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Properties of Backwards Difference Frequency Mapping

$\displaystyle s \leftarrow \frac{1-z^{-1}}{T}
$

\epsfbox{eps/freqmap.eps}

The continuous and discrete frequency axes are related by

$\displaystyle j\omega_a \leftarrow \frac{1-e^{-j\omega_d T}}{T}
= j\omega_d + {\cal O}(\omega_d^2 T)
$

Thus, accurate results can be expected at low frequencies relative to the sampling rate $ 1/T$.


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Download SMAC03S.pdf
Download SMAC03S_2up.pdf

``Recent Developments in Musical Sound Synthesis Based on a Physical Model'', by Julius O. Smith III, (Stockholm Musical Acoustics Conference (SMAC-03), August 6--9, 2003).
Copyright © 2006-02-19 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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