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# Vector Processor Method for Waveform-Sampling Rate Change

IP.com Disclosure Number: IPCOM000036887D
Original Publication Date: 1989-Nov-01
Included in the Prior Art Database: 2005-Jan-29
Document File: 3 page(s) / 22K

IBM

## Related People

Bakis, R: AUTHOR [+3]

## Abstract

Disclosed is a technique for using the vector processing facility of a large mainframe to quickly and efficiently alter the sampling rate of a waveform.

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Vector Processor Method for Waveform-Sampling Rate Change

Disclosed is a technique for using the vector processing facility of a large mainframe to quickly and efficiently alter the sampling rate of a waveform.

To change the sampling rate of a waveform by a factor of n/m, one must pad each sample of the waveform with n-1 zeros, low-pass filter the padded waveform with a filter of cutoff frequency 3.14159/n (interpolation), and select every mth point [1] (decimation). When m and n are not small integers, the above technique can result in a substantial amount of computation. Computation can be saved by observing that most of the waveform to be filtered consists of zeroes, but only at the expense of program complexity. This disclosure describes an efficient technique for sampling rate changes that utilizes the 3090 vector processor with minimal program complexity.

Let x denote the signal whose sampling rate is to be changed. Define z as

x(i) if j = ni

z(j) =

0 otherwise

Define y as the interpolated version of x, and h the low-pass filter. Then, y(k) = S z(j)h(k - j)

j

z only contributes to the above convolution for j = n*i. One may then write y(k) = S z(ni)h(k - ni)

i

Let k = 1 * n + p, p < n - 1. Then y(ln + p) = S z(ni)h(ln + p - ni)

i

Define

yp(l) = y(ln + p)

hp(l) = h(ln + p)

Then

yp(l) = S x(i)hp(l - i)

i where we have substituted x for z as per the original definition.

The above equation says that we can produce y from x by dividing h into n filters, using each of these shorter sequences to filter y and then to merge the filtered sequences together. This operation can be done efficiently using the ESSL routine SCON [2] which implements FIR filtering with multiple filters using the vector processor. In particular, by correctly...