Signals and Systems

6.5 z-TRANSFORM OF LEFT-SIDED EXPONENTIAL SEQUENCES

The right-sided exponential sequence can be determined mathematically as

 

 

This sequence exists for negative values of n.

Fig. 6.3 shows the plot of this sequence.

 

 

Fig6.3 Plot of x(n)

 

The z-transform of x(n) is given by

 

 

Here x(n) = aⁿ for n ≤ 0 and hence the above equation becomes

 

 

where m = −n.

Expanding the above equation we can write

 

 

X(z) will converge for | a⁻¹