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Exercise

Perform the bilinear transform defined above and calculate the coefficients of a first-order digital low shelf filter. Find the pole and zero as a function of $ B_0$ , $ \omega_1$ , and $ T$ . Set $ z = 1$ and verify that you get a gain of $ 1+B_0$ . Set $ z = -1$ and verify that you get a gain of 1 there.


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA