阅读说明：本技术 一种tiadc系统频响非一致性误差的校正方法 (method for correcting frequency response non-uniformity error of TIADC system ) 是由 潘志翔 叶芃 杨扩军 黄武煌 赵禹 高舰 吴悔 于 2019-09-25 设计创作，主要内容包括：本发明公开了一种基于采样重构滤波器组的TIADC系统频响非一致性误差校正方法,首先测量TIADC系统各ADC的频响,再确定理想频响函数,并利用理想频响和各ADC频响计算采样重构滤波器频响；根据采样重构滤波器频响求得其幅频响应与群延时,然后根据幅频设计第一级线性相位幅频补偿滤波器组,并根据群延时设计第二级全通滤波器组与第三级分数延时滤波器组,再计算整体整数延时,这三级滤波器组构成了采样重构滤波器组；将实际采样数据通过采样重构滤波器组,并根据整体延时确定与实际采样序列对应的重构采样序列,最后根据实际采样序列与重构采样序列计算校正后的采样序列,这样就解决了TIADC系统在较大频响差异下的频响非一致性误差校正问题。(the invention discloses a sampling reconstruction filter bank-based TIADC system frequency response non-uniformity error correction method, which comprises the steps of firstly measuring the frequency response of each ADC of a TIADC system, then determining an ideal frequency response function, and calculating the frequency response of a sampling reconstruction filter by using the ideal frequency response and each ADC frequency response; obtaining the amplitude-frequency response and the group delay of the sampling reconstruction filter according to the frequency response of the sampling reconstruction filter, designing a first-stage linear phase amplitude-frequency compensation filter bank according to the amplitude frequency, designing a second-stage all-pass filter bank and a third-stage fractional delay filter bank according to the group delay, and calculating the integral delay, wherein the three filter banks form a sampling reconstruction filter bank; and finally, calculating a corrected sampling sequence according to the actual sampling sequence and the reconstructed sampling sequence, so that the problem of frequency response non-uniformity error correction of the TIADC system under large frequency response difference is solved.)

1. A TIADC system frequency response non-uniformity error correction method based on an error reconstruction filter bank is characterized by comprising the following steps:

(1) Designing a sampling reconstruction filter bank

(1.1) respectively measuring the frequency response of ADCs (analog to digital converter) numbered from 0 to M-1 by using a dot frequency method or broadband signals, wherein M is the number of ADCs in the TIADC system, and the mth ADC_mIs noted as H_m(j ω), ω is the digital angular frequency;

(1.2) selecting ideal frequency response H_ideal(jω)；

Filter design module selects ideal frequency response H_ideal(j ω) is the average of the frequency response of each channel, i.e.:

(1.3) calculating error reconstruction frequency response Q_m(jω)；

Q_m(jω)＝H_m(jω)/H_ideal(jω)

(1.4) calculating Q_mAmplitude-frequency response A of (j omega)_Qm(j ω) and group delay τ_m(ω)；

A_Qm(jω)＝|Q_m(jω)|

τ(ω)＝[arg(Q_m(j(ω+Δω)))-arg(Q_m(jω))]/Δω

Wherein, | - | represents taking an absolute value, and arg (·) represents taking a phase;

(1.5) designing an even-order linear phase amplitude-frequency compensation filter to make the amplitude-frequency response equal to A_Qm(j ω) group delay D_m1(ii) a Since the linear phase FIR order is even, D_m1Is an integer;

(1.6) designing an all-pass filter by using a complex cepstrum method to ensure that the group delay of the all-pass filter is equal to tau_m(ω)+D_m2wherein D is_m2Is the overall extra delay introduced by designing an all-pass filter;

(1.7) designing a fractional delay FIR filter by utilizing a sinc function method to enable group delay to approachWherein the content of the first and second substances,Indicating rounding up, D_m3Is the overall extra delay introduced due to the design of the fractional delay filter;

(1.8) calculating the integral time delay of the channel filter;

(2) Correction of sampled data

(2.1) inputting the signal to be acquired into the TIADC system, and respectively obtaining N-point sampling sequences by each ADC, and recording the N-point sampling sequences as y_m(N), wherein N satisfies:

(2.2) sampling each path with a sequence y_m(n) splicing according to the sampling time sequence to obtain a spliced sequence y (n), and inputting y (n) into a FIFO (first in first out) for caching; simultaneously inputting y (n) to a sample reconstruction filter bank;

(2.3) in each sampling reconstruction filter, the sampling sequence y (n) sequentially passes through an even-order linear phase amplitude-frequency compensation filter, an all-pass filter and a fractional delay FIR filter, wherein the reconstruction output of the m-th sampling reconstruction filter is y_Qm(n)；

(2.4) enabling the reading enable of the FIFO to be effective, then reading the sampling sequence y (n), and inputting the sampling sequence y (n) to the multiplier respectively;

(2.5) multiplying the read sampling sequence y (n) by a fixed coefficient 2 by a multiplier, and inputting the result to a subtracter;

(2.6) selecting a corresponding channel to output y by a data selector in the sampling reconstruction filter bank according to a source channel m of the current data of a read sampling sequence y (n)_Qm(n) to the subtracter, and the output sequence of the selected sampling reconstruction filter bank is set as y_Q(n)；

(2.7) calculating a corrected sampling value y by a subtracter_c(n)；

y_c(n)＝2·y(n)-y_Q(n)

(2.8) mixing_cAnd (n) sending the data to an upper computer for data caching and displaying, and finishing the frequency response non-uniformity error correction of the TIADC system.

