Method and apparatus for analyzing measurements

Abstract

A method, apparatus, and article of manufacture for analyzing measurements. The invention provides a method for separating and analyzing the components of a distribution, such as deterministic and random components. The method performs the steps of collecting data from a measurement apparatus, constructing a histogram based on the data such that the histogram defines a distribution, fitting tails regions wherein deterministic and random components and associated statistical confidence levels are estimated.

1 - 17 . (Cancelled)  
     
     
         18 . In a system employing a clock or communication signal comprised of transitions intended to occur at ideal points in time, but which actually occur at non-ideal points in time, a method of analyzing a distribution that represents actual timing of the transitions, the method comprising: 
 fitting a model distribution to a tail region of the distribution representing actual timing of the transitions, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         19 . The method of  claim 18 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution representing actual timing of the transitions;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         20 . The method of  claim 19 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         21 . The method of  claim 19 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         22 . The method of  claim 21 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         23 . The method of  claim 21 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         24 . A method of identifying a random component of jitter from a distribution representing both random and deterministic jitter of a signal, the method comprising: 
 identifying a region of the distribution that is shaped by a random jitter component; and    fitting a Gaussian distribution to the region, thereby representing a random jitter component with the Gaussian distribution.    
     
     
         25 . The method of  claim 24 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         26 . The method of  claim 25 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         27 . The method of  claim 25 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         28 . The method of  claim 27 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         29 . The method of  claim 27 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         30 . An apparatus for analyzing a distribution that represents actual timing of transitions collected from a system employing a clock or communication signal comprised of transitions intended to occur at ideal points in time, but which actually occur at non-ideal points in time, the apparatus comprising: 
 an analyzing unit for fitting a model distribution to a tail region of a distribution representing actual timing of the transitions, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         31 . The apparatus of  claim 30 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the distribution representing actual timing of the transitions;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         32 . The apparatus of  claim 31 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         33 . The apparatus of  claim 31 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         34 . The apparatus of  claim 33 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         35 . The apparatus of  claim 33 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         36 . An apparatus for identifying a random component of jitter from a distribution representing both random and deterministic jitter of a signal, the apparatus comprising: 
 an analyzing unit for 
 identifying a region of the distribution that is shaped by a random jitter component; and  
 fitting a Gaussian distribution to the region, thereby representing a random jitter component with the Gaussian distribution.  
   
     
     
         37 . The apparatus of  claim 36 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         38 . The apparatus of  claim 37 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         39 . The apparatus of  claim 37 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         40 . The apparatus of  claim 39 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         41 . The apparatus of  claim 39 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         42 . In a system employing a clock or communication signal comprised of signals components intended to have an ideal amplitude, but which in fact have a non-ideal amplitude, a method of analyzing a distribution that represents actual amplitudes of the components, the method comprising: 
 fitting a model distribution to a tail region of the distribution representing actual amplitudes of the components, the fitted model distribution providing information regarding deterministic and random noise components within the signal.    
     
     
         43 . The method of  claim 42 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution representing actual amplitudes of the signal components;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         44 . The method of  claim 43 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         45 . The method of  claim 43 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         46 . The method of  claim 45 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         47 . The method of  claim 45 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         48 . A method of identifying a random component of jitter from a distribution representing both random and deterministic amplitude jitter of a signal, the method comprising: 
 identifying a region of the distribution that is shaped by a random amplitude jitter component; and    fitting a Gaussian distribution to the region, thereby representing a random amplitude jitter component with the Gaussian distribution.    
     
     
         49 . The method of  claim 48 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         50 . The method of  claim 49 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         51 . The method of  claim 49 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         52 . The method of  claim 51 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         53 . The method of  claim 51 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         54 . An apparatus for analyzing a distribution that represents actual amplitudes of signal components collected from a system employing a clock or communication signal comprised of signals components intended to have an ideal amplitude, but which in fact have a non-ideal amplitude, the apparatus comprising: 
 an analyzing unit for fitting a model distribution to a tail region of the distribution representing actual amplitudes of the components, the fitted model distribution providing information regarding deterministic and random noise components within the signal.    
     
     
         55 . The apparatus of  claim 54 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the histogram;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         56 . The apparatus of  claim 55 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         57 . The apparatus of  claim 55 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         58 . The apparatus of  claim 57 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         59 . The apparatus of  claim 57 , wherein the random component is calculated according to the following formula (ρ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         60 . An apparatus for identifying a random component of amplitude jitter from a distribution representing both random and deterministic amplitude jitter of a signal, the apparatus comprising: 
 an analyzing unit for 
 identifying a region of the distribution that is shaped by a random amplitude jitter component; and  
 fitting a Gaussian distribution to the region, thereby representing a random amplitude jitter component with the Gaussian distribution.  
   
     
     
         61 . The apparatus of  claim 60 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         62 . The apparatus of  claim 61 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         63 . The apparatus of  claim 61  wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         64 . The apparatus of  claim 63 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         65 . The apparatus of  claim 63 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         66 . In a system employing a clock or communication signal comprised of waveforms intended to have an ideal phase, but which in fact have a non-ideal phase, a method of analyzing a distribution that represents actual phases of the waveforms, the method comprising: 
 fitting a model distribution to a tail region of the distribution representing actual phases of the waveforms, the fitted model distribution providing information regarding deterministic and random phase jitter components within the signal.    
     
