Time interleaved ADC adaptive filtering

Abstract

The present disclosure is directed to a method and system for compensating mismatches among sub-converters in a time interleaved analog digital converter structure. A digital finite impulse response (FIR) equalization filtering unit is coupled to outputs of the sub-converters. The FIR filtering unit includes a digital FIR filter dedicated to each sub-converter. The FIR filtering coefficient is adapted specifically for each sub-converter to achieve a compensation for sub-converter mismatches and inter-symbol interference (ISI) equalization.

Claims

1. A device, comprising: a time interleaved analog to digital converter (ADC) having: an input terminal configured to receive an analog input signal; a first sub-converter coupled to the input terminal and configured to sample the analog input signal and convert a first set of samples of the analog input signal into a first set of digital output values; a second sub-converter coupled to the input terminal and configured to sample the analog input signal and convert a second set of samples of the analog input signal into a second set of digital output values; and a finite impulse response (FIR) digital filtering unit coupled to outputs of the first sub-converter and the second sub-converter, the FIR digital filtering unit having a first set of filtering coefficients of a first set of filtering taps dedicated to the first sub-converter and a second set of filtering coefficients of a second set of filtering taps dedicated to the second sub-converter, a first filtering coefficient of the first set of filtering coefficients being determined based on a time domain error associated with the first sub-converter only, a second filtering coefficient of the first set of filtering coefficients being determined based at least partially on the time domain error associated with the first sub-converter and a weighted average of the time domain error associated with the first sub-converter and a time domain error associated with the second sub-converter.

2. The device of claim 1, wherein the first filtering coefficients is determined based on:
f.sub.ni=f.sub.ni.Math.err.sub.n.Math.y.sub.ni, where f.sub.ni denotes the filtering coefficient of an ith filtering tap of the first set of filtering taps dedicated to the first sub-converter, err.sub.n denotes the time domain error associated with the first sub-converter, y.sub.ni denotes an input to the ith filtering tap, n denotes a nth sub-converter, and is a constant.

3. The device of claim 1, wherein the second filtering coefficient is determined at least partially based on: $f_{nj}=f_{nj}-.Math.\left({\mathrm{err}}_n.Math.y_{nj}-\frac{\underset{n=1}{\overset{N}{.Math.}}{\mathrm{err}}_n.Math.y_{nj}}{N}\right),$ wherein f.sub.nj denotes a filtering coefficient of an jth filtering tap of the first set of filtering taps dedicated to the first sub-converter, err.sub.n denotes a time domain error associated with a nth sub-converter, y.sub.nj denotes an input to an jth filtering tap of filtering taps dedicated to the nth sub-converter, N denotes a number of sub-converters, n denotes a nth sub-converter, and is a constant.

4. The device of claim 1, wherein the second filtering coefficient is determined at least partially based on: $f_{nj}=f_{nj}-.Math.{\mathrm{err}}_n.Math.y_{nj}-\left(\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}-m_j-.Math.\frac{\underset{n=1}{\overset{N}{.Math.}}\left(2.Math.{\mathrm{err}}_n.Math.y_{nj}\right)}{N}\right),$ wherein f.sub.nj denotes a filtering coefficient of an jth filtering tap of filtering taps dedicated to an nth sub-converter, err.sub.n denotes a time domain error associated with the nth sub-converter, y.sub.nj denotes an input to the jth filtering tap, m.sub.j is a constant, N denotes a number of sub-converters, n denotes a nth sub-converter, and is a constant.

5. The device of claim 1, wherein the second filtering coefficient is determined at least partially based on: $\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}=m_j,$ wherein f.sub.nj denotes a filtering coefficient of an jth filtering tap of filtering taps dedicated to an nth sub-converter, N denotes a number of sub-converters, n denotes a nth sub-converter, and m.sub.j is a constant.

6. The device of claim 1, wherein the second filtering coefficient includes only one filtering coefficient.

7. The device of claim 1, wherein the second filtering coefficient includes a filtering coefficient for a center filtering tap of the first set of filtering taps.

8. The device of claim 1, wherein the second set of filtering coefficients include a third filtering determined based on a time domain error associated with the second sub-converter only.

9. The device of claim 1, wherein a filtering coefficient of an nth filtering tap of the first set of filtering taps dedicated to the first sub-converter is different from a filtering coefficient of an nth filtering tap of the second set of filtering taps dedicated to the second sub-converter.

10. A device, comprising: a time interleaved analog to digital converter (ADC) having: an input terminal configured to receive an analog input signal; a first sub-converter coupled to the input terminal and configured to sample the analog input signal and convert a first set of samples of the analog input signal into a first set of digital output values; a second sub-converter coupled to the input terminal and configured to sample the analog input signal and convert a second set of samples of the analog input signal into a second set of digital output values; a first finite impulse response (FIR) filter coupled to an output of the first sub-converter, the first FIR filter having a first set of filtering coefficients of a first set of filtering taps; and a second FIR filter coupled to an output of the second sub-converter, the second FIR filter having a second set of filtering coefficients of a second set of filtering taps, the filtering coefficients of the second set being different from the filtering coefficients of the first set; wherein at least one filtering coefficient of the first FIR filter is determined based at least partially on a time domain error associated with the first sub-converter and a first weighted average of the time domain error associated with the first sub-converter and a time domain error associated with the second sub-converter; and at least one filtering coefficient of the second FIR filter is determined based at least partially on the time domain error associated with the second sub-converter and a second weighted average of the time domain error associated with the first sub-converter and the time domain error associated with the second sub-converter.

