A variant of the impulse invariance method is the step invariance method of digital filter synthesis. In this method, for a given Hc(s), we design H(z) in Fig. 8.1b such that its output y[n] is...

A variant of the impulse invariance method is the step invariance method of digital filter synthesis. In this method, for a given Hc(s), we design H(z) in Fig. 8.1b such that its output y[n] is identical to yc(nT ) in Fig. 8.1a for the input xc(t) = u(t).

(a) For the step invariance method, show that

(b) Using the step invariance method, determine H(z) when

(c) Use the step invariance method to synthesize a discrete-time integrator. Compare its magnitude response with that of an ideal integrator.