Question

Transfer function of a causal LSI-filter is: \frac{(1 + 0.2 z^{-1})(1 - 9 z^{-1})}{(1 + 0.81 z^{-1})} H(z) = a) Is the filter stable? b) Find H(z) = H_{min}(z) H_{AP}(z) H_{min}(z) is a minimum phase filter and H_{AP}(z) is an all-pass filter.

          Transfer function of a causal LSI-filter is:
\frac{(1 + 0.2 z^{-1})(1 - 9 z^{-1})}{(1 + 0.81 z^{-1})}
H(z) = 

a) Is the filter stable?
b) Find
H(z) = H_{min}(z) H_{AP}(z)
H_{min}(z) is a minimum phase filter and H_{AP}(z) is an all-pass filter.

Transfer function of a causal LSI-filter is:
((1 + 0.2 z^-1)(1 - 9 z^-1))/((1 + 0.81 z^-1))
H(z) =

a) Is the filter stable?
b) Find
H(z) = Hmin(z) HAP(z)
Hmin(z) is a minimum phase filter and HAP(z) is an all-pass filter.

Added by Jose Carlos J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Darshan Maheshwari

Step 1

The poles are the values of z that make the denominator of the transfer function equal to zero. In this case, the denominator is (1 + 0.81 z^(-1)), so the pole is z = -1/0.81 = -1.2346. Since the pole is outside the unit circle (|z| > 1), the filter is Show more…

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Transfer function of a causal LSI-filter is: (1 + 0.2 z^(-1))(1 - 9 z^(-1))/(1 + 0.81 z^(-1)) H(z) (1 + 0.81 z^(-1)) a) Is the filter stable? b) Find H(z)=Hmin(z) HAp(z) Hmin(z) is a minimum phase filter and HAr(z) is an all-pass filter.