11. The device of claim 10, wherein at least one filtering coefficient of the first FIR filter is determined based on the time domain error associated with the first sub-converter only and at least one filtering coefficient of the second FIR filter is determined based on the time domain error associated with the second sub-converter only.

12. An analog-to-digital converting method, comprising: sampling an analog signal using a time interleaved analog-to-digital converting circuit that includes a first sub-converter and a second sub-converter to generate a first digital output by the first sub-converter and a second digital output by the second sub-converter; processing the first digital output and the second digital output using a finite impulse response (FIR) digital filtering unit, the FIR digital filtering unit having a first set of filtering coefficients of a first set of filtering taps dedicated to the first sub-converter and a second set of filtering coefficients of a second set of filtering taps dedicated to the second sub-converter, the first set of filtering coefficients including a first filtering coefficient of an nth filtering tap in the first set of filtering taps and the second set of filtering coefficients including a second filtering coefficient, of an nth filtering tap in the second set of filtering taps, the second filtering coefficient being different from the first filtering coefficient; and generating a digital signal by combining processing outputs of the FIR digital filtering unit; wherein the first filtering coefficient is determined based on:
f.sub.ni=f.sub.ni.Math.err.sub.n.Math.y.sub.ni, wherein f.sub.ni denotes the filtering coefficient of an ith filtering tap of the first set of filtering taps dedicated to the first sub-converter, err.sub.n denotes the time domain error associated with the first sub-converter, y.sub.ni denotes an input to the ith filtering tap, n denotes a nth sub-converter, and is a constant.

13. The method of claim 12, wherein the second filtering coefficient is determined based on a time domain error associated with the second sub-converter only.

14. The device of claim 12, wherein: the first filtering coefficient is determined based at least partially on a time domain error associated with the first sub-converter and a first weighted average of the time domain error associated with the first sub-converter and a time domain error associated with the second sub-converter; and the second filtering coefficient is determined based at least partially on the time domain error associated with the second sub-converter and a second weighted average of the time domain error associated with the first sub-converter and the time domain error associated with the second sub-converter.

15. The method of claim 14, wherein the first filtering coefficient is determined at least partially based on: $f_{nj}=f_{nj}-.Math.\left({\mathrm{err}}_n.Math.y_{nj}-\frac{\underset{n=1}{\overset{N}{.Math.}}{\mathrm{err}}_n.Math.y_{nj}}{N}\right),$ wherein f.sub.nj denotes a filtering coefficient of an jth filtering tap of the first set of filtering taps dedicated to the first sub-converter, err.sub.n denotes a time domain error associated with a nth sub-converter, y.sub.nj denotes an input to an jth filtering tap of filtering taps dedicated to the nth sub-converter, N denotes a number of sub-converters, n denotes a nth sub-converter, and is a constant.

16. The method of claim 14, wherein the first filtering coefficient is determined at least partially based on: $f_{nj}=f_{nj}-.Math.{\mathrm{err}}_n.Math.y_{nj}-\left(\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}-m_j-.Math.\frac{\underset{n=1}{\overset{N}{.Math.}}\left(2.Math.{\mathrm{err}}_n.Math.y_{nj}\right)}{N}\right),$ wherein f.sub.nj denotes a filtering coefficient of an jth filtering tap of filtering taps dedicated to an nth sub-converter, err.sub.n denotes a time domain error associated with the nth sub-converter, y.sub.nj denotes an input to the jth filtering tap, m.sub.j is a constant, N denotes a number of sub-converters, n denotes a nth sub-converter, and is a constant.

17. The method of claim 14, wherein the first filtering coefficient is determined at least partially based on: $\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}=m_j,$ wherein f.sub.nj denotes a filtering coefficient of an jth filtering tap of filtering taps dedicated to an nth sub-converter, N denotes a number of sub-converters, n denotes a nth sub-converter, and m.sub.j is a constant.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) The foregoing and other purposes, features, aspects and advantages of embodiments of the present disclosure will become apparent from the following detailed description of embodiments, given by way of illustration and not limitation with reference to the accompanying drawings, in which:

(2) FIG. 1 illustrates an example conventional interleaved ADC;

(3) FIG. 2 illustrates an ADC converting device according to an example embodiment of the present disclosure;

(4) FIG. 3 illustrates an example allocation of FIR filtering coefficient according to an example embodiment of the present disclosure;

(5) FIG. 4 illustrates an example ADC method process according to an example embodiment of the present disclosure; and

(6) FIGS. 5A-5E illustrate the example ADC method process of FIG. 4 with example ADC sampling instances.

DETAILED DESCRIPTION

(7) Throughout the following description, only those elements useful for an understanding of the various embodiments will be described in detail. Other aspects, such as the particular type and form of the analog to digital converter circuitry implementations, have not been described in detail. The following embodiments applying to a wide range of converter types, such as pipeline converters or successive approximation register (SAR) ADCs.

