Browse Prior Art Database

Linear Interpolation With Delta Slope Minimization for Data Reduction of Waveform Harmonic or Sequency Values

IP.com Disclosure Number: IPCOM000041260D
Original Publication Date: 1987-Nov-01
Included in the Prior Art Database: 2005-Feb-02
Document File: 3 page(s) / 31K

Publishing Venue

IBM

Related People

Curtis, BA: AUTHOR [+2]

Abstract

A technique is described whereby an algorithm is utilized to provide computerized data reduction of waveforms which are represented in their equivalent frequency or sequency spectrum. The algorithm is particularly useful in applications, such as digital music synthesis, which require waveforms to be transformed to frequency domain using Fourier transform or to the sequency domain Walsh transform for later reproduction. The technique described herein provides a means of reducing the amount of storage required to digitally synthesize the original waveform by using linear interpolation with delta slope minimization. An example of a waveform data storage problem can be visualized using a 500 Hz, four-second duration waveform digitized at a 32 KHz sampling rate.

This text was extracted from a PDF file.
At least one non-text object (such as an image or picture) has been suppressed.
This is the abbreviated version, containing approximately 53% of the total text.

Page 1 of 3

Linear Interpolation With Delta Slope Minimization for Data Reduction of Waveform Harmonic or Sequency Values

A technique is described whereby an algorithm is utilized to provide computerized data reduction of waveforms which are represented in their equivalent frequency or sequency spectrum. The algorithm is particularly useful in applications, such as digital music synthesis, which require waveforms to be transformed to frequency domain using Fourier transform or to the sequency domain Walsh transform for later reproduction. The technique described herein provides a means of reducing the amount of storage required to digitally synthesize the original waveform by using linear interpolation with delta slope minimization. An example of a waveform data storage problem can be visualized using a 500 Hz, four-second duration waveform digitized at a 32 KHz sampling rate. After transforming the waveform and generating 32 harmonics (real or imaginary parts) or 64 sequences, the resultant digitizaton requires 128K words, or 256K bytes of data storage. The algorithm used to reduce the amount of storage required is based on the concept that any given harmonic/sequence set can be approximated by line segments. Using the above example, the 500 Hz waveform transformed at a rate of 500 Hz for a four-second duration using a 64-point Fourier or Walsh transformation will yield 128K numbers. Plotting the numbers (amplitude) against time, as shown in Fig. 1, it can be seen that the terms can be approximated by line segments, thereby reducing the amount of data to be stored. The procedure used to implement the algorithm is divided into five steps: 1. Determine all slopes between neighboring line segments. 2. Calculate the delta slope between two neighboring

segments throughout all points. 3. Remove the common point shared by the segments (the minimum delta slope), and then save the end points. 4. Repeat steps 1, 2 and 3, until a...