Apparatus, methods, and computer program products for reducing the number of computations and number of required stored values for information processing methods

Abstract

Apparatus, methods, and computer program products are provided for generating a second set of equations requiring reduced numbers of computations from a first set of general equations, wherein each general equation defines coefficients in terms of a set of samples and a plurality of functions having respective values. A first set of tokens is initially assigned to the plurality of functions such that every value of the functions that has a different magnitude is assigned a different token, thereby permitting each general equation to be defined by the set of samples and their associated tokens. Each general equation is then evaluated and the samples having the same associated token are grouped together. A second set of tokens is then assigned to represent a plurality of unique combinations of the samples. The second set of equations is then generated based at least on the first and second sets of tokens.

1 . A method of generating a second set of equations requiring reduced numbers of computations from a first set of general equations, wherein each general equation defines a coefficient in terms of a set of samples and a plurality of functions having respective values dependent upon each sample, said method comprising the steps of: 
 assigning a first set of tokens to the plurality of functions such that every value of the plurality of functions having a different magnitude is assigned a different token, thereby permitting each general equation to be defined by the set of samples and their associated tokens;    evaluating each of the general equations as defined by the set of samples and associated tokens and grouping the samples having the same associated token together into separate groups;    assigning a second set of tokens to represent a plurality of unique combinations of the samples; and    generating the second set of equations based on at least the first and second sets of tokens.    
   
   
       2 . A method according to  claim 1  further comprising after said assigning a second set of tokens step the step of assigning an nth set of tokens to represent a plurality of unique combinations of the (n−1)th set of tokens, and wherein said generating step comprises generating the second set of equations based on at least the first through the nth sets of tokens.  
   
   
       3 . A method according to  claim 1  wherein the general equation defines a discrete Fourier transform, and wherein said generating step generates a second set of equations that define a discrete Fourier transform.  
   
   
       4 . A method according to  claim 1  wherein the general equation defines a discrete cosine transform, and wherein said generating step generates a second set of equations that define a discrete cosine transform.  
   
   
       5 . A method according to  claim 1  wherein the general equation defines a function selected from the group consisting of Fourier transform, two-dimensional Fourier transform, cosine transform, two-dimensional cosine transform, Bessel functions, Legendre Polynomials, Tschebysheff Polynomials of First and Second Kind, Jacoby Polynomials, Generalized Laguerre Polynomials, Hermite Polynomials, Bernoulli Polynomials, Euler Polynomials, Matrices used in Quantum Mechanics, Linear Algebra and wavelets, and wherein said generating step generates a second set of equations that define the function.  
   
   
       6 . A method according to  claim 1  wherein the method is developed using universal approximators.  
   
   
       7 . A method according to  claim 1  further comprising the step of using the second set of equations generated in said generating step to determine the coefficients based on a set of samples.  
   
   
       8 . An apparatus for generating a second set of equations requiring reduced numbers of computations from a first set of general equations, wherein each general equation defines a coefficient in terms of a set of samples and a plurality of functions having respective values dependent upon each sample, said apparatus comprising a processor capable of performing the following functions: 
 assigning a first set of tokens to the plurality of functions such that every value of the plurality of functions having a different magnitude is assigned a different token, thereby permitting each general equation to be defined by the set of samples and their associated tokens;    evaluating each of the general equations as defined by the set of samples and associated tokens and grouping the samples having the same associated token together into separate groups;    assigning a second set of tokens to represent a plurality of unique combinations of samples; and    generating the second set of equations based on at least the first and second sets of tokens.    
   
   
       9 . An apparatus according to  claim 8  wherein said processor is further capable of after assigning a second set of tokens, assigning an nth set of tokens to represent a plurality of unique combinations of the (n−1)th set of tokens and generating the second set of equations based on at least the first through the nth sets of tokens.  
   
   
       10 . An apparatus according to  claim 8  wherein the general equation defines a discrete Fourier transform, and wherein said processor is capable of generating a second set of equations that define a discrete Fourier transform.  
   
   
       11 . An apparatus according to  claim 8  wherein the general equation defines a discrete cosine transform, and wherein said processor is capable of generating a second set of equations that define a discrete cosine transform.  
   
   
       12 . An apparatus according to  claim 8  wherein said processor is further capable of using the second set of equations generated in said generating step to determine the coefficients based on a set of samples.  
   
   
       13 . A computer program product for generating a second set of equations requiring reduced numbers of computations from a first set of general equations, wherein each general equation defines a coefficient in terms of a set of samples and a plurality of functions having respective values dependent upon each sample, wherein the computer program product comprises: 
 a computer readable storage medium having computer readable program code means embodied in said medium, said computer-readable program code means comprising:    first computer instruction means for assigning a first set of tokens to the plurality of functions such that every value of the plurality of functions having a different magnitude is assigned a different token, thereby permitting each general equation to be defined by the set of samples and their associated tokens;    second computer instruction means for evaluating each of the general equations as defined by the set of samples and associated tokens and grouping the samples having the same associated token together into separate groups;    third computer instruction means for assigning a second set of tokens to represent a plurality of unique combinations of samples; and    fourth computer instruction means for generating the second set of equations based on at least the first and second sets of tokens.    
   
   
       14 . A computer program product according to  claim 13  comprising after said third computer instruction means, fifth computer instruction means for assigning an nth set of tokens to represent a plurality of unique combinations of the (n−1)th set of tokens, and wherein said fourth computer instruction means generates the second set of equations based on at least the first through the nth sets of tokens.  
   
   
       15 . A computer program product according to  claim 13  wherein the general equation defines a discrete Fourier transform, and wherein said fourth computer instruction means generates a second set of equations that define a discrete Fourier transform.  
   
   
       16 . A computer program product according to  claim 13  wherein the general equation defines a discrete cosine transform, and wherein said fourth computer instruction means generates a second set of equations that define a discrete cosine transform.  
   
   
       17 . A computer program product according to  claim 13  further comprising fifth computer instruction means for using the second set of equations generated in said generating step to determine the coefficients based on a set of samples.  
   
   
       18 .- 23 . (canceled)