(8) FIG. 2 illustrates time interleaved ADC device 200 according to one embodiment. As an illustrative example, the TI ADC 200 includes a switch circuit 205, a converter block 210 that includes multiple sub-converters 212, three (ADC.sub.1, ADC.sub.2, ADC.sub.3) shown as an illustrative example, each coupled to an analog input terminal A.sub.in through the switch circuit 205. Sub-converters 212 operate to sequentially sample an analog input signal at input terminal A.sub.in, with a time interval T.sub.s through the timing control of the switch circuit 205. Note that switch circuit 205 may include multiple switches for the multiple sub-converters 212 or may include a single switch configured to sequentially connect each sub-converter 212 to the analog input terminal A.sub.in, which are all included in the disclosure. Sub-converters 212 then process the analog samplings into ADC instance digital outputs y (y.sub.1, y.sub.2, y.sub.3). The digital outputs y.sub.1, y.sub.2, y.sub.3 of sub-converters ADC.sub.1, ADC.sub.2, ADC.sub.3 are then processed by a finite impulse response (FIR) digital filter unit 220 before entering a multiplexer (MUX) 230. As appreciated, digital outputs y.sub.1, y.sub.2, y.sub.3 are affected by mismatches among sub-converters 212 in respective gains G.sub.1, G.sub.2, G.sub.3, offsets O.sub.1, O.sub.2, O.sub.3, and timing skews .sub.1, .sub.2, .sub.3 (T.sub.s is sampling interval). FIR digital filter unit 220 includes separate sub-filters 222(1), 222(2) and 222(3) shown as illustrative examples, for each sub-converter 212, namely the FIR filtering coefficients of FIR filter unit 220 include multiple separate sets of FIR filtering coefficients for the multiple sub-converters 212, each set dedicated to and specifically adapted for each sub-converter 212, ADC.sub.1, ADC.sub.2, ADC.sub.3.

(9) FIG. 3 illustrates example FIR filtering operation architecture 300 of the FIR digital filter unit 220. Referring to FIG. 3, in the example FIR architecture 300, three sub-filters 222(1), 222(2) and 222(3) are each dedicated to the respective sub-converter 212, in the sense that each sub-filter 222(1), 222(2) and 222(3) receives the current sampling instance only from the respective sub-converter 212. Each sub-filter 222(1), 222(2) and 222(3) also receive sampling instances prior to the current sampling instance of the respective sub-converter 212 and have filtering coefficients for the previous sampling instances. The previous sampling instances include sampling instances obtained by multiple sub-converters 2121 at different sampling time points. Each filtering coefficient of a sub-filter other filtering 222(1), 222(2) and 222(3) is specifically adapted to be applied to a sampling instance obtained by a specific respective sub-converter 212. Specifically, sub-filter 222(1) is dedicated to sub-converter ADC.sub.1, sub-filter 222(2) is dedicated to sub-converter ADC.sub.2 and sub-filter 222(3) is dedicated to sub-converter ADC.sub.3. It should be appreciated that each sub-filter 222(1), 222(2) and 222(3) is not necessarily a separate filter unit and may just refer to a separate set of filtering coefficients dedicated to filtering the digital output y.sub.1, y.sub.2, y.sub.3 of a specific sub-converter 212. Each sub-filter 222(1), 222(2) and 222(3) may include multiple filtering terms (taps) each with its own filtering coefficient. In an example, at each filtering tap of a sub-filter 222(1), 222(2), 222(3), a delayed digital sampling value of the digital output y.sub.1, y.sub.2, y.sub.3 is combined, e.g., multiplied, with the respective filtering coefficient to generate a filtering product. The filtering products of the multiple filtering taps of the respective sub-filter 222(1), 222(2), 222(3) are combined, e.g., added, in the respective adder 224(1), 224(2), 224(3) to generate the respective filtering results D1, D2, D3.

(10) Note that the filtering coefficient for a filtering tap of a sub-filter 222(1), 222(2) and 222(3) is specifically adapted for the respective sub-converter 212. As shown in FIG. 3 as an illustrative example, sub-filter 222(1) includes filtering coefficient f.sub.1,1, f.sub.1,2, f.sub.1,3, f.sub.1,4, f.sub.1,5, f.sub.1,6 for the six filtering taps t.sub.1,1, t.sub.1,2, t.sub.1,3, t.sub.1,4, t.sub.1,6. Sub-filter 222(2) includes filtering coefficient f.sub.2,1, f.sub.2,2, f.sub.2,3, f.sub.2,4, f.sub.2,5, f.sub.2,6 for their respective filtering taps t.sub.2,1, t.sub.2,2, t.sub.2,3, t.sub.2,4, t.sub.2,5, t.sub.2,6 and sub-filter 222(3) includes filtering coefficient f.sub.3,1, f.sub.3,2, f.sub.3,3, f.sub.3,4, f.sub.3,5, f.sub.3,6 for their respective filtering taps t.sub.3,1, t.sub.3,2, t.sub.3,3, t.sub.3,5, t.sub.3,6. For example, the filtering coefficient f.sub.1,1 for the first filtering tap t.sub.1,1 of sub-filter 222(1) is different from the filtering coefficient f.sub.2,1 for the first filtering tap t.sub.2,1 of sub-filter 222(2).

