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.
is causal it has ROC then can be expressed as
is non-causal it has ROC then can be expressed as
Partial fraction Method:-
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
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
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 .