27. We have studied six methods for approximating an analog filter by an IIR dig

Question

27. We have studied six methods for approximating an analog filter by an IIR digital filter Impulse Invariant, Step Invariant, Finite Difference, Matched-z, Direct Substitution and Bilinear (a) Which method(s) can be done without using any time-domain functions in the process? b) Which method(s) squeeze(s) the entire continuous-time frequency from zero to infinity into the discrete-time radian- frequency range zero to ?. (c) Which two methods are almost the same, differing only by a time-domain delay? d) Which method can design an unstable digital filter while trying to approximate a stable analog filter and, if constrained to only stable designs, restricts the flexibility of the design to only certain types of filters?

Explanation / Answer

A) matched z method does not use any time domain function response. Because it map all poles and zeros of s plane to z plane.

B) impulse invariant method. As in this method the frequency response of discrete time system is the sum of shifted copies of continuous time system 's frequency response.

3) impulse invariant and step invariant. Step invariant provide delay in time domain.

4) direct substitution method. As this method is fact based that roots of equations varies with loop parameters continuously.  

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