Question

Which of the following is true relation among s-domain and z-domain?

(a) s=(1+z^-1)/T

(b) s=(1+z )/T

(c) s=(1-z^-1)/T

(d) None of the mentioned

This question was posed to me in homework.

I need to ask this question from IIR Filter Design by Approximation of Derivatives topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (c) s=(1-z^-1)/T

To elaborate: The analog differentiator with output dy(t)/dt has the system function H(s)=s, while the digital system that produces the output [y(n)-y(n-1)]/T has the system function H(z) =(1-z^-1)/T. Thus the relation between s-domain and z-domain is given as

s=(1-z^-1)/T.