Method and apparatus for analyzing measurements

• US 20050027477A1
• Filed: 08/25/2004
• Published: 02/03/2005
• Est. Priority Date: 12/11/1998
• Status: Abandoned Application

• Current Assignee: Wavecrest Corporation
• Original Assignee: Wavecrest Corporation
• Inventors: Petrich, Dennis, Jessen, Ross Adam, Li, Peng, Wilstrup, Jan Brian
• Application Number:
  US10/926,698
• Publication Number:
  US 20050027477A1
• Time in Patent Office: Days
• US Class Current: 702/181
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06F 2218/00 Aspects of pattern recognition specially adapted for signal processing

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.

Claims

1-17. -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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (ρ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 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:

μ

1−

μ

2, μ

1 representing the mean of the first model distribution, and μ

2 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 (σ

1+σ

2)/2, σ

1 representing the standard deviation of the first model distribution, and σ

2 representing the standard deviation of the second model distribution.