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.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS [0001] The present application claims priority from U.S. provisional patent application Ser. No. 60 / 210,661, entitled: METHODS AND APPARATUS FOR PROCESSING INFORMATION USING SPECIAL CASE PROCESSING, filed on Jun. 9, 2000, the contents of which are incorporated herein by reference.FIELD OF THE INVENTION [0002] The present invention relates generally to the determination of coefficients of a function. More particularly, the methods and computer program products of the present invention relate to reducing the number of computations and values that must be stored in the determination of the coefficients. BACKGROUND OF THE INVENTION [0003] Signal processing is an important function of many electronic systems. In particular, in many electronic systems, data is transmitted in signal form. Further, some electronic systems analyze and monitor the operation of mechanical or chemical systems by observing the characteristics of signals, such as vibration ...

AI Technical Summary

Benefits of technology

[0012] As set forth below, the apparatus, methods, and computer program products of the present invention overcome many of the deficiencies identified with processing signals using functions, such as Fourier Transforms. In particular, the present invention provides methods and computer program products that determine the coefficients of a function representative of an input signal with reduced calculation complexity, such that the coefficients of the function are made available within a decreased time from receipt of the last sample of the signal. The present invention also provides methods and computer program products that reduce the amount calculations that must be performed in order to determine the coefficients of a function, such that less complex hardware designs can be implemented. Specifically, the time for performing computations can be conserved by reusing previously calculated terms so that terms having the same value are calculated fewer than the number of times that the term appears in the original equations; preferably only one calculation for each repeating term having the same value for the entire calculation process. In addition, some embodiments of the present invention also use a reduced number of values to represent the possible mathematical terms of a function.

Problems solved by technology

Although Fourier transforms and the other functions mentioned above are useful in determining characteristics of signals for use in data processing, there are some drawbacks to their use.

Specifically, application of these functions to signals is typically computationally intensive.

This is disadvantageous as it may require the use of specialized processors in order to perform data processing.

Further, and even more importantly, the time required to perform the number of computations using these functions may cause an unacceptable delay for many data processing applications.

As many samples of a signal are typically required to perform an adequate approximation of the signal, the DFT of a signal is typically computational and time intensive.

Although the Butterfly method reduces the number of computations over the more traditional DFT method, it also adds complexity to the Fourier transformation of a signal.

This complexity can require the use of specialized processors and increase time for computation of the Fourier Transform.

Consequently, this method causes latency in the determination of the coefficients of the function, where the time between the arrival of the last sample and the availability of the coefficients is defined as the latency of the system.

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