(11) Among the filtering taps of each sub-filter 222(1), 222(2), 222(3), the respective first filtering taps, t.sub.1,1, t.sub.2,1, t.sub.3,1, apply to a current digital sampling y.sub.1, y.sub.2, y.sub.3, and the rest filtering taps, e.g., t.sub.1,2, t.sub.1,3, t.sub.1,4, t.sub.1,5, t.sub.1,6 of sub-filter 222(1), apply to some previous digital samplings obtained by the three sub-converters 212, namely delayed digital samplings. In the description herein, a current digital sampling is also referred to as a delayed digital sampling in a general sense. As illustratively shown in FIG. 2, sub-converters ADC.sub.1, ADC.sub.2 and ADC.sub.3 sequentially sample analog input A.sub.in in the listed order. In FIG. 3, for descriptive purposes, delayed digital samplings of a sub-converter ADC.sub.1, ADC.sub.2, ADC.sub.3 are referred to a d.sub.x,y, where x indicate the sub-converter and y indicates the delay position of the digital sampling in the overall sequence of the sampling by all the sub-converters 212. Note that the three sub-converters ADC.sub.1, ADC.sub.2, ADC.sub.3 sequentially sample the input A.sub.in. For example, sub-converter ADC.sub.1 includes sampling instances d.sub.1,2, d.sub.1,3, d.sub.1,4, d.sub.1,5, d.sub.1,6, where d.sub.1,1 is the current digital sampling. After ADC.sub.1, the second sub-converter ADC.sub.2 sequentially obtains its current digital sampling, the previously digital sampling d.sub.1,1 will become d.sub.1,2, indicting its second delay position in the overall sampling sequence; after ADC.sub.2, the third sub-converter ADC.sub.3 sequentially obtains its current digital sampling, the digital sampling d.sub.1,2 will become d.sub.1,3, i.e., in the third delay position in the overall sampling sequence; after ADC.sub.3, the first sub-converter ADC.sub.1 sequentially obtains its new current digital sampling, i.e., a new d.sub.1,1, the previously digital sampling d.sub.1,3 will become d.sub.1,4, i.e., in the fourth delay position in the overall sampling sequence; after ADC.sub.1, the second sub-converter ADC.sub.2 sequentially obtains its new current digital sampling, the previously digital sampling d.sub.1,1 will become d.sub.1,2 and the previously digital sampling d.sub.1,4 will become d.sub.1,5, indicating their respective second and fifth delay positions in the overall sampling sequence; and again after ADC.sub.2, the third sub-converter ADC.sub.3 sequentially obtains its new current digital sampling, the previously digital sampling d.sub.1,2 will become d.sub.1,3 and the previously digital sampling d.sub.1,5 will become d.sub.1,6, indicating their respective third and sixth delay positions in the overall sampling sequence.

(12) Similarly, delayed digital samplings of sub-converter ADC.sub.2 includes d.sub.2,1, d.sub.2,2, d.sub.2,3, d.sub.2,4, d.sub.2,5, d.sub.2,6, where d.sub.2,1 is the current digital sampling and d.sub.2,2, d.sub.2,3, d.sub.2,4, d.sub.2,5, d.sub.2,6 are previous sampling values obtained by sub-converter ADC.sub.2 in the overall sampling sequence. Delayed digital samplings of sub-converter ADC.sub.3 includes d.sub.3,1, d.sub.3,2, d.sub.3,3, d.sub.3,4, d.sub.3,5, d.sub.3,6, where d.sub.3,1 is the current digital sampling and d.sub.3,2, d.sub.3,3, d.sub.3,4, d.sub.3,5, d.sub.3,6 are previous sampling values of ADC.sub.3 in the overall sampling sequence.

(13) As sub-converters ADC.sub.1, ADC.sub.2 and ADC.sub.3 sequentially sample analog input A.sub.in in an interleaved manner, the retrospective time sequence (i.e., from present time point to previous time point) includes digital samplings obtained by/from different sub-converters ADC.sub.1, ADC.sub.2 and ADC.sub.3 in an interleaved manner. For example, when sub-converter ADC.sub.1 is currently sampling analog input A.sub.in, the retrospective time sequence is d.sub.1,1, d.sub.3,2, d.sub.2,3, d.sub.1,4, d.sub.3,5, d.sub.2,6, where d.sub.1,1 is the current sampling among all sub-converter ADC.sub.1, ADC.sub.2 and ADC.sub.3, d.sub.3,2 is the immediately previous sampling, i.e., one sampling interval T.sub.s before d.sub.1,1, d.sub.2,3 is two sampling interval T.sub.s before, d.sub.1,4 is three sampling interval T.sub.s before, d.sub.3,5 is four sampling interval T.sub.s before, and d.sub.2,6 is five sampling interval T.sub.s before. When sub-converter ADC.sub.2 is currently sampling analog input A.sub.in, the retrospective time sequence is d.sub.2,1, d.sub.1,2, d.sub.3,3, d.sub.2,4, d.sub.1,5, d.sub.3,6, where d.sub.2,1 is the current sampling among all sub-converter ADC.sub.1, ADC.sub.2 and ADC.sub.3. When sub-converter ADC.sub.3 is currently sampling analog input A.sub.in, the retrospective time sequence is d.sub.3,1, d.sub.2,2, d.sub.1,3, d.sub.3,4, d.sub.2,5, d.sub.1,6, where d.sub.3,1 is the current sampling among all sub-converter ADC.sub.1, ADC.sub.2 and ADC.sub.3.

