# Inverse Z-Transform -Methods

Long Division  (or) Power Series ExpansionMethod:-

can be expressed either in positive powers of Z or negative powers of Z.

if the sequence is causal  has negative powers of Z similarly the Non-causal sequence     negative powers of Z.

Let  .

is causal it has ROC    then  can be expressed as

is non-causal it has ROC  then  can be expressed as

Partial fraction Method:-

Let      and

if       ,     is a proper function .

if     ,     is improper function  so convert the improper function to proper function as

.

.

express      into powers of Z  as follows

then divide     by   Z

.

Now  express     into partial fractions using different cases and find out the inverse Z-transform  for the function

.

Convolution Method:-

express    as a product of two functions    and   as follows

then find the inverse Z- transforms of individual functions

by using convolution method find convolution of   and

i.e,

now    is the inverse Z-transform of  .

Cauchy Residue Theorem:-

a function in Z if the derivative    exists on and inside contour C and  has no poles at    then.

.

if    the derivative  of    exists on and has no poles at    then.

.

the values on the right hand side are called Residue’s of the pole  .

if there are n no of poles inside C .     (1 votes, average: 5.00 out of 5) Loading... ## Author: vikramarka

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.

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