Technical Field

The invention belongs to the technical field of time domain testing, and particularly relates to a TIADC system frequency response non-uniformity error correction method based on a sampling reconstruction filter bank.

Background

In the scheme of constructing the ultra-high-speed acquisition system, a time-interleaved adc (tiadc) architecture is widely applied due to its simple implementation. Using M slices with a sampling rate of f_sThe ADC of/M alternately samples the same signal in a time sequence with equal intervals, and the equivalent sampling rate f can be obtained_sthe sampled data of (1). Theoretically, when all ADCs are identical, the system and sampling rate is f_sThe single ADC acquisition system is equivalent to generate ideal sampling output.

However, in an actual TIADC system, the ADCs are not identical; furthermore, in order to sample the input signal by all ADCs, analog devices (such as power splitters) must be used to split the signal into multiple paths, which are subject to different deviations from the original signal via different transmission paths. The differences of the performance parameters of the analog devices, the transmission paths and the ADC cause the frequency response performance of each sampling path to be inconsistent, errors are inevitably introduced into sampling output, and the performance of the system is seriously degraded. In order to be able to bring the sampled output of the TIADC as close as possible to the ideal sampled output, the error has to be corrected.

in conventional TIADC error correction, the error is considered to be a combination of bias error, amplitude error and time error. Wherein the offset error is independent of the system frequency response, so the correction is mainly studied in terms of amplitude error and time error. The frequency response modeling of the mth channel is as follows:

Wherein g is_mAnd r_mThe gain error coefficient and the time error coefficient of the mth channel, respectively, are independent of the input signal frequency. A large number of patentsError estimation and correction methods are studied based on such error models. For example, patent CN106209103A uses spectrum analysis to analyze the sampled data of each channel ADC and perform error correction by the built-in correction unit of the ADC; patent CN107147392A uses an adaptive fractional delay filter for amplitude and time error correction. Common to these patents is that the error of the TIADC system is considered to be frequency-independent, i.e., the magnitude of the error is independent of the frequency of the input signal.

In a TIADC system, however, the nature of the error generation is to sample the difference in frequency response of each channel. That is, the difference between the respective sampling paths is not necessarily the same at different frequency points. This results in the errors generated by the TIADC system being not exactly the same for input signals of different frequencies, the errors being frequency dependent. Based on such consideration, patent CN108923784A and patent CN108809308A estimate full-bandwidth errors from amplitude and time, respectively, and correct the error at the point where the signal energy is maximum frequency by using the dot-frequency method, but this method still belongs to dot-frequency correction per se; patent US7978104 writes the frequency response of the sampling path in the form of a frequency domain polynomial and uses a polynomial filter for reconstruction, but this method is only suitable for the case of regular frequency response, and when the frequency response of the actual system is irregular, the frequency response of the sampling path is difficult to write in the form of a low-order polynomial, and the filter cannot be designed effectively.

In summary, there is no general method for correcting the TIADC frequency response non-uniformity error under the condition of large frequency response difference of the sampling channels. Therefore, it is very important to design a TIADC frequency response non-uniformity error correction method suitable for large channel frequency response differences.

Disclosure of Invention

the invention aims to overcome the defects of the prior art and provides a method for correcting frequency response non-uniformity errors of a TIADC system based on a sampling reconstruction filter bank, so that the error correction can still be carried out on the full bandwidth under the condition that the frequency response non-uniformity errors of the TIADC are large.

In order to achieve the above object, the present invention provides a method for correcting a frequency response inconsistency error of a TIADC system, which is characterized by comprising the following steps:

(1) designing a sampling reconstruction filter bank

(1.1) respectively measuring the frequency response of ADCs numbered from 0 to M-1 by using a dot frequency method or a broadband signal, wherein M is the number of ADCs in the TIADC system, and the mth ADC (namely the numbered ADC)_mIs noted as H_m(j ω), ω is the digital angular frequency;

(1.2) selecting ideal frequency response H_ideal(jω)；

filter design module selects ideal frequency response H_ideal(j ω) is the average of the frequency response of each channel, i.e.:

(1.3) calculating error reconstruction frequency response Q_m(jω)；

Q_m(jω)＝H_m(jω)/H_ideal(jω)

(1.4) calculating Q_mAmplitude-frequency response A of (j omega)_Qm(j ω) and group delay τ_m(ω)；