(14) Filtering taps of each sub-filter 222(1), 222(2), 222(3) apply to the current digital sampling of the respective sub-converter 212, and the retrospective sequence of the delayed digital samplings including the current digital sampling. For example, for sub-filter 222(1), the first filtering tap t.sub.1,1 applies to the current digital sampling d.sub.1,1 of sub-converter ADC.sub.1, the second filtering tap t.sub.1,2 applies to the immediately previous digital sampling d.sub.3,2. And filtering taps t.sub.1,3, t.sub.1,4, t.sub.1,5, t.sub.1,6 apply to further previous digital samplings d.sub.2,3, d.sub.1,4, d.sub.3,5, d.sub.2,6, respectively. Similarly, filtering taps t.sub.2,1, t.sub.2,2, t.sub.2,3, t.sub.2,4, t.sub.2,5, t.sub.2,6 of sub-filter 212(2) apply to the retrospective sequence of digital samplings d.sub.2,1, d.sub.1,2, d.sub.3,3, d.sub.2,4, d.sub.1,5, d.sub.3,6, with first filtering tap t.sub.2,1 applying to digital sampling d.sub.2,1 of ADC.sub.2 as the current digital sampling. Filtering taps t.sub.3,1, t.sub.3,2, t.sub.3,3, t.sub.3,4, t.sub.3,5, t.sub.3,6 of sub-filter 212(3) apply to the retrospective sequence of digital samplings d.sub.3,1, d.sub.2,2, d.sub.1,3, d.sub.3,4, d.sub.2,5, d.sub.1,6, with first filtering tap t.sub.3,1 applying to digital sampling d.sub.3,1 of ADC.sub.3 as the current digital sampling. Note that, d.sub.1,1 and d.sub.1,2, for example, are the same sampling instance obtained sub-converter ADC.sub.1, and a current sampling d.sub.1,1 will become d.sub.1,2, i.e., second delay position in the overall sampling sequence, when next sampling of analog input A.sub.in by sub-converter ADC.sub.2 is obtained. In the illustrative example of three sub-converters 212, d.sub.1,1 and d.sub.1,4 are the sequential sampling instances obtained by sub-converter ADC.sub.1, and d.sub.1,4 is obtained prior to d.sub.1,1.

(15) Further, a FIR filtering coefficient of each sub-filter 222(1), 222(2), 222(3) is specifically adapted with respect to the respective sub-converter 212. For example, for the first filtering taps of sub-filters 222(1), 222(2) and 222(3), three separate filtering coefficient f.sub.1,1, f.sub.2,1 and f.sub.3,1 are specifically adapted to be applied to the digital samplings d.sub.1,1, d.sub.2,1, d.sub.3,1 (i.e., the current sampling values of y.sub.1, y.sub.2, y.sub.3) obtained by the sub-converters ADC.sub.1, ADC.sub.2, ADC.sub.3, respectively. Similarly, for the third filtering taps of sub-filters 222(1), 222(2) and 222(3), three different filtering coefficients f.sub.1,3, f.sub.2,3 and f.sub.3,3 are specifically adapted for the sub-converters ADC.sub.1, ADC.sub.2, ADC.sub.3, respectively. Note that different filtering coefficients, e.g., f.sub.1,1, f.sub.2,1, are different in the sense that they are adapted differently, which does not necessarily mean that they have different values.

(16) FIG. 3 shows, as an illustrative example, how previous digital samplings are used in the filtering, which does not limit the scope of the disclosure. Other patterns of applying filtering coefficients to delayed digital samplings are also possible and included in the disclosure.

(17) Within each sub-filter 222, the processing results of the respective filtering taps will be combined by respective adders 224(1), 224(2), 224(3), that separately generate the respective filtering results D.sub.1, D.sub.2, D.sub.3.

(18) In an example, the set of filtering coefficients of each sub-filter 222(1), 222(2) and 222(3), i.e., specifically for a respective sub-converter 212, e.g., filtering coefficient f.sub.1,1, f.sub.1,2, f.sub.1,3, f.sub.1,4, f.sub.1,5, f.sub.1,6 of sub-filter 222(1) for sub-converter ADC.sub.1, may include a first group of filtering coefficients and a second group of filtering coefficients. For the first group of filtering coefficients of the sub-filter 222, e.g., sub-filter 222(1), the coefficient values are adapted based on the time domain error (referred herein as error) associated only with the corresponding sub-converter 212, here e.g., ADC.sub.1, and errors of other sub-converters 212, here e.g., ADC.sub.2 and ADC.sub.3, are not factored in. For the second group of filtering coefficients of sub-filter 222(1), the coefficient values are adapted based on the error associated with the corresponding sub-converter 212, here ADC.sub.1, and a weighted average of errors of all sub-converters 212, here ADC.sub.1, ADC.sub.2 and ADC.sub.3. In an example, the first group includes more elements than the second group. In an example, the second group includes only the filtering coefficient(s) for the center filtering tap, t.sub.1,3 and/or t.sub.1,4, of the sub-filter 222(1) for sub-converter ADC.sub.1. In the example six filtering taps of FIG. 3, the second group of filtering coefficient of each sub-filter 222 may include the respective filtering coefficients for the respective center taps, namely one or both of the third filtering tap or the fourth filtering tap of each sub-filter 222, e.g., one or both of f.sub.1,3 and f.sub.1,4 of sub-filter 222(1) for sub-converter ADC.sub.1.

