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 mentionedThe question was posed to me in homework.This interesting question is from Bilinear Transformations topic in section Digital Filters Design of Digital Signal Processing

Which of the following substitution is done in Bilinear transformation

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

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