An ideal analog integrator is described by the system function A digital integrator wit...

An ideal analog integrator is described by the system function A digital integrator with system function H(z) can be obtained by use of the bilinear transformation. That is,

(a) Write the difference equation for the digital integrator relating the input x(n) to the output y (n).

(b) Roughly sketch the magnitude and phase of the analog integrator.

(c) It is easily verified that the frequency response of the digital integrator is

(d) Compare the magnitude and phase characteristics obtained in parts (b) and (c). How well does the digital integrator match the magnitude and phase characteristics of the analog integrator?

(e) The digital integrator has a pole at z = 1. If you implement this filter on a digital computer, what restrictions might you place on the input signal sequence x(n) to avoid computational difficulties?