(19) As the first group of FIR filtering coefficients of each sub-filter 222 are adapted using only the error(s) associated with the respective same sub-converter 212, the skew mismatches among various sub-converters 212 are compensated for. As the second group of FIR filtering coefficients of each sub-filter 222 for the respective sub-converter 212 are adapted using the error(s) associated with the respective sub-converter 212 and a weighted average of errors of all sub-converters 212, the gain mismatches among different sub-converters 212 are effectively compensated for.

(20) According to an example, the second group of FIR filtering coefficients of a sub-filter 222 may be adapted following the below algorithms:

(21) $\begin{array}{cc}\min \left\{{\mathrm{err}}^2\right\}=\min \left\{{\left(\underset{i=1}{\overset{L}{.Math.}}{f}_{\mathrm{ni}}.Math.y_{\mathrm{ni}}-d_n\right)}^2\right\},& \left(1\right)\end{array}$

(22) $\begin{array}{cc}\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{\mathrm{nj}}}{N}=M_j\mathrm{constraint},& \left(2\right)\end{array}$
where, N indicates the number of sub-converters 212, here for the example of FIG. 3, N=3; L indicates the number of filtering taps of a sub-filter 222, here for the example of FIG. 3, L=6; f.sub.ni indicates a filtering coefficient of the ith filtering tap of the sub-filter 222 for nth sub-converter 212; y.sub.ni indicates the delayed ADC instance input to the ith filtering tap for the nth sub-converter 212, here for the example of FIG. 3, y.sub.1,2 of the 2nd tap of sub-filter 212(1) for sub-converter ADC.sub.1 is the delayed sampling data from ADC.sub.3; and d.sub.n indicates the decision output of the sub-filter 222 for the specific sub-nth converter 212, e.g., for example of FIG. 3, d.sub.1 is filtered output of sub-converter ADC.sub.1.

(23) In the algorithm (2), constant m.sub.j is determined as a constraint on the jth FIR filtering taps within the second group of filtering coefficients for each of the sub-converters 212. This value constraint functions to compensate for the gain mismatches among different sub-converters 212. As provided by algorithm (2), the average value of the jth FIR filtering taps of all the sub-filters 222 respectively for all the sub-converters 212 shall be equal to the constraint value m.sub.j.

(24) With the m.sub.j value set, the below algorithms may be used to determine a filtering coefficient in the second group

(25) A Lagrange optimization function is:

(26) $\begin{array}{cc}\left(f_{nj},\right)={\left(\underset{i=1}{\overset{L}{.Math.}}{f}_{\mathrm{ni}}.Math.y_{\mathrm{ni}}-d_n\right)}^2+.Math.\left(\left(\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}\right)-m_j\right),& \left(3\right)\end{array}$

(27) With FIR adaptation procedures applied:

(28) $\begin{array}{cc}\frac{}{f_{nj}}=2.Math.{\mathrm{err}}_n.Math.y_{\mathrm{nj}}+\frac{}{N}=0,& \left(4\right)\end{array}$
where, n=1, . . . N; j=a filtering tap in the second group, for example, the central tap(s). And,

(29) $\begin{array}{cc}\frac{}{}=\left(\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}\right)-m_j=0,& \left(5\right)\end{array}$
With algorithms (3), (4) and (5) applied together, it can be obtained that:

(30) $\begin{array}{cc}=-\underset{n=1}{\overset{N}{.Math.}}2.Math.{\mathrm{err}}_n.Math.y_{nj},& \left(6\right)\end{array}$

(31) Therefore, a filtering coefficient in the second group might be determined as:

(32) $\begin{array}{cc}{f}_{nj}=f_{nj}-.Math.\left({\mathrm{err}}_n.Math.y_{nj}-\frac{\underset{n=1}{\overset{N}{.Math.}}{\mathrm{err}}_n.Math.y_{nj}}{N}\right),& \left(7\right)\end{array}$
where is a constant. Note that in the adaptation of coefficient f.sub.nj, it is factored in both the error that is associated only to the specific sub-converter 212, i.e., err.sub.n for nth sub-converter 212, and the weighted average of errors of all sub-converters 212, i.e., (.sub.n=1.sup.N err.sub.n.Math.y.sub.nj)/N.

