- A filter is said to be stable if its impulse response
decays to 0 as goes to infinity.
- Recall, the transfer function is the transform of the impulse
response.
- Consider a causal impulse response of the form
which is a damped complex sinusoid when and is exponentially
increasing when .
- The signal has the transform
where the last step is a closed form representation of a
geometric series and holds for
, which is true
whenever .
``Mus 270a: Introduction to Digital Filters''
by Tamara Smyth,
Department of Music, University of California, San Diego.
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Copyright © 2019-02-25 by Tamara Smyth.
Please email errata, comments, and suggestions to Tamara Smyth<trsmyth@ucsd.edu>