1.

Which of the following in z-domain is equal to s-domain of second order derivate?(a) \((\frac{1-z^{-1}}{T})^2\)(b) \((\frac{1+z^{-1}}{T})^2\)(c) \((\frac{1+z^{-1}}{T})^{-2}\)(d) None of the mentionedI had been asked this question during a job interview.My question is based upon IIR Filter Design by Approximation of Derivatives topic in portion Digital Filters Design of Digital Signal Processing

Answer»

Correct OPTION is (a) \((\frac{1-z^{-1}}{T})^2\)

To explain I WOULD SAY: We know that for a second order derivative

d^2y(t)/dt^2=[y(n)-2y(n-1)+y(n-2)]/T^2

=>s^2 = \(\frac{1-2z^{-1}+z^{-2}}{T^2} = (\frac{1-z^{-1}}{T})^2\)



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