     
         67 . The method of  claim 66 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution representing actual phases of the waveforms;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         68 . The method of  claim 67 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         69 . The method of  claim 67 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         70 . The method of  claim 69 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         71 . The method of  claim 69 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         72 . An apparatus for analyzing a distribution that represents actual phases of waveforms collected from a system employing a clock or communication signal comprised of waveforms intended to have an ideal phase, but which in fact have a non-ideal phase, the apparatus comprising: 
 an analyzing unit for fitting a model distribution to a tail region of the distribution representing actual phases of the waveforms, the fitted model distribution providing information regarding deterministic and random phase jitter components within the signal.    
     
     
         73 . The apparatus of  claim 72 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         74 . The apparatus of  claim 73 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         75 . The apparatus of  claim 73 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         76 . The apparatus of  claim 75 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         77 . The apparatus of  claim 75  wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         78 . In a system employing a clock signal intended to have a particular period, but which actually has an irregular period, a method of analyzing a distribution that represents actual periods within the signal, the method comprising: 
 fitting a model distribution to a tail region of the distribution representing actual periods within the signal, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         79 . The method of  claim 78 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution representing actual periods within the signal;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         80 . The method of  claim 79 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         81 . The method of  claim 79 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         82 . The method of  claim 81 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         83 . The method of  claim 81 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         84 . An apparatus for analyzing a distribution that represents actual periods within a clock signal collected from a system employing a clock signal intended to have a particular period, but which actually has an irregular period, the apparatus comprising: 
 an analyzing unit for fitting a model distribution to a tail region of the distribution representing actual periods within the signal, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         85 . The apparatus of  claim 84 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         86 . The apparatus of  claim 85 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         87 . The apparatus of  claim 85 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         88 . The apparatus of  claim 87 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         89 . The apparatus of  claim 87 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         90 . In a system employing a clock signal intended to have a particular frequency, but which actually has an irregular frequency, a method of analyzing a distribution that represents actual frequencies within the signal, the method comprising: 
 fitting a model distribution to a tail region of the distribution representing actual frequencies within the signal, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         91 . The method of  claim 90 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution representing actual frequencies within the signal;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         92 . The method of  claim 91 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         93 . The method of  claim 91 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         94 . The method of  claim 93 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         95 . The method of  claim 93 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         96 . An apparatus for analyzing a distribution that represents actual frequencies within a clock signal collected from a system employing a clock signal intended to have a particular frequency, but which actually has an irregular frequency, the apparatus comprising: 
 an analyzing unit for fitting a model distribution to a tail region of the distribution representing actual frequencies within the signal, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         97 . The apparatus of  claim 96 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         98 . The apparatus of  claim 97 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         99 . The apparatus of  claim 97 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         100 . The apparatus of  claim 99 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         101 . The apparatus of  claim 99 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         102 . In a system employing a clock or communication signal comprised of waveforms intended to have a particular rise or fall time, but which in fact have a non-ideal rise or fall time, a method of analyzing a distribution that represents actual rise or fall times of the signal, the method comprising: 
 fitting a model distribution to a tail region of the distribution representing actual rise or fall times of the signal, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         103 . The method of  claim 102 , wherein the fitting step comprises the steps of: 
 (a) finding a first and a second tail region of the distribution representing actual rise or fall times of the waveforms;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         104 . The method of  claim 103 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         105 . The method of  claim 103 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         106 . The method of  claim 105 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         107 . The method of  claim 105 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.  
     
     
         108 . An apparatus for analyzing a distribution that represents actual rise or fall times of waveforms collected from a system employing a clock or communication signal comprised of waveforms intended to have a particular rise or fall time, but which in fact have a non-ideal rise or fall time, the method comprising: 
 an analyzing unit for fitting a model distribution to a tail region of the distribution representing actual rise or fall times of the signal, the fitted model distribution providing information regarding deterministic and random jitter components within the signal.    
     
     
         109 . The apparatus of  claim 108 , wherein the analyzing unit performs the following steps: 
 (a) finding a first and a second tail region of the distribution;    (b) fitting the first and second tail regions to a predefined first model distribution and second model distribution, respectively; and    (c) estimating fitted parameters of the first model distribution and the second model distribution.    
     
     
         110 . The apparatus of  claim 109 , wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.  
     
     
         111 . The apparatus of  claim 109 , wherein the model parameters comprise mean (μ) and standard deviation (σ).  
     
     
         112 . The apparatus of  claim 111 , wherein the deterministic component is calculated according to the following formula: μ1−μ2, μ1 representing the mean of the first model distribution, and μ2 representing the mean of the second model distribution.  
     
     
         113 . The apparatus of  claim 111 , wherein the random component is calculated according to the following formula (σ1+σ2)/2, σ1 representing the standard deviation of the first model distribution, and σ2 representing the standard deviation of the second model distribution.