### ASA 124th Meeting New Orleans 1992 October

## 5aMU1. Considerations in the resampling of digital audio signals.

**Julius O. Smith III
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*Ctr. for Comput. Res. in Music and Acoust. CCRMA), Music Dept., Stanford
Univ., Stanford, CA 94305
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The ``digital audio revolution'' has made it possible to routinely analyze
and process acoustic signals entirely in the ``digital domain.'' In this
domain, some conceptually simple operations, such as ``speeding up'' or
``slowing down'' the playback of a sound are no longer so simple; one can no
longer merely change the speed of the tape-drive mechanism. Since the sampling
rate in a D/A converter is usually not variable in a general way, changing the
playback speed requires resampling the stream of numbers that represent the
signal, or sampling rate conversion. Sampling-rate conversion is a special case
of the problem of evaluating a sampled signal at an arbitrary time. The easiest
algorithm, analogous to a sample-and-hold circuit, is to simply take the sample
nearest the desired sample time. A much higher quality algorithm, costing two
additions and one multiply per sample, is to linearly interpolate using the two
samples on either side of the desired sample time. Doing it ``really right''
requires bandlimited interpolation which is implemented by convolving the
signal samples with a sin(x)/x function translated to the desired sample time
and sampled at the signal's sampling instants. The cost is of course an
infinity of multiplies and adds per sample of output, so this is not possible
in practice. This presentation will describe practical algorithms for
sampling-rate conversion and discuss some of the tradeoffs involved.