Signals and Systems

6.13 z-TRANSFORM OF CAUSAL COSINE SEQUENCE

The causal cosine sequence is given by

 

x(n) = cos (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 ...