A_Qm(jω)＝|Q_m(jω)|

τ(ω)＝[arg(Q_m(j(ω+Δω)))-arg(Q_m(jω))]/Δω

wherein, | - | represents taking an absolute value, arg (·) represents taking a phase, and Δ ω represents a sampling interval of a frequency domain;

(1.5) designing an even-order linear phase amplitude-frequency compensation filter to enable amplitude-frequency response to be equal to A_Qm(j ω) group delay D_m1(ii) a Since the linear phase FIR order is even, D_m1Is an integer;

(1.6) designing an all-pass filter by using a complex cepstrum method to ensure that the group delay of the all-pass filter is equal to tau_m(ω)+D_m2Wherein D is_m2Is the overall extra delay introduced by designing an all-pass filter;

(1.7) designing a fractional delay FIR filter by utilizing a sinc function method to enable group delay to approachWherein the content of the first and second substances,Indicating rounding up, D_m3Is the overall extra delay introduced due to the design of the fractional delay filter;

(1.8) calculating the integral time delay of the channel filter;

(2) Correction of sampled data

(2.1) inputting the signal to be acquired into the TIADC system, and respectively obtaining N-point sampling sequences by each ADC, and recording the N-point sampling sequences as y_m(N), wherein N satisfies:

(2.2) sampling each path with a sequence y_m(n) splicing according to the sampling time sequence to obtain a spliced sequence y (n), and inputting y (n) into a FIFO (first in first out) for caching; while y (n) is input to the sample reconstruction filter bank.

(2.3) in each sampling reconstruction filter, a sampling sequence y (n) sequentially passes through an even-order linear phase amplitude-frequency compensation filter, an all-pass filter and a fractional delay FIR filter, and the reconstruction output of the m-th sampling reconstruction filter is set as y_Qm(n)；

(2.4) enabling the reading enable of the FIFO to be effective, then reading the sampling sequence y (n), and inputting the sampling sequence y (n) to the multiplier respectively;

(2.5) multiplying the read sampling sequence y (n) by a fixed coefficient 2 by a multiplier, and inputting the result to a subtracter;

(2.6) selecting a corresponding channel to output y by a data selector in the sampling reconstruction filter bank according to a source channel m of the current data of a read sampling sequence y (n)_Qm(n) to the subtractor. Setting the output sequence of the selected sampling reconstruction filter bank as y_Q(n)；

(2.7) calculating a corrected sampling value y by a subtracter_c(n)；

y_c(n)＝2·y(n)-y_Q(n)

(2.8) mixing_cAnd (n) sending the data to an upper computer for data caching and displaying, and finishing the frequency response non-uniformity error correction of the TIADC system.

the invention aims to realize the following steps:

The invention relates to a TIADC system frequency response non-uniformity error correction method based on a sampling reconstruction filter bank, which comprises the steps of firstly measuring the frequency response of each ADC of the TIADC system, then determining an ideal frequency response function, and calculating the frequency response of a sampling reconstruction filter by using the ideal frequency response and each ADC frequency response; obtaining the amplitude-frequency response and the group delay of the sampling reconstruction filter according to the frequency response of the sampling reconstruction filter, designing a first-stage linear phase amplitude-frequency compensation filter bank according to the amplitude frequency, designing a second-stage all-pass filter bank and a third-stage fractional delay filter bank according to the group delay, and calculating the integral delay, wherein the three filter banks form a sampling reconstruction filter bank; and finally, calculating a corrected sampling sequence according to the actual sampling sequence and the reconstructed sampling sequence, so that the problem of frequency response non-uniformity error correction of the TIADC system under large frequency response difference is solved.

meanwhile, the TIADC system frequency response non-uniformity error correction method based on the sampling reconstruction filter bank also has the following beneficial effects:

(1) by carrying out digital filtering and digital time alternation under the full sampling rate on the whole sampling, the problem that the frequency response non-uniformity error across a single ADC nano-domain is difficult to correct by the original TIADC error estimation and correction method is solved, and the TIADC frequency response non-uniformity error correction of the broadband signal becomes possible.

(2) And through the design of the compensation filter bank, the limitation of TIADC frequency response non-uniformity errors on ADC frequency response differences is relieved, and the frequency response non-uniformity errors under larger frequency response differences can be corrected.

Drawings

FIG. 1 is a schematic diagram of a 4-channel TIADC system frequency response non-uniformity error correction method based on a sampling reconstruction filter bank;

FIG. 2 is a schematic diagram of a TIADC system;

FIG. 3 is an equivalent system diagram of a TIADC;

FIG. 4 is another equivalent system diagram of a TIADC;

FIG. 5 is a schematic diagram of sample reconstruction in an ideal case;

FIG. 6 is a three-stage filter exploded view of a sample reconstruction filter;

FIG. 7 is a data correspondence of sampled data to filter reconstruction data;

Detailed Description

the following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.