration precision, determining the gain correction value A.sub.m(i) of the i.sup.th iterative computation and the offset correction value B.sub.m(i) of the i.sup.th iterative computation as the gain correction value A.sub.m and the offset correction value B.sub.m; or when the error .sub.m(i) is equal to or greater than the set iteration precision, determining i=i+1 and returning and performing the step 1.2; step 2, obtaining delays of the M channels, constructing a fractional delay filter with a Farrow structure, and performing delay correction on the M channels; wherein the step 2 comprises the following steps: step 2.1, obtaining the delays of the target channels, comprising: inputting standard signals with same frequency and same phase into the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M; performing fast Fourier transform (FFT) on the sampling data of the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M to obtain results corresponding to the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M; and obtaining phases .sub.m, m=1, 2, . . . , M of the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M according to real parts RE.sub.m and imaginary parts IM.sub.m, m=1, 2, . . . , M of the results by using the following formula: ${}_m=\mathrm{arc}\tan \left(\frac{{\mathrm{IM}}_m}{{\mathrm{RE}}_m}\right),m=1,2,.Math.,M;$ obtaining phase differences .sub.1, .sub.2, . . . , .sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 by the following formula: ${}_m={}_{m+1}-{}_1,m=1,2,.Math.,M-1;$ obtaining the delays .sub.m, m=1, 2, . . . , M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 by the following formula: ${}_m=\frac{k^{}}{360f_0}{}_m;$ where f.sub.0 represents a frequency of each of the standard signals, and k represents a sampling rate of each of the multiple ADCs; step 2.2, designing the fractional delay filter with the Farrow structure, comprising: determining a coefficient of a fractional delay filter base on Lagrange interpolation by obtaining a maximum flatness in a passband of the fractional delay filter based on Lagrange interpolation; and the coefficient of the fractional delay filter based on Lagrange interpolation being expressed as follows: $h\left(n\right)={.Math.}_{\begin{array}{c}k=0\\ kn\end{array}}^P\frac{D-k}{n-k},n=0,1,2,.Math.,P;$ wherein P represents an order of the fractional delay filter based on Lagrange interpolation, D=P2+d, and d represents a fractional delay within a range of 0d1; using a wave filter with a Farrow structure to approximate the determined coefficient h(n) of the fractional delay filter based on Lagrange interpolation, thereby obtaining the fractional delay filter with the Farrow structure within the fractional delay of 0d1 by using the wave filter with the Farrow structure, and obtaining a polynomial h(n) for the coefficient h(n) of the fractional delay filter based on Lagrange interpolation according to D=P2+d, and the polynomial h(n) for the coefficient h(n) of the fractional delay filter based on Lagrange interpolation being expressed by the following formula: $h^{}\left(n\right)={.Math.}_{P=0}^P{c}_P\left(n\right)d^P,n=0,1,2,.Math.,P;$ wherein c.sub.P(n) represents a coefficient of the fractional delay filter with the Farrow structure; wherein for the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M, the delays .sub.m, m=1, 2, . . . , M1 are determined as d respectively, and a polynomial for the coefficient of the fractional delay filter with the Farrow structure corresponding to the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M respectively is obtained as follows: $h_m\left(n\right)={.Math.}_{P=0}^P{c}_P\left(n\right){}_m^P,n=0,1,2,.Math.,P,m=1,2,.Math.,M-1;$ wherein for the channel CH.sub.1, a decimal delay .sub.0 is a constant and is determined as d, and a polynomial for the coefficient of the fractional delay filter with the Farrow structure corresponding to the channel CH.sub.1 is obtained as follows: $h_0\left(n\right)={.Math.}_{P=0}^P{c}_P\left(n\right){}_0^P,n=0,1,2,.Math.,P;$ step 2.3, performing the delay correction on the M channels, comprising: performing half-band interpolation on the sampling data X.sub.1 corresponding to the channel CH.sub.1 and the sampling data X.sub.2, . . . , X.sub.M corresponding to the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M after the gain-offset error correction performed in the step 1 to obtain processed sampling data, and inputting the processed sampling data into the fractional delay filters h.sub.0(n), h.sub.1(n), . . . , h.sub.M1(n) with the Farrow structure corresponding to the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M respectively to perform delay filtering, and then performing half-band extraction after the delay filtering to obtain delay-corrected sampling data X.sub.1, X.sub.2, . . . , X.sub.M, thereby completing the delay correction on the M channels; and step 3, data integration, comprising: integrating the delay-corrected sampling data X.sub.1, X.sub.2, . . . , X.sub.M to obtain a multi-ADC acquisition signal.

