Question

Find the Z-Transform of \(^nC_p\).

(a) (1-z^-1)^n

(b) (1+z^-1)^n

(c) (1-z^-1)^-n

(d) (1+z^-1)^-n

The question was posed to me during a job interview.

The question is from Linear Difference Equations and Z in section Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

The correct option is (b) (1+z^-1)^n

Best explanation: Using the Z-Transform formula, it can be written as

\(Z(^nC_p) = 1+ ^nC_1 z^{-1}+ ^nC_2 z^{-2} + ^nC_3 z^{-3} \)+……… which can be further equated to (1+z^-1)n.