Methods and systems for analyzing decomposed uncorrelated signal impairments

Abstract

Method and systems are described for estimating signal impairments, in particular jitter that includes uncorrelated, non-periodic signal impairments. One system may take the form of an oscilloscope. The estimates may take the form of a probability density function (PDF) for uncorrelated signal impairments that has been modified to replace low probability regions with a known approximation and an extrapolation of the known approximation.

We claim: 
     
         1 . A method for estimating a probability density function (PDF) for uncorrelated signal impairments comprising:
 modifying a compound distribution representing acquired data that comprises uncorrelated signal impairments by,
 identifying low probability regions in the distribution; 
 identifying a known approximation that models a distribution of the low probability regions; 
 removing the low probability regions; and 
 replacing the low probability regions with the known approximation and an extrapolation of the known approximation. 
   
     
     
         2 . The method as in  claim 1  wherein the low probability regions are located at extremes of the compound distribution. 
     
     
         3 . The method as in  claim 1  further comprising extrapolating the known approximation to extremes of a specified probability. 
     
     
         4 . The method as in  claim 1 , wherein the known approximation comprises a polynomial approximation. 
     
     
         5 . The method as in  claim 1 , further comprising generating a cumulative distribution function (GDF) estimate based on the compound distribution. 
     
     
         6 . The method as in  claim 5 , wherein the known approximation comprises a linear polynomial approximation having a Gaussian distribution in Q space. 
     
     
         7 . The method as in  claim 5 , further comprising converting the GDF estimate into a modified PDF distribution. 
     
     
         8 . The method as in  claim 7 , wherein the signal impairments comprise uncorrelated jitter, the method further comprising generating an accurate estimate of total jitter by convolving the modified PDF distribution with a data-dependent deterministic PDF in order to calculate a total jitter distribution and a total jitter value at a specified bit error rate. 
     
     
         9 . The method as in  claim 1 , further comprising:
 Identifying lower probability regions of the compound distribution of uncorrelated signal impairments, whose probability of occurrence of impairments is lower than a probability of occurrence of impairments within a central region of the distribution;   determining that the probability of occurrence of the impairments within the lower probability regions is sufficiently characterized by the acquired data to model the lower probability regions as the known approximation;   identifying lowest probability regions of the compound distribution of uncorrelated signal impairments, whose probability of occurrence of impairments is lowest than a probability of occurrence of impairments within the central region of the estimate and insufficiently represented by the acquired data; and   replacing the lower probability region with the known approximation and replacing the lowest probability region with at least an extrapolation of the known approximation.   
     
     
         10 . The method as in  claim 1 , wherein the uncorrelated signal impairments comprise comprises non-periodic, uncorrelated jitter. 
     
     
         11 . The method as in  claim 1 , wherein the uncorrelated signal impairments comprise noise. 
     
     
         12 . A system for estimating a probability density function (PDF) for uncorrelated signal impairments comprising:
 a controller operable to execute instructions for modifying a compound distribution representing acquired data that comprises uncorrelated signal impairments by,
 identifying low probability regions in the distribution; 
 identifying a known approximation that models a distribution of the low probability regions; 
 removing the low probability regions; and 
 replacing the low probability regions with the known approximation and an extrapolation of the known approximation. 
   
     
     
         13 . The system as in  claim 12 , wherein the known approximation comprises a polynomial approximation. 
     
     
         14 . The system as in  claim 12 , wherein the controller is further operable to execute instructions for generating a cumulative distribution function (GDF) estimate based on the compound distribution. 
     
     
         15 . The system as in  claim 14 , wherein the known approximation comprises a linear polynomial approximation having a Gaussian distribution in Q space. 
     
     
         16 . The system as in  claim 14 , wherein the signal impairments comprise non-periodic, uncorrelated jitter, and the controller is further operable to execute instructions for,
 converting the GDF estimate into a modified PDF distribution, and   generating an accurate estimate of total jitter by convolving the modified PDF distribution with a data-dependent deterministic PDF in order to calculate a total jitter distribution and a total jitter value at a specified bit error rate.   
     
     
         17 . The system as in  claim 12 , wherein the system comprises an oscilloscope. 
     
     
         18 . The system as in  claim 12 , further comprising:
 a user interface for activating signal impairment analysis, and for indicating when the analysis is completed; and   a display unit for displaying the user interface.