2. The digital correction method for dynamic range expansion of multiple ADCs according to claim 1, further comprising: determining a channel with a minimum gain of the M channels as the channel CH.sub.1.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 illustrates a schematic diagram of a flowchart of a digital correction method for dynamic range expansion of multiple ADCs according to an embodiment of the disclosure.

(2) FIG. 2 illustrates a flowchart of obtaining a gain correction value A.sub.m and an offset correction value B.sub.m in step 1 illustrated in FIG. 1.

(3) FIG. 3 illustrates a schematic diagram of a principle of the digital correction method for dynamic range expansion of multiple ADCs according to the embodiment of the disclosure.

(4) FIG. 4 illustrates a schematic diagram of obtaining a phase difference.

(5) FIG. 5A illustrates a schematic diagram of an output signal before digital correction.

(6) FIG. 5B illustrates a schematic diagram of the output signal after the digital correction.

DETAILED DESCRIPTION OF EMBODIMENTS

(7) Embodiments of the disclosure are described below with reference to attached drawings, so that those skilled in the related art can better understand the disclosure. It should be noted that in the following description, these detailed descriptions will be omitted here when the detailed descriptions of the known functions and designs may fade the main content of the disclosure.

(8) FIG. 1 illustrates a schematic diagram of a flowchart of a digital correction method for dynamic range expansion of multiple analog-to-digital converters (ADCs) according to an embodiment of the disclosure.

(9) In the embodiment, as shown in FIG. 1, a number of channels of the multiple ADCs is M; and the digital correction method for dynamic range expansion of multiple ADCs according to the disclosure includes the following steps.

(10) Step 1, a gain correction value A.sub.m, 1mM1 and an offset correction value B.sub.m, 1mM1 of each channel in target channels of the M channels are obtained by iterative computations, and gain-offset error correction is performed on each of the target channels based on the gain correction value A.sub.m and the offset correction value B.sub.m.

(11) The M channels have different gains and different offset errors, and the M channels are denoted as CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M; sampling data of the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M are respectively denoted as X.sub.1, X.sub.2, . . . , X.sub.M; and the channel CH.sub.1 of the M channels is determined as a reference channel. In the embodiment, a channel with a minimum gain of the M channels is determined as the channel CH.sub.1, which avoids a loss of dynamic range during digital correction process.

(12) The gain-offset error correction is performed on the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M, as the target channels, of the M channels according to gain correction values A.sub.1, A.sub.2, . . . , A.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 and offset correction values B.sub.1, B.sub.2, . . . , B.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 by the following formula:

(13) $\{\begin{array}{c}{X}_2=A_1{X}_2+B_1\\ X_3=A_2{X}_3+B_2\\ .Math.\\ X_M=A_{M-1}{X}_M+B_{M-1}\end{array}.$

(14) In an embodiment, the gain correction values A.sub.1, A.sub.2, . . . , A.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 and the offset correction values B.sub.1, B.sub.2, . . . , B.sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 are obtained by performing the iterative computations on bipolar signals of the sampling data of two channels (i.e., a to-be-corrected channel selected from the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M and the reference channel CH.sub.1) of the M channels. Since the bipolar signals are divided into positive amplitude and negative amplitude, the iterative computations introduce several additional auxiliary values, including: using a positive maximum value of a higher gain channel between the to-be-corrected channel and the reference channel CH.sub.1 as a positive base value X.sub.PMax, using a negative maximum value of the higher gain channel between the to-be-corrected channel and the reference channel CH.sub.1 as a negative base value X.sub.NMax, a positive amplitude auxiliary value P(i), and a negative amplitude auxiliary value N(i). P(i) and N(i) are used for calculating the gain correction values A.sub.1, A.sub.2, . . . , A.sub.M1 and the offset correction values B.sub.1, B.sub.2, . . . , B.sub.M1 during the iteration computations.

(15) Specifically, as shown in FIG. 2, the obtaining the gain correction value A.sub.m and the offset correction value B.sub.m includes the following steps.

