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Exercise

Perform the bilinear transform defined above and calculate the coefficients of a first-order digital low shelving 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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