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Signals and Systems by Smarajit Ghosh

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6.5 z-TRANSFORM OF LEFT-SIDED EXPONENTIAL SEQUENCES

The right-sided exponential sequence can be determined mathematically as

 

image

 

This sequence exists for negative values of n.

Fig. 6.3 shows the plot of this sequence.

 

Plot of x(n)

 

Fig6.3 Plot of x(n)

 

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

 

image

 

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

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