(16) Step 1.1, an initialization is performed.

(17) A sampling data segment (also referred to a first sampling data segment) with a length L is selected from the sampling data of the channel CH.sub.1 and a sampling data segment (also referred to a second sampling data segment) with the length L is selected from the sampling data of the channel CH.sub.m+1, the sampling data segment corresponding to the channel CH.sub.1 is denoted as X.sub.1(0), X.sub.1(1), . . . , X.sub.1(L1) and the sampling data segment corresponding to the channel CH.sub.m+1 is denoted as X.sub.m+1(0), X.sub.m+1(1), . . . , X.sub.m+1(L1); a number of the iterative computations is initialized by i=1, a positive amplitude auxiliary value is initialized by P(0)=X.sub.1(0), a negative amplitude auxiliary value is initialized by N(0)=X.sub.1(0), the gain correction value is initialized by A.sub.m(0)=1, and the offset correction value is initialized by B.sub.m(0)=0.

(18) Step 1.2, a positive amplitude auxiliary value P(i) of an i.sup.th iterative computation and a negative amplitude auxiliary value N(i) of the i.sup.th iterative computation are calculated according to the following formula:

(19) $P\left(i\right)=P\left(i-1\right)+$$\left[X_1\left(i-1\right)+\left(X_{\mathrm{PMax}}-X_{m+1}\left(i-1\right)\right)A_m\left(i-1\right)+B_m\left(i-1\right)-P\left(i-1\right)\right]D^{};$$N\left(i\right)=N\left(i-1\right)+$$\left[X_1\left(i-1\right)+\left(X_{\mathrm{NMax}}-X_{m+1}\left(i-1\right)\right)A_m\left(i-1\right)+B_m\left(i-1\right)-N\left(i-1\right)\right]D^{}.$

(20) In the above formula, X.sub.PMax represents a positive base value and is determined as a positive maximum value of a higher gain channel between the channel CH.sub.1 and the channel CH.sub.m+1; X.sub.NMax represents a negative base value and is determined as a negative maximum value of the higher gain channel between the channel CH.sub.1 and the channel CH.sub.m+1; A.sub.m(i1) represents a gain correction value of an (i1).sup.th iterative computation; B.sub.m(i1) represents an offset correction value of the (i1).sup.th iterative computation; and D represents an iteration speed.

(21) Step 1.3, a gain correction value A.sub.m(i) of the i.sup.th iterative computation and an offset correction value B.sub.m(i) of the i.sup.th iterative computation are calculated according to the following formula:

(22) $A_m\left(i\right)=\frac{P\left(i\right)-N\left(i\right)}{X_{\mathrm{PMax}}-X_{\mathrm{NMax}}};B_m\left(i\right)=\frac{X_{\mathrm{PMax}}N\left(i\right)-X_{\mathrm{NMax}}P\left(i\right)}{2\left(X_{\mathrm{PMax}}-X_{\mathrm{NMax}}\right)}.$

(23) Step 1.4, an error .sub.m(i) of the i.sup.th iterative computation is calculated according to the following formula:

(24) ${}_m\left(i\right)=X_1\left(i\right)-\left[A_m\left(i\right)X_{m+1}\left(i\right)+B_m\left(i\right)\right].$

(25) Step 1.5, whether the error .sub.m(i) is less than a set iteration precision is determined; when the error .sub.m(i) is less than the set iteration precision, the gain correction value A.sub.m(i) of the i.sup.th iterative computation and the offset correction value B.sub.m(i) of the i.sup.th iterative computation are determined as the gain correction value A.sub.m and the offset correction value B.sub.m; or when the error .sub.m(i) is equal to or greater than the set iteration precision, i=i+1 is determined and step 1.2 is returned and performed.

(26) Since the multiple ADCs are similar, in an illustrated embodiment, as shown in FIG. 3, two ADCs are used as an example for description. In the embodiment, the disclosure only needs to calculate the gain correction value A.sub.1 and the offset correction value B.sub.1 of the channel CH.sub.2, and to perform the gain-offset error correction on the channel CH.sub.2 according to a formula as follows:

(27) $X_2=A_1{X}_2+B_1.$

(28) Step 2: delays of the M channels are obtained, a fractional delay filter with a Farrow structure is constructed (the multiple M channels corresponding to multiple fractional delay filters with the Farrow structure), and delay correction is performed on the M channels.

