Method and apparatus for analysis of variables
First Claim
1. A method for analysis of variables operable to transform an input variable into an output variable 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 a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function to produce a second scalar field of said Displacement Variable.
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Abstract
Various components of the present invention are collectively designated as Analysis of Variables Through Analog Representation (AVATAR). It is a method, processes, and apparatus for measurement and analysis of variables of different type and origin. 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 (e.g., if the incoming variables are themselves scalar or vector fields), and/or time (if the variables depend on time). 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. However, this invention significantly extends the scope and applicability of these techniques and enables their analog implementation. The invention also introduces a wide range of signal analysis tools which do not exist, and cannot be defined, in the digital domain. In addition, by the present invention, all existing techniques for statistical processing of data, and for studying probability fluxes, are made applicable to analysis of any variable.
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Citations
81 Claims
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1. A method for analysis of variables operable to transform an input variable into an output variable comprising the following steps:
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(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 a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function to produce a second scalar field of said Displacement Variable. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23)
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24. A method for Rank Normalization of an input variable with respect to a reference variable comprising the following steps:
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(a) applying a Discriminator to a difference of a Displacement Variable and a reference variable producing a first scalar field of said Displacement Variable; (b) filtering said first scalar field of step (a) with a first Averaging Filter operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function to produce a second scalar field of said Displacement Variable; (c) applying a Probe to a difference of said Displacement Variable and an input variable producing a third scalar field of said Displacement Variable; and (d) multiplying said third scalar field of step (c) by said second scalar field of step (b) and integrating the product over the values of said Displacement Variable to output a Rank Normalized variable. - View Dependent Claims (25, 26, 27)
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28. A method for analysis of variables operable to transform an input variable into an output variable comprising the following steps:
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(a) applying a Probe to a difference of a Displacement Variable and a reference variable producing a first scalar field of said Displacement Variable; (b) modulating said first scalar field of step (a) by an input variable producing a modulated first scalar field of said Displacement Variable; (c) filtering said modulated first scalar field of step (b) with a first Averaging Filter to produce a second scalar field of said Displacement Variable where said first Averaging Filter is operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function; and (d) dividing said second scalar field of step (c) by said first scalar field of step (a) where said first scalar field has been first filtered with a second Averaging Filter operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function producing an output variable.
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29. A method for analysis of variables operable to transform an input variable into an output variable comprising the following steps:
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(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 a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function to produce 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 operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function 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 produce an output variable. - View Dependent Claims (30, 31)
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32. A method for analysis of variables operable to transform an input scalar field variable into an output variable comprising the following steps:
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(a) applying a Probe to a difference between a feedback of an output variable and an input variable producing a first scalar function of said output variable; (b) filtering said first scalar function of step (a) with a first Averaging Filter operable to perform time and spatial averaging of said first scalar function producing a first averaged scalar function of said output variable; (c) applying a Discriminator to the difference between the feedback of said output variable and the input variable wherein said Discriminator is a respective discriminator of said Probe producing a second scalar function of said output variable; (d) subtracting said second scalar function of step (c) from a quantile value and filtering the difference with a second Averaging Filter wherein the impulse response of said second Averaging Filter is a first time derivative of the impulse response of said first Averaging Filter producing a second averaged scalar function of said output 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 output variable. - View Dependent Claims (33)
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34. A method for analysis of variables operable to transform an input scalar field variable into an output variable comprising the following steps:
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(a) applying a Probe to a difference between a feedback of an output variable and an input variable producing a first scalar function of said output variable where said first scalar function is modulated by a Modulating Variable; (b) filtering said first scalar function of step (a) with a first Averaging Filter operable to perform time and spatial averaging of said first scalar function producing a first averaged scalar function of said output variable; (c) applying a Discriminator to the difference between the feedback of said output variable and the input variable wherein said Discriminator is a respective discriminator of said Probe producing a second scalar function of said output variable; (d) subtracting said second scalar function of step (c) from a quantile value and filtering the difference with a second Averaging Filter wherein said difference between said quantile value and said second scalar function is modulated by said Modulating Variable and wherein the impulse response of said second Averaging Filter is a first time derivative of the impulse response of said first Averaging Filter producing a second averaged scalar function of said output 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 output variable. - View Dependent Claims (35, 36, 37)
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38. A method for analysis of variables operable to transform an input variable into an output variable comprising the following steps:
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(a) applying a Probe to a difference between a feedback of an output variable and an input variable producing a first scalar function of the output variable; (b) filtering said first scalar function of step (a) with a Time Averaging Filter having an exponentially forgetting impulse response and a first Spatial Averaging Filter operable on the spatial coordinates of the input variable producing a first averaged scalar function of the output variable; (c) applying a Discriminator to the difference between the feedback of the output variable and the input variable wherein said Discriminator is a respective discriminator of said Probe producing a second scalar function of the output variable; (d) filtering the difference between a quantile value and said second scalar function of step (c) with a second Spatial Averaging Filter operable on the spatial coordinates of the input variable producing a second averaged scalar function of the output variable; and (e) dividing said second averaged scalar function of step (d) by said first averaged scalar function of step (b) and by the time constant of the impulse response of said Time Averaging Filter and time-integrating the quotient to produce said output variable.
