1.

What is the z-transform of the first backward difference equation of y(n)?(a) \(\frac{1+z^{-1}}{T}\) Y(z)(b) \(\frac{1-z^{-1}}{T}\) Y(z)(c) \(\frac{1+z^1}{T}\) Y(z)(d) None of the mentionedI got this question in an interview.I need to ask this question from Backward Difference Method in chapter Digital Filters Design of Digital Signal Processing

Answer»

Right option is (b) \(\frac{1-Z^{-1}}{T}\) Y(z)

Explanation: The FIRST backward difference of y(n) is GIVEN by the EQUATION

[y(n)-y(n-1)]/T

Thus the z-transform of the first backward difference of y(n) is given as

\(\frac{1-z^{-1}}{T}\) Y(z).



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