Question

If f(k)=cos alpha k k>=0 ,then Z -transform of {cos alpha k} is given by​

Answer 1

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Ratio of the sides of the two figures (fig 2:fig 1) = 2:1

Ratio of the areas of the two figures (fig 2:fig 1) = 3:1

Ratio of the perimeter of the two figures (fig 2:fig 1) = 2:1

Answer 2

Concept:

A discrete-time signal, which is a sequence of real or complex values, is transformed into a complex frequency-domain (z-domain or z-plane) representation using the Z-transform. It may be thought of as a discrete-time equivalent of the Laplace transform (s-domain). The theory of time-scale calculus investigates this similarity.

Given:

The function $f(k) = cos\alpha k$.

Find:

The Z-transform of the given function.

Solution:

$X(z)=\sum_{n=-\infty}^{\infty} x(n) z^{-n}\\X(z) = \sum_{n=-\infty}^{\infty} cos(\alpha k)z^{-n}$

Hence, the Z-transform of the given is shown.