Waveform construction using interpolation of data points
A method of constructing a waveform from N sampled data captured at N successive points in time, includes, in part, applying the N sampled data, K data at a time, to each of M delayed replicas of a filter that includes K taps so to generate N×M interpolated data. The waveform is then constructed from the N sampled data and the N×M interpolated data.
1. A method of constructing a waveform from N sampled data captured at N successive points in time, the method comprising:
applying K data at a time of the N sampled data to each of M delayed replicas of a filter comprising K taps thereby to generate N×M interpolated data, wherein values of the K taps associated with an i th delayed replica of the filter are determined by shifting a function characterizing the filter by a delay between the i th delayed replica of the filter and the (i−1) th delayed replica of the filter, wherein i is an integer varying from 1 to M; and
constructing the waveform using the N sampled data and the N×M interpolated data, wherein K, N and M are integers and wherein K is smaller than N.
2. The method of claim 1 wherein the waveform is an eye-diagram characterizing a quality of a communications link receiver.
3. The method of claim 1 wherein the waveform defines a pulse response received by a communication link.
4. The method of claim 1 wherein the filter is of a finite length and is non-recursive.
5. The method of claim 1 wherein the filter is of a finite length and is recursive.
6. The method of claim 1 wherein the N data points are sampled at periodic time intervals.
7. The method of claim 1 wherein a delay between i th and (i+1) th delayed replicas of the filter is a same as a delay between (i+1) th and (1+2) th delayed replicas of the filter.
8. The method of claim 1 further comprising:
storing the filter coefficients associated with each of the delayed replicas of the filter in a read-only memory.
9. The method of claim 1 wherein the N sampled data are defined by 2 Q levels, wherein Q is an integer equal to or greater than 2.
10. The method of claim 1 further comprising:
applying the sampled data and a subset of the N×M interpolated data to the filter to generate a second set of interpolated data.
11. A system configured to construct a waveform from N sampled data captured at N successive points in time, the system comprising:
a data collection unit adapted to collect the N sampled data;
a filter comprising K taps;
a control logic configured to cause the filter to receive K data points at a time of the N sampled data to each of M delayed replicas of the filter thereby to generate N×M interpolated data, wherein values of the K taps associated with an i th delayed replica of the filter are determined by shifting a function characterizing the filter by a delay between the i th delayed replica of the filter and the (i−1) th delayed replica of the filter, wherein i is an integer varying from 1 to M; and
a waveform construction logic configured to construct the waveform using the N sampled data and the N×M interpolated data, wherein K, N and M are integers and wherein K is smaller than N.
12. The system of claim 11 wherein the waveform is an eye-diagram characterizing a quality of a communications link receiver.
13. The system of claim 11 wherein the waveform defines a pulse response received by a communication link.
14. The system of claim 11 wherein the filter is of a finite length and is non-recursive.
15. The system of claim 11 wherein the filter is of a finite length and is recursive.
16. The system of claim 11 wherein a delay between i th and (i+1) th delayed replicas of the filter is a same as a delay between (i+1) th and (i+2) th delayed replicas of the filter.
17. The system of claim 11 further comprising:
a read-only memory adapted to store the filter coefficients associated with each of the delayed replicas of the filter.
18. The system of claim 11 wherein the N sampled data are defined by 2 Q levels, wherein Q is an integer equal to or greater than 2.
19. The system of claim 11 wherein the filter is formed in a silicon substrate.
20. A non-transitory computer readable storage medium comprising stored instructions, the instructions when executed by a processor, cause the processor to:
apply K data at a time of the N sampled data to each of M delayed replicas of a filter comprising K taps thereby to generate N×M interpolated data, wherein values of the K taps associated with an i th delayed replica of the filter are determined by shifting a function characterizing the filter by a delay between the i th delayed replica of the filter and the (i−1) th delayed replica of the filter, wherein i is an integer varying from 1 to M; and
construct the waveform using the N sampled data and the N×M interpolated data, wherein K, N and Mare integers and wherein K is smaller than N.