Question

The Z transform of δ (n − m) is ___________

(a) z^-n

(b) z^-m

(c) \(\frac{1}{z-n}\)

(d) \(\frac{1}{z-m}\)

This question was posed to me in a dream while sleeping

This question is from Discrete Fourier Transform in chapter Fourier Transform of Signals and Systems

Answer 1

Correct answer is (b) z^-m

Explanation: δ (n − m) is a delayed impulse function which is delayed by m units. We know that the Z-transform of a delayed function f (n-m) is (z-m) times the Z-transform of the function f (n). So, the Z transform of δ (n − m) is z^-m.