US 7,133,568 B2 · Method and apparatus for analysis of variables

Abstract

Various components of the present invention are collectively designated as Analysis of Variables Through Analog Representation (AVATAR). AVATAR offers an analog solution to those problems of the analysis of variables which are normally handled by digital means. The invention allows (a) the improved perception of the measurements through geometrical analogies, (b) effective solutions of the existing computational problems of the order statistic methods, and (c) extended applicability of these methods to analysis of variables. The invention employs transformation of discrete or continuous variables into normalized continuous scalar fields, that is, into objects with mathematical properties of density and/or cumulative distribution functions. In addition to dependence on the displacement coordinates (thresholds), these objects can also depend on other parameters, including spatial coordinates. Moreover, this transformation of the measured variables may be implemented with respect to any reference variable. Thus, the values of the reference variable provide a common unit, or standard, for measuring and comparison of variables of different natures, for assessment of mutual dependence of these variables, and for evaluation of changes in the variables and their dependence with time. The invention enables, on a consistent general basis, a variety of new techniques for analysis of variables, which can be implemented through various physical means in continuous action machines as well as through digital means or computer calculations. Several of the elements of these new techniques do have digital counterparts, such as some rank order techniques in digital signal and image processing.

Claims55

Dependent claims

A method for analysis of variables operable to transform an input variable into an output variable having mathematical properties of a scalar field comprising the following steps:

(a) applying a Threshold Filter to a difference of a Displacement Variable and an input variable producing a first scalar field of said Displacement Variable;
and
(b) filtering said first scalar field of step (a) with a first Averaging Filter operable to perform time averaging of said first scalar field and operable to perform spatial averaging of said first scalar field producing a second scalar field of said Displacement Variable.

A method for analysis of variables operable to transform an input scalar field variable into an output Rank Filtered variable comprising the following steps:

(a) applying a first Probe to a difference of a Displacement Variable and an input variable producing a first scalar function of said Displacement Variable;
(b) filtering said first scalar function of step (a) with a first Averaging Filter operable to perform time averaging of said first scalar function and operable to perform spatial averaging of said first scalar function producing a first averaged scalar function of said Displacement Variable;
(c) applying a Discriminator to the difference of said Displacement Variable and the input variable wherein said Discriminator is a respective discriminator of said first Probe producing a second scalar function of said Displacement Variable;
(d) filtering said second scalar function of step (c) with a second Averaging Filter where said second Averaging Filter has an impulse response identical to the impulse response of said first Averaging Filter producing a second averaged scalar function of said Displacement Variable;
(e) applying a second Probe to a difference of a quantile value and said second averaged scalar function of step (d) wherein the width parameter of said second Probe is substantially smaller than unity producing an output of the second Probe;
and
(f) multiplying said output of the second Probe of step (e) by said first averaged scalar function of step (b) and by said Displacement Variable and integrating the product over the values of said Displacement Variable to output said Rank Filtered variable.

4 more elements

A method for Rank Filtering operable to transform an input scalar variable into an output Rank Filtered variable comprising the following steps:

(a) applying a Probe to a difference between a feedback of a Rank Filtered variable and an input variable producing a first scalar function of said Rank Filtered variable;
(b) filtering said first scalar function of step (a) with a first Time Averaging Filter operable to perform time averaging of said first scalar function producing a first averaged scalar function of said Rank Filtered variable;
(c) applying a Discriminator to the difference between the feedback of said Rank Filtered variable and the input variable wherein said Discriminator is a respective discriminator of said Probe producing a second scalar function of said Rank Filtered variable;
(d) subtracting said second scalar function of step (c) from a quantile value and filtering the difference with a second Time Averaging Filter wherein the impulse response of said second Time Averaging Filter is a first derivative of the impulse response of said first Time Averaging Filter producing a second averaged scalar function of said Rank Filtered variable;
and
(e) dividing said second averaged scalar function of step (d) by said first averaged scalar function of step (b) and time-integrating the quotient to output said Rank Filtered variable.

3 more elements

A method for Rank Filtering transforming an ensemble of input scalar variables into an output Rank Filtered variable comprising the following steps:

(a) applying a Probe to each difference between a feedback of a Rank Filtered variable and each component of an ensemble of input variables producing a first ensemble of scalar functions of said Rank Filtered variable;
(b) multiplying each component of said first ensemble of scalar functions of step (a) by the weight of the respective component of the ensemble of input variables and summing the products producing a first scalar function of said Rank Filtered variable;
(c) filtering said first scalar function of step (b) with a first Time Averaging Filter producing a first averaged scalar function of said Rank Filtered variable;
(d) applying a Discriminator to each difference between the feedback of said Rank Filtered variable and each component of the ensemble of input variables wherein said Discriminator is a respective discriminator of said Probe producing a second ensemble of scalar functions of said Rank Filtered variable;
(e) multiplying each difference between a quantile value and each component of said second ensemble of scalar functions of step (d) by the weight of the respective component of the ensemble of input variables and summing the products producing a second scalar function of said Rank Filtered variable;
(f) filtering said second scalar function of step (e) with a second Time Averaging Filter wherein the impulse response of said second Time Averaging Filter is a first derivative of the impulse response of said first Time Averaging Filter producing a second averaged scalar function of said Rank Filtered variable;
and
(g) dividing said second averaged scalar function of step (f) by said first averaged scalar function of step (c) and time-integrating the quotient to output said Rank Filtered variable.

5 more elements

Dependencies are inferred from the claim text.

Method and apparatus for analysis of variables

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Method and apparatus for analysis of variables

Life of this patent

Abstract

Claims55