Question

Find the Z – Transform of n^p.

(a) \(-z\frac{d}{dz}(Z(n^{p-1})) \)

(b) \(z\frac{d}{dz}(Z(n^p)) \)

(c) \(-z\frac{d}{dz}(Z(n^{p+1})) \)

(d) \(z\frac{d}{dz}(Z(n^{p+1})) \)

The question was asked in final exam.

I would like to ask this question from Linear Difference Equations and Z in chapter Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

Correct choice is (a) \(-z\frac{d}{dz}(Z(n^{p-1})) \)

The explanation is: The Z Transform of 1 can be found just by infinite G.P. sum. The Z- Transform can be found by differentiating the Z-Transform of 1 and multiplying by (-z). And the Z-Transform of n^2, can also be found by differentiating the Z-Transform of n and multiplying by (-z). Hence the general form is \(-z\frac{d}{dz}(Z(n^{p-1})) \).