NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "The Digital Audio Resampling Home Page", by Julius O. Smith III, Copyright © 2016-05-17 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
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Conclusions
A digital resampling method has been described which is convenient forbandlimited interpolation at arbitrary times and for smoothly varyingsampling rates, and which is attractive for hardware implementation. We have presented the case which assumes uniform sampling of the input signal; however, extensions to variable sampling rates and isolated-point evaluation are straightforward.
A quantization error analysis led to the conclusion that for
-bitfilter coefficients, the number of impulse-response samples stored in the filter lookup table should be on the order of
times the number of ``zero-crossings'' in the impulse response, and the number of bits in the interpolation between impulse-response samples should be about
. With these choices, the linear interpolation error and the error due to quantized interpolation factors are each about equal to the coefficient quantization error. A signal resampler designed according to these rules will typically be limited primarily by the lowpass filter design, rather than by quantization effects.
We note that the error analysis presented here is pessimistic in the sense that it assumes worst-case input signal conditions (e.g., a sinusoid at half the sampling rate or white noise). A different type of error analysis is possible by treating the filter coefficients as exact but subject to time jitter. In this approach, the error can be expressed in terms of the input signal Taylor series expansion, and consequently in terms of the input signal bandwidth (or maximum slope). Such an analysis reveals that for most practical signals, the quantization error is considerably less than the levels derived here.