(33) For the value adaptation of a filtering coefficient in the first group, only the error associated to the specific nth sub-converter 212 is used:
f.sub.ni=f.sub.ni.Math.err.sub.n.Math.y.sub.ni where, n=1, . . . N,i=1, . . . L,ij(8)

(34) For a filtering coefficient in the second group, the constraint value m.sub.j may be setup as a predetermined value or may be dynamically adapted. In an example, the value m.sub.j may be used as a constraint in the following procedures:
f.sub.nj=f.sub.nj(2.Math.err.sub.n.Math.y.sub.nj+/N)(9),

(35) $\begin{array}{cc}\frac{\underset{n=1}{\overset{N}{.Math.}}\left[f_{nj}-\left(2.Math.{\mathrm{err}}_n.Math.y_{nj}+\frac{}{N}\right)\right]}{N}=m_j,& \left(10\right)\end{array}$
.sub.n=1.sup.Nf.sub.nj.sub.n=1.sup.N(2.Math.err.sub.n.Math.y.sub.nj)=m.sub.jN(11),

(36) $\begin{array}{cc}=\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{}-\underset{n=1}{\overset{N}{.Math.}}\left(2.Math.{\mathrm{err}}_n.Math.y_{nj}\right)-\frac{m_{j}N}{},& \left(12\right)\end{array}$

(37) Based on algorithms (9)-(12), an updated FIR coefficient adaptation algorithm could be obtained for a filtering tap in the second group:

(38) 0$\begin{array}{cc}{f}_{nj}=f_{nj}-.Math.{\mathrm{err}}_n.Math.y_{nj}-\left(\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}-m_j-.Math.\frac{\underset{n=1}{\overset{N}{.Math.}}\left(2.Math.{\mathrm{err}}_n.Math.y_{nj}\right)}{N}\right),& \left(13\right)\end{array}$
where n=1, . . . N; and where j=a filtering tap in the second group.

(39) With the example algorithm (13) for adapting/determining the FIR filtering coefficient of a filtering tap in the second group of a sub-filter 222, the constraint value m.sub.j may be dynamically adapted to a desired value, which could be different than the initial value. Note that if the term

(40) $\frac{\underset{n=1}{\overset{N}{.Math.}}{f}_{nj}}{N}-m_j$
is omitted from algorithm (13), the algorithm (13) becomes the same as algorithm (7) described herein.

(41) In an example, the initial value of f.sub.ni in algorithm (8) for a filtering tap in the first group may be set up as 0 and the initial value f.sub.nj in algorithm (7) or (13) for a filtering tap in the second group may be set up as 1.

(42) FIG. 4 illustrates an example process 400 of converting an analog signal to a digital signal. Referring to FIG. 4, in example operation 410, an analog signal is sampled sequentially by sub-converters 212 of a TI ADC 210 as shown in FIG. 2 as an example embodiment, to generate ADC instance digital outputs (ADC instances) y, each ADC instance y.sub.1, y.sub.2, y.sub.3 being a digital output of the respective sub-converter 212.

(43) In example operation 420, the ADC instances of the sub-converters 212 are fed into a FIR filtering unit 220 for a digital FIR filtering processing. The digital FIR filtering unit 220 has multiple sub-filters 222 each dedicated to a respective sub-converter 212. A sub-filter 222 includes FIR filtering coefficients specifically adapted for the respective sub-converter 212. Specifically, the filtering coefficients of a sub-filter 222 for a sub-converter 212 includes a first group of filtering coefficients for a first group of filtering taps of the sub-filter 222, which are determined based on errors of the respective sub-converter 212 only and a second group of filtering coefficients for a second group of filtering taps of the sub-filter 222, which are determined based on errors of the respective sub-converter 212 and a weighted average of errors of all the sub-converters 212 that sample the analog signal.

(44) In an example, the filtering coefficients of the first group of filtering taps may be determined using example algorithm (8) described herein. In an example, the filtering coefficients of the second group of filtering taps may be determined using one of example algorithms (7) or (13) described herein.

(45) In example operation 430, the results of the sub-filters 222 of FIR filtering unit 220 are fed into the multiplexer 230 to be combined to generate a digital signal.

(46) FIGS. 5A-5E illustrates the operation of the example process 400 and/or the system 200 using illustrative example samplings.

(47) Referring to FIG. 5A, the example ADC samplings are sequential ADC sampling instances y.sub.1, y.sub.2, y.sub.3, y.sub.4, y.sub.5, y.sub.6, y.sub.7, y.sub.8, y.sub.9. The sequential samplings are obtained by multiple sub-converters 212, ADC.sub.1, ADC.sub.2, ADC.sub.3 sequentially. Specifically, y.sub.1, y.sub.4, y.sub.7 are obtained by ADC.sub.1, y.sub.2, y.sub.5, y.sub.8 are obtained by ADC.sub.2, and y.sub.3, y.sub.6, y.sub.9 are obtained by ADC.sub.3. As shown in FIG. 4A, until a new sampling instance y.sub.4 is obtained by the sub-converter ADC.sub.1, sampling instance y.sub.1 is the delay sampling instances that the sub-converter ADC.sub.1 provides to the filtering taps of the sub-filters 222(1), 222(2), 222(3) (not specifically shown in FIG. 4A for simplicity). Similarly, until a new sampling instance y.sub.7 is obtained by the sub-converter ADC.sub.1, sampling instance y.sub.4 is the delay sampling instances that the sub-converter ADC.sub.1 provides to the filtering taps of the sub-filters 222(1), 222(2), 222(3).

