Browse Prior Art Database

Five-Point Bifore Transform

IP.com Disclosure Number: IPCOM000100482D
Original Publication Date: 1990-Apr-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 3 page(s) / 99K

Publishing Venue

IBM

Related People

Grice, DG: AUTHOR [+4]

Abstract

Disclosed is a method that includes five points from the unit circle for the signal transformation from the time domain to the frequency domain. This is a great enhancement to the Walsh-Hadamard (BiFore transform) that, despite its efficiency (its binary values allow for only additions and subtractions in the butterfly loop), it lacks higher resolution of its frequency spectrum. In the case of a Fourier transform, a large number of multiplications are required. although it is an N*log(N) operation, each loop requires multiplications and either trigonometric calculations or lookup tables. This method would be particularly useful if implemented on low-cost hardware that has no multiplier. it would result in higher spectral resolution than the BIFORE transform but at a much lower cost than computing the FFT.

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Five-Point Bifore Transform

       Disclosed is a method that includes five points from the
unit circle for the signal transformation from the time domain to the
frequency domain.  This is a great enhancement to the Walsh-Hadamard
(BiFore transform) that, despite its efficiency (its binary values
allow for only additions and subtractions in the butterfly loop), it
lacks higher resolution of its frequency spectrum.  In the case of a
Fourier transform, a large number of multiplications are required.
although it is an N*log(N) operation, each loop requires
multiplications and either trigonometric calculations or lookup
tables.  This method would be particularly useful if implemented on
low-cost hardware that has no multiplier.  it would result in higher
spectral resolution than the BIFORE transform but at a much lower
cost than computing the FFT.

      BIFORE analysis resembles Fourier harmonic analysis both in
geometrical and analytical characteristics.  In essence, the Walsh
functions are square waves related directly to the harmonic sinusoid
bases of Fourier analysis. The coefficients used in Fourier analysis
are sequences obtained from increasing multiples of the fundamental
frequency.  In the case of an 8000-Hz sampling rate and a 256-point
input sequence, the fundamental frequency will be 8000/256 or 32 Hz.
Thus, the first sequence would be of frequency 32 Hz.  The second 64
Hz., the third would be 96 Hz., etc.

      In discrete Fourier analysis, these are represented as discrete
points uniformly spaced along the x axis of a SINE wave.  In a BIFORE
transform, these trigonometric values are converted to binary 1's and
0's.  This five-point method will allow for two additional points on
the unit circle, namely the values for the SINE and COSINE for 45
degrees (see the figure).

      This method allows for a much finer frequency spectrum
resolution, but must allow for a few multiplications.  A BIFORE
transform allows for analysis to be performed without multiplication.
 The major advantage in using this method over normal FFT analysis is
in implementation.  The trigonometric values must either be
calculated as they are needed, or preferably looked up from a stored
label.

      With this method, the only multiplication will be for the SIN
and COS of 45 degrees.  This value is roughly equal to .70...