Question

Which of the following substitution is done in Bilinear transformations?

(a) s = \(\frac{2}{T}[\frac{1+z^{-1}}{1-z^1}]\)

(b) s = \(\frac{2}{T}[\frac{1+z^{-1}}{1+}]\)

(c) s = \(\frac{2}{T}[\frac{1-z^{-1}}{1+z^{-1}}]\)

(d) None of the mentioned

The question was posed to me in homework.

This interesting question is from Bilinear Transformations topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (c) s = \(\frac{2}{T}[\frac{1-z^{-1}}{1+z^{-1}}]\)

To explain I would say: In bilinear transformation of an analog filter to digital filter, using the trapezoidal rule, the substitution for ‘s’ is given as

s = \(\frac{2}{T}[\frac{1-z^{-1}}{1+z^{-1}}]\).