(29) In an embodiment, the step 2 includes the following steps.

(30) Step 2.1: the delays of the target channels are obtained.

(31) In the step 2.1, in combination with spectrum analysis, a corresponding phase spectrum is obtained according to a corresponding real part and a corresponding imaginary part based on fast Fourier transform (FFT), which is convenient for measuring a phase difference of a signal at a certain frequency point. When measuring the delay of a single frequency point, the standard signal corresponding to the single frequency point is input through a signal source, the standard signals with same frequency and same phase are input into the M channels, the channel CH.sub.1 is used as the reference channel, phases of M standard frequency points corresponding to the M channels are calculated based on FFT, and then phase differences of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 at the same frequency point are obtained, thereby estimating the delay of the to-be-corrected channel relative to the channel CH.sub.1 according to the corresponding phase difference of the single frequency point.

(32) Specifically, the step of obtaining the delays of the target channels includes the following steps: inputting standard signals with same frequency and same phase into the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M; performing fast Fourier transform (FFT) on the sampling data of the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M to obtain results corresponding to the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M; and obtaining phases .sub.m, m=1, 2, . . . , M of the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M according to real parts RE.sub.m and imaginary parts IM.sub.m, m=1, 2, . . . , M of the results by using the following formula:

(33) ${}_m=\mathrm{arc}\tan \left(\frac{{\mathrm{IM}}_m}{{\mathrm{RE}}_m}\right);$ obtaining phase differences .sub.1, .sub.2, . . . , .sub.M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 by the following formula:

(34) ${}_m={}_{m+1}-{}_1,m=1,2,.Math.,M-1;$ obtaining the delays .sub.m, m=1, 2, . . . , M1 of the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M relative to the channel CH.sub.1 by the following formula:

(35) ${}_m=\frac{k^{}}{360f_0}{}_m;$ where f.sub.0 represents a frequency of each of the standard signals, and k represents a sampling rate of each of the multiple ADCs.

(36) In an illustrated embodiment, the sampling rate of the ADC is 262.144 kilohertz (kHz), and an analysis bandwidth of the multi-ADS system is 102.4 kHz. As shown in FIG. 4, a host computer obtains the phase difference corresponding to the certain frequency point according to the real parts RE.sub.1 and RE.sub.2 and the imaginary part IM.sub.1 and IM.sub.2 based on the FFT. When the delay of the single frequency point is measured, the standard signal with a frequency of 1.024 kHz is input into each channel of the M channels through the signal source, the sampling rate is 262.144 kHz, and an FFT analysis at 8192 points is performed, so that the standard signal with the frequency of 1.024 kHz is located at a point of the 32.sup.th FFT, and then the corresponding imaginary part and the corresponding real part are IM.sub.1 and IM.sub.2 and RE.sub.1 and RE.sub.2, the phase difference .sub.1 between the phase .sub.1 and the phase .sub.2 is obtained by .sub.1=.sub.2.sub.1; and the phase .sub.1 and the phase .sub.2 are calculated by arctangent values between the real parts of RE.sub.1 RE.sub.2 and the imaginary parts of IM.sub.1 IM.sub.2 of the two channels (i.e., the channel CH.sub.1 and the channel CH.sub.2) based on the FFT. If the phase difference .sub.1 between the two channels at the same frequency point is 0.08, and the delay .sub.1 between the two channels is estimated according to the phase difference of the single frequency point as follows:

(37) 0${}_1=\frac{k^{}}{360f_0}{}_1=\frac{262.144\mathrm{kHz}0.08}{1.024\mathrm{kHz}360}=0.05689.$

(38) Step 2.2: the fractional delay filter with the Farrow structure is designed, including the following steps: determining a coefficient of a fractional delay filter base on Lagrange interpolation by obtaining a maximum flatness in a passband of the fractional delay filter based on Lagrange interpolation; and the coefficient of the fractional delay filter based on Lagrange interpolation being expressed as follows:

(39) $h\left(n\right)=\underset{\begin{array}{c}k=0\\ kn\end{array}}{\overset{P}{.Math.}}\frac{D-k}{n-k},n=0,1,2,.Math.,P$ where P represents an order of the fractional delay filter based on Lagrange interpolation, D=P2+d, and d represents a fractional delay within a range of 0 d1.

