Question

What is the z-transform of the following finite duration signal?
x(n)={2,4,5,7,0,1}?
1
a) 2 + 4z + 5z2+723 + 24
b) 2 + 4z + 5z2 + 723 + 25
c)2 + 4z-1 + 5z2 + 72-3 + 2-5
d) 2-2 +47 +5+77-1 + 7.3
c​

Answer 1

Answer:

2z2 + 4z + 5 +7z-1 + z-3

Step-by-step explanation:

We know that, for a given signal x(n) the z-transform is defined as

Substitute the values of n from -2 to 3 and the corresponding signal values in the above formula

We get, X(z) = 2z2 + 4z + 5 +7z-1 + z-3.

Answer 2

We recall the concept of z transform

Z-transform converts a discrete-time signal, into a frequency-domain (z-domain or z-plane) representation.

Given:

$X(n)=${$2,4,5,7,0,1$}

We can write it as

$X(z)=2+4z^{-1}+5 z^{-2}+7z^{-3}+z^{-5}$

Option c) is correct