Signals and Systems

6.14 z-TRANSFORM OF CAUSAL SINE SEQUENCE

The causal sine sequence is given by

 

x(n) = sin (nω)u(n)

 

Using Euler’s identity, we can write cos (nω) as follow:

 

 

The z-transform of above equation is given below.

 

 

Let us put α = e^jω and β = e ^−jω in the above expression, we get

 

 

We know that    

 

 

Substituting the individual z-transform ...