(40) In an illustrated embodiment, the order P of the fractional delay filter based on Lagrange interpolation is P=3, which is taken as an example, the coefficient of the fractional delay filter based on Lagrange interpolation is shown in Table 1 as follows:

(41) TABLE-US-00001 TABLE 1 h(0) h(1) h(2) h(3) P = 3 (D 1)(D 2) D(D 2) D(D 1) D(D 1)(D 2)/6 (D 3)/6 (D 3)/2 (D 3)/2

(42) The step 2.2 further includes: using a wave filter with a Farrow structure to approximate the determined coefficient h(n) of the fractional delay filter based on Lagrange interpolation, thereby obtaining an optimal fractional delay filter (i.e., the fractional delay filter with the Farrow structure) within the fractional delay of 0d1 by using the wave filter with the Farrow structure, and obtaining a polynomial h(n) for the coefficient h(n) of the fractional delay filter based on Lagrange interpolation according to D=P2+d, and the polynomial h(n) for the coefficient h(n) of the fractional delay filter based on Lagrange interpolation being expressed by the following formula: h(n)=.sub.P=0.sup.Pc.sub.P(n)d.sup.P, n=0, 1, 2, . . . , P, where c.sub.P(n) represents a coefficient of the fractional delay filter with the Farrow structure.

(43) In an illustrated embodiment, the order P of the fractional delay filter based on Lagrange interpolation is P=3, an expression of the coefficient of the fractional delay filter based on Lagrange interpolation with third-order Farrow structure is expressed as follows:

(44) $\{\begin{array}{c}{h}_d\left(0\right)=-\frac{1}{6}{d}^3+\frac{1}{2}{d}^2-\frac{1}{3}d\\ h_d\left(1\right)=\frac{1}{2}{d}^3-d^2-\frac{1}{2}d+1\\ h_d\left(2\right)=-\frac{1}{2}{d}^3+\frac{1}{2}{d}^2+d\\ h_d\left(3\right)=\frac{1}{6}{d}^3-\frac{1}{6}d\end{array}.$

(45) The coefficient c.sub.P(n) of the fractional delay filter with the third-order Farrow structure according to the Lagrange interpolation is obtained as follows:

(46) $c_p\left(n\right)=\left(\begin{array}{cccc}{c}_3\left(0\right)& c_2\left(0\right)& c_1\left(0\right)& c_0\left(0\right)\\ c_3\left(1\right)& c_2\left(1\right)& c_1\left(1\right)& c_0\left(1\right)\\ c_3\left(2\right)& c_2\left(2\right)& c_1\left(2\right)& c_0\left(2\right)\\ c_3\left(3\right)& c_2\left(3\right)& c_1\left(3\right)& c_0\left(3\right)\end{array}\right)=\left(\begin{array}{cccc}-\frac{1}{6}& \frac{1}{2}& -\frac{1}{3}& 0\\ \frac{1}{2}& -1& -\frac{1}{2}& 1\\ -\frac{1}{2}& \frac{1}{2}& 1& 0\\ \frac{1}{6}& 0& -\frac{1}{6}& 0\end{array}\right).$

(47) For the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M, the delays .sub.m, m=1, 2, . . . , M1 obtained in the step 2.1 are determined as d respectively, and therefore the fractional delay filters h.sub.m(n) with the Farrow structure (also referred to the polynomials for the coefficient of the fractional delay filter with the Farrow structure) corresponding to the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M are obtained as follows:

(48) $h_m\left(n\right)=\underset{P=0}{\overset{P}{.Math.}}{c}_P\left(n\right){}_m^P,n=0,1,2,.Math.,P,m=1,2,.Math.,M-1$

(49) For the channel CH.sub.1, a decimal delay .sub.0 with a precision of ten thousandth of a sampling point is determined as d, and the polynomial h.sub.0(n) for the coefficient of the fractional delay filter with the Farrow structure corresponding to the channel CH.sub.1 is obtained as follows:

(50) $h_0\left(n\right)=\underset{P=0}{\overset{P}{.Math.}}{c}_P\left(n\right){}_0^P,n=0,1,2,.Math.,P$

(51) Specially, the decimal delay .sub.0 is a constant.

