|
Rational discrete system functions.
Considering
the function
when  is
the pole of order 1 { (<
1) is the assumption } , 
is a pole of order 1 (>1)
.
Now considering
the Inverse transform of 
we have ,
as | z | =1
is contained in the ROC and <1,
hence the only possible option for inverse is  .
Similarly for
the function
( since >1and
| z | =1 is contained in the ROC of
the function )
Therefore,
| The contribution of
is a right sided exponentially decaying term (possibly
multiplied by a polynomial in n
if the order of pole >1 ) |
The contribution of
is a left sided exponentially decaying term ( possibly
multipled by a polynomial in n
if the order of the pole >1 ) |
|
|
|
|
αnu[n]
|
-(βnu[-n-1])
|
|