(48) The example sampling instances y.sub.1, y.sub.2, y.sub.3, y.sub.4, y.sub.5, y.sub.6, y.sub.7, y.sub.8, y.sub.9 are obtained at sampling time points t.sub.1, t.sub.2, t.sub.3, t.sub.4, t.sub.5, t.sub.6, t.sub.7, t.sub.8, t.sub.9, respectively.

(49) Referring to FIG. 5B, at the time point t.sub.6, the current sampling instance y.sub.6 is obtained by the sub-converter ADC.sub.3 and is fed into the first filtering tap of the respective sub-filter 222(3), which has a filtering coefficient f.sub.3,1. Previous sampling instances y.sub.5, y.sub.4, y.sub.3, y.sub.2, y.sub.1 are also received by the sub-filter 222(3) and are processed with the filtering coefficients f.sub.3,2, f.sub.3,3, f.sub.3,4, f.sub.3,5, f.sub.3,6 respectively. The result D3 of the sub-filter 222(3) will be output as the digital output D.sub.out.

(50) Referring to FIG. 5C, at the time point t.sub.7, the current sampling instance y.sub.7 is obtained by the sub-converter ADC.sub.1 and is fed into the first filtering tap of the respective sub-filter 222(1), which has a filtering coefficient f.sub.1,1. Sampling instance y.sub.6 now becomes a previous sampling instance. Previous sampling instances y.sub.6, y.sub.5, y.sub.4, y.sub.3, y.sub.2 are also received by the sub-filter 222(1) and are processed with the filtering coefficients f.sub.1,2, f.sub.1,3, f.sub.1,4, f.sub.1,5, f.sub.1,6 respectively. The result D1 of the sub-filter 222(1) will be output as the digital output D.sub.out. FIG. 4C shows that for the sub-filters 222(2) and 222(3), the filtering coefficients are shown as applied to previous sampling instances, which indicates that the procedures in each sub-filters 222 may be conducted partially in parallel with one another.

(51) Referring to FIG. 5D, at the time point t.sub.8, the current sampling instance y.sub.8 is obtained by the sub-converter ADC.sub.2 and is fed into the first filtering tap of the respective sub-filter 222(2), which has a filtering coefficient f.sub.2,1. Sampling instance y.sub.7 now becomes a previous sampling instance. Previous sampling instances y.sub.7, y.sub.6, y.sub.5, y.sub.4, y.sub.3 are also received by the sub-filter 222(2) and are processed with the filtering coefficients f.sub.2,2, f.sub.2,3, f.sub.2,4, f.sub.2,5, f.sub.2,6 respectively. The result D2 of the sub-filter 222(1) will be output as the digital output D.sub.out.

(52) Referring to FIG. 5E, at the time point t.sub.9, the current sampling instance y.sub.9 is obtained by the sub-converter ADC.sub.3 and is fed into the first filtering tap of the respective sub-filter 222(3), which has a filtering coefficient f.sub.3,1. Sampling instance y.sub.8 now becomes a previous sampling instance. Previous sampling instances y.sub.8, y.sub.7, y.sub.6, y.sub.5, y.sub.4 are also received by the sub-filter 222(3) and are processed with the filtering coefficients f.sub.3,2, f.sub.3,3, f.sub.3,4, f.sub.3,5, f.sub.3,6 respectively. The result D3 of the sub-filter 222(3) will be output as the digital output D.sub.put.

(53) Referring to FIGS. 5B and 5E together, it show that the filtering coefficients f.sub.3,1, f.sub.3,2, f.sub.3,3, f.sub.3,4, f.sub.3,5, f.sub.3,6 of sub-filter 222(3) each is applied to a sampling instance obtained by a respective same sub-converter 212. The first filtering coefficient f.sub.3,1 is always applied to a current sampling instance obtained by the respective sub-converter ADC.sub.3. The second filtering coefficient f.sub.3,2 is always applied to a delayed sampling instance obtained by the sub-converter ADC.sub.2. The third filtering coefficient f.sub.3,3 is always applied to a delayed sampling instance obtained by the sub-converter ADC.sub.1. The fourth filtering coefficient f.sub.3,4 is always applied to a delayed sampling instance obtained by the sub-converter ADC.sub.3. The fifth filtering coefficient f.sub.3,5 is always applied to a delayed sampling instance obtained by the sub-converter ADC.sub.2. The sixed filtering coefficient f.sub.3,6 is always applied to a delayed sampling instance obtained by the sub-converter ADC.sub.1. At the same time, the filtering coefficients f.sub.3,1, f.sub.3,2, f.sub.3,3, f.sub.3,4, f.sub.3,5, f.sub.3,6 are adapted using the time domain error of the respective sub-converter ADC.sub.3. Similar descriptions also apply to sub-filters 222(1) and 222(2).

(54) Having thus described at least one illustrative embodiment of the disclosure, various alterations, modifications and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and the scope of the present disclosure. Accordingly, the foregoing description is by way of example only and is not intended to be limiting.

(55) The various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.