(52) Step 2.3: the delay correction is performed on the M channels as follows.

(53) The delay correction uses the fractional delay filters with the Farrow structure corresponding to the M channels to eliminate delay inconsistency of the sampling data of the M channels. Meanwhile, due to the fact that a bandwidth of the fractional delay filter with the Farrow structure is designed to be low by using the maximum flatness in the passband of the fractional delay filter based on Lagrange interpolation, the interpolation can be used to improve data rate, and data extraction can be performed after the delay correction is realized by the fractional delay filter with the Farrow structure. Specifically, the step 2.3 includes the following steps: performing half-band interpolation on the sampling data X.sub.1 corresponding to the channel CH.sub.1 and the sampling data X.sub.2, . . . , X.sub.M corresponding to the channels CH.sub.2, CH.sub.3, . . . , CH.sub.M after the gain-offset error correction performed in the step 1 to obtain processed sampling data, and inputting the processed sampling data into the fractional delay filters (also referred to the polynomials for the coefficient of the fractional delay filter with the Farrow structure corresponding to the M channels obtained in the step 2.2) h.sub.0(n), h.sub.1(n), . . . , h.sub.M1(n) with the Farrow structure corresponding to the M channels CH.sub.1, CH.sub.2, CH.sub.3, . . . , CH.sub.M respectively to perform delay filtering, and then performing half-band extraction after the delay filtering to obtain delay-corrected sampling data X.sub.1, X.sub.2, . . . , X.sub.M, thereby completing the delay correction on the M channels.

(54) In an illustrated embodiment, as shown in FIG. 3, the sampling data X.sub.1 corresponding to the channel CH.sub.1 and the sampling data X.sub.2 corresponding to the channel CH.sub.2 after the gain-offset error correction is performed in the step 1 are respectively subjected to the half-band interpolation, and then respectively sent to the corresponding fractional delay filter with the Farrow structure respectively, i.e., h.sub.0(n) and h.sub.1(n), to perform the delay filtering, and then the half-band extraction is performed after the delay filtering to obtain delay-corrected sampling data X.sub.1 and X.sub.2, thereby completing the delay correction on the channel CH.sub.1 and the channel CH.sub.2.

(55) In an illustrated embodiment, the disclosure use a seven-order wave filter with the Farrow structure to perform channel fixed delay correction based on linear phase characteristic, a normalized passband of the seven-order wave filter with the Farrow structure is only 52 kHz at the sampling rate of 262.144 kHz, the sampling rate is first increased to 524.288 kHz by using the half-band interpolation, and at this time, the passband of the seven-order wave filter with the Farrow structure meets a passband requirement of 105 kHz.

(56) The sampling data of the two channels are corrected by the seven-order wave filter with the Farrow structure respectively. Specially, the fractional delay filter with the Farrow structure is set with a small delay of 0.0001 (i.e., the constant for the decimal delay) to compensate for the amplitude and full cycle delay of the sampling data in the channel CH.sub.1.

(57) Step 3: data integration is performed.

(58) The step 3 includes: integrating the delay-corrected sampling data X.sub.1, X.sub.2, . . . , X.sub.M to obtain a multi-ADC acquisition signal.

(59) According to an actual application scenario of dynamic range expansion, sampling data with different amplitudes needs to be selected for integration by more different gains of the multiple channels. In an illustrated embodiment, the input signal is a sine wave, as shown in FIG. 5A, circles illustrated in FIG. 5A indicate occurrence points of vertical nonlinearity caused by delay error after data integration, and it can be seen that due to the existence of the delay error, time domain waveform of an output signal generates obvious distortion. Meanwhile, as shown in FIG. 5B, after the digital correction is performed, the two lines illustrated in FIG. 5B coincide with each other to represent the correction filter to well correct the delay error, so that the waveform distortion is improved.

(60) Although the foregoing has been described with respect to the illustrated embodiments of the disclosure, it will be apparent to those skilled in the related art that the disclosure is not limited to the scope of the illustrated embodiments. Moreover, it will be apparent to those skilled in the related art that such variations are obvious to those skilled in the related art, as long as the variations fall within the spirit and scope of the disclosure, all of which are protected by the disclosure.