# US 6,298,315 B1 · Method and apparatus for analyzing measurements

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- Number: US 6,298,315 B1
- Document ID: US6298315B1
- Status: Granted
- Kind: B1
- Application number: 09/210,269
- Filed: 1998-12-11
- Granted: 2001-10-02
- Earliest claimed: 1998-12-11
- Assignees: Wavecrest Corporation
- Inventors: Peng Li; Ross Adam Jessen; Jan Brian Wilstrup; Dennis Petrich
- Web page: https://patentgrep.com/patent/US6298315B1

## CPC

- 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)}
- G06F 2218/00: Aspects of pattern recognition specially adapted for signal processing
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## 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

### Claim 1

A method of analyzing a distribution, comprising steps of:
(a) collecting data from a data source;
(b) constructing a histogram based on the data such that the histogram defines a distribution; and
(c) fitting tail regions of the distribution wherein deterministic and random components of the distribution are estimated.

### Claim 2 (depends on 1)

The method of claim 1, 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 region to a predefined first model and second model, respectively; and
(c) estimating fitted parameters of the first model and the second model.

### Claim 3 (depends on 2)

The method of claim 2, further comprising the step of checking the fitting of the first and second tail region.

### Claim 4 (depends on 2)

The method of claim 2, further comprising the step of calculating the statistical confidence of the fitted parameters.

### Claim 5 (depends on 1)

The method of claim 1, further comprising the step of displaying the deterministic and random components of the distribution.

### Claim 6 (depends on 2)

The method of claim 2, wherein the finding step comprises the step of finding the fist and second tail region based on a first derivative and second derivative method.

### Claim 7 (depends on 2)

The method of claim 2, wherein the first model and second model are Gaussian models.

### Claim 8 (depends on 2)

The method of claim 2, wherein the first model and second model are multiple Gaussian models.

### Claim 9 (depends on 2)

The method of claim 2, wherein the model parameters comprise μ and σ.

### Claim 10 (depends on 9)

The method of claim 9, wherein the deterministic component is calculated according the following formula: μ1−2.

### Claim 11 (depends on 10)

The method of claim 10, wherein the random component is calculated according the following formula (σ1+σ2)/2.

### Claim 12 (depends on 1)

The method of claim 1, wherein the distribution comprises a signal distribution.

### Claim 13 (depends on 12)

The method of claim 12, wherein the signal distribution is a jitter signal distribution.

### Claim 14

An apparatus for analyzing a distribution, the apparatus comprising:
(a) a measurement apparatus for collecting data; and
(b) an analyzing unit, operatively connected to the measurement apparatus, for collecting data from the measurement apparatus, constructing a histogram based on the data such that the histogram defines a distribution, fitting tail regions of the distribution, wherein deterministic and random components of the distribution are estimated.

### Claim 15 (depends on 14)

The apparatus of claim 14, wherein the analyzing unit further comprises:
(a) means for finding a first and a second tail region of the distribution;
(b) means for fitting the first and second tail region to a predefined first model and second model; and
(c) means for determining fitted parameters of the first model and the second model.

### Claim 16

An article of manufacture comprising a program storage medium readable by a computer having a memory, the medium tangibly embodying one or more programs of instructions executable by the computer to perform method steps for performing operations analyzing a distribution, the method comprising the steps of:
(a) collecting data from a data source;
(b) constructing a histogram based on the data such that the histogram defines a distribution; and
(c) fitting tail regions of the distribution wherein deterministic and random components of the distribution are estimated.

### Claim 17 (depends on 16)

The article of manufacture of claim 16, wherein the fitting step further comprises the steps of:
(a) finding a first and a second tail region of the distribution;
(b) fitting the first and second tail region to a predefined first model and second model; and
(c) determining the fitted parameters of the first model and the second model.