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Note on the Bilinear Transform

Recall the mapping $ s\to\frac{2}{T}\frac{1-z^{-1}}{1+z^{-1}}$ , which maps real frequencies to real frequencies. In fact, the mapping takes the RHP to the outside of the unit circle and the LHP to the inside. Thus:

\epsfbox{eps/bilinear.eps}


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``Wave Digital Filters'', by Stefan Bilbao and Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-25 by Stefan Bilbao and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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