Question

The equation s = \(\frac{2}{T}[\frac{1-z^{-1}}{1+z^{-1}}]\) is a true frequency-to-frequency transformation.

(a) True

(b) False

This question was posed to me by my college professor while I was bunking the class.

My enquiry is from Bilinear Transformations topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (a) True

For explanation: Unlike the backward difference method, the left-half s-plane is now mapped entirely inside the unit circle, |z|=1, rather than to a part of it. Also, the imaginary axis is mapped to the unit circle. Therefore, equation s = \(\frac{2}{T}[\frac{1-z^{-1}}{1+z^{-1}}]\) is a true frequency-to-frequency transformation.