Question

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Find the z-transforms of sin n pi/2

Answer 1

Answer:

2y2 - 67,2 33 your correct answer

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. In signal processing, system design and analysis, and control theory, the z-transform is a very useful and significant tool.

Given:

The expression $sin\frac{n \pi}{2}$.

Find:

The Z-transform of the expression.

Solution:

$Z(sin\frac{n \pi}{2} ) = \sum_{n=a}^{\infty} sin\frac{n \pi}{2} z^{-n}\\\\Z(sin\frac{n \pi}{2} ) = 0+1*z^{-1}+0+(-1)*z^{-3}+0+1*z^{-5}+0+(-1)*z^{-7}\\\\Z(sin\frac{n \pi}{2} ) = \frac{1}{z}+ (\frac{-1}{z^{3}}) + \frac{1}{z^5}+ (\frac{-1}{z^{7}})$

$Z(sin\frac{n \pi}{2} ) = \frac{\frac{1}{z}}{1-(\frac{-1}{z^{2}})} \\Z(sin\frac{n \pi}{2} ) = \frac{z}{z^2+1}$

Hence, the Z-transform of $sin\frac{n \pi}{2}$ is $\frac{z}{z^2+1}$.