Period determination of a periodic NRZ signal

• US 20050273285A1
• Filed: 05/24/2005
• Published: 12/08/2005
• Est. Priority Date: 05/25/2004
• Status: Active Grant

• Current Assignee: Tektronix Incorporated (Fortive Corp.)
• Original Assignee: Tektronix Incorporated (Fortive Corp.)
• Inventors: Onu, Dan
• Granted Patent: US 7,379,830 B2
• Time in Patent Office: Days
• US Class Current: 702/67
• CPC Class Codes: G11B 20/14 using self-clocking codes
• CPC Class Codes: G11B 20/1403 characterised by the use of two levels

Abstract

A method and apparatus for determining the period T_p of a signal representing a digitally modulated waveform using NRZ coding with a discrete/integer number of a clock periods between signal transitions, where a periodic sequence of logic “1s” and logic “0s” is transmitted, is disclosed. The method comprises the steps of sampling an input periodic signal, constructing an estimate of the autocorrelation sequence r_k of the sequence of samples, constructing a sequence of peaks p_k, and computing the period T_p to be the time between the first p_k sample (k=0), and the time location of the maximum value of p_k based on the known T_s spacing of the p_k sequence samples.

Claims

1. A method for determining the period of a periodic non-return-to-zero signal, the method comprising the steps of:

sampling said periodic no-return-to-zero signal at a predetermined sample rate having a predetermined sample interval;

constructing an estimate of an autocorrelation sequence of said samples;

constructing a sequence of peaks based upon said autocorrelation estimate; and

computing said period of said periodic non-return-to-zero signal as the interval between a time location of a first peak of said sequence of peaks and a time location of a peak having a maximum value with respect to other peaks based upon said predetermined sample interval.

2. The method if claim 1 wherein,

said sequence of samples is X(k)=X(T_k) where said predetermined sample interval is T_s, and T_k=n* T_s.

3. The method if claim 2 wherein,

said step of constructing an estimate includes the step of:

computing

$r_k=\frac{1}{N}<br><br>\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i<br><br>x_{i+k},$

for k=0;

(N−

1), where x_j=0 for j<

1 or j>

N.

4. The method of claim 3, wherein the step of constructing a sequence of peaks, comprises the step of:

constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated by averaging based on adjacent r_k samples.

5. The method of claim 4 wherein the computing step comprises:

computing a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.

6. The method of claim 3, wherein the step of constructing a sequence of peaks, comprises the step of:

constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated using interpolation.

7. The method of claim 6 wherein the computing step comprises:

computing a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.

8. The method of claim 2 wherein, said step of constructing an estimate includes the steps of:

computing a Fourier transform sequence X_k of x_k;

squaring magnitudes of values of X_k point-by-point to obtain a sequence of power spectral density S_k of x_k;

and computing an inverse Fourier Transform of S_k to obtain a sequence r_k.

9. The method of claim 8, wherein the step of constructing a sequence of peaks, comprises the step of:

constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated by averaging based on adjacent r_k samples.

10. The method of claim 9 wherein the computing step comprises:

computing a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.

11. The method of claim 8, wherein the step of constructing a sequence of peaks, comprises the step of:

constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated using interpolation.

12. The method of claim 11 wherein the computing step comprises:

computing a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.

13. An oscilloscope having a program determining the period of a periodic non-return-to-zero signal, comprising:

an acquisition circuit sampling said periodic no-return-to-zero signal at a predetermined sample rate having a predetermined sample interval;

a waveform memory for storing said samples;

a memory for storing said program;

a processor constructing an estimate of an autocorrelation sequence of said samples;

said processor constructing a sequence of peaks based upon said autocorrelation estimate;

said processor computing said period of said periodic non-return-to-zero signal as the interval between a time location of a first peak of said sequence of peaks and a time location of a peak having a maximum value with respect to other peaks based upon said predetermined sample interval; and

a display screen;

wherein

at least one of said autocorrelation, said estimate, and said sequence of peaks is displayed on said display screen.

14. The oscilloscope of claim 13 wherein,

said sequence of samples is X(k)=X(T_k) where said predetermined sample interval is T_s, and T_k=n* T_s.

15. The oscilloscope of claim 14 wherein,

said processor constructs said estimate by computing

$r_k=\frac{1}{N}$

∑

i=1N⁢

xi⁢

xi+k,

for k=0;

(N−

1), where x_j=0 for j<

1 or j>

N.

16. The oscilloscope of claim 15 wherein,

said processor constructs said sequence of peaks by constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated by averaging based on adjacent r_k samples.

17. The oscilloscope of claim 16 wherein,

said processor computes a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.

18. The oscilloscope of claim 15 wherein,

said processor constructs said sequence of peaks by constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated using interpolation.

19. The oscilloscope of claim 18 wherein,

said processor computes a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.

20. The oscilloscope of claim 14 wherein,

said processor constructs said estimate includes by computing a Fourier transform sequence X_k of x_k;

squaring magnitudes of values of X_k point-by-point to obtain a sequence of power spectral density S_k of x_k;

and computing an inverse Fourier Transform of S_k to obtain a sequence r_k.

21. The oscilloscope of claim 17 wherein,

said processor constructs said sequence of peaks by constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated by averaging based on adjacent r_k samples.

22. The oscilloscope of claim 21 wherein,

said processor computes a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.

23. The oscilloscope of claim 17 wherein,

said processor constructs said sequence of peaks by constructing a sequence

$p_k=\frac{r_k-r_{k/2}}{r_0-r_{k/2}},$

wherein odd values of k the value of r_k/2 are estimated using interpolation.

24. The oscilloscope of claim 23 wherein,

said processor computes a period T_p as a time between a first p_k sample (k=0), and a time of a maximum value of p_k based upon said T_s spacing of said p_k sequence samples.