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39. A method for image analysis operable to transform an input image signal into an output signal comprising the following steps:
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(a) applying a Threshold Filter to a difference of a Displacement Variable and an input image signal 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 a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function to produce a second scalar field of said Displacement Variable. - View Dependent Claims (40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55)
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56. An apparatus for analysis of variables operable to transform an input variable into an output variable comprising:
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a Threshold Filter operable to apply a Threshold Filter to a difference of a Displacement Variable and an input variable producing a first scalar field of said Displacement Variable; and a first Averaging Filter operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function so as to filter said first scalar field to produce a second scalar field of said Displacement Variable. - View Dependent Claims (57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72)
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73. An apparatus for Rank Normalization of an input variable with respect to a reference variable comprising:
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a Discriminator operable to apply a Discriminator to a difference of a Displacement Variable and a reference variable producing a first scalar field of said Displacement Variable; a first Averaging Filter operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function so as to alter said first scalar field to produce a second scalar field of said Displacement Variable; a Probe operable to apply a Probe to a difference of said Displacement Variable and an input variable producing a third scalar field of said Displacement Variable; a multiplier operable to multiply said third scalar field by said second scalar field to produce a product; and an integrator operable to integrate said product over the values of said Displacement Variable to output a Rank Normalized variable. - View Dependent Claims (74, 75, 76)
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77. An apparatus for analysis of variables operable to transform an input variable into an output variable comprising:
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a Probe operable to apply a Probe to a difference of a Displacement Variable and a reference variable producing a first scalar field of said Displacement Variable; a modulator operable to modulate said first scalar field by an input variable producing a modulated first scalar field of said Displacement Variable; a first Averaging Filter operable to alter said modulated first scalar field, said first Averaging Filter operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function so as to produce a second scalar field of said Displacement Variable; a second Averaging Filter operable to alter said first scalar field, said second Averaging Filter operable to perform a function selected from the group consisting of time averaging function, spatial averaging function, and time and spatial averaging function so as to produce an averaged first scalar field; and a divider operable to divide said second scalar field by said averaged first scalar field.
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78. An apparatus for Rank Normalization of an input variable with respect to a reference variable comprising:
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(a) a component operable to determine a measure of central tendency of an Amplitude Density of a reference variable; (b) a component operable to determine a measure of variability of said Amplitude Density of the reference variable; and (c) a Discriminator operable to apply a Discriminator to a difference of said measure of central tendency and the input variable wherein the width parameter of said Discriminator is indicative of said measure of variability. - View Dependent Claims (79)
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80. An apparatus for Rank Normalization of an input variable with respect to a reference variable comprising:
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(a) a component operable to determine a measure of central tendency of a Modulated Threshold Density of a reference variable; (b) a component operable to determine a measure of variability of said Modulated Threshold Density of the reference variable; and (c) a Discriminator operable to apply a Discriminator to a difference of said measure of central tendency and the input variable wherein the width parameter of said Discriminator is indicative of said measure of variability. - View Dependent Claims (81)
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Specification