Question

if Z{f(n)} = F(z) then Z{n f(n)} =​

Answer 1

Concept Introduction:

Z-transform is used for discrete time signals and analysis of the same.

Given Information:

An equation  $Z{f(n)}=F(z)$

To find:

The value of $Z{nf(n)}$

Solution:

According to the problem,

$Z[f(n)]=F(z)$

$f(0)= \lim_{z \to \infty} F(z)$

$Z[f(n)]=summation[f(n)z^-n]$

$f(0)+\frac{f(1)}{z}+\frac{f(2)}{z^{2} }+........$

$\lim_{x \to \infty} Z[f(n)]= \lim_{z \to \infty} [f(0)+\frac{f(1)}{z} +\frac{f(2)}{z^{2} }+....]$

$\lim_{x \to \infty} F(z)=f(0)$

Final Answer:

The value is$\lim_{x \to \infty} F(z)=f(0)$