Signals and Systems

6.16 z-TRANSFORM OF aⁿ sin (nω) u(n)

Let x₁(n) = sin (nω)u(n). Now we can write

 

 

The given expression is x(n) = aⁿcos (nω)u(n) = aⁿx₁(n)

 

∴                X(z) = Z[aⁿx₁(n)]

 

Using scaling property, we can write

 

 

Hence, the obtained z-transformation pair is

 

 

Table 6.1 gives the standard z-transform pairs.

 

Table 6.1 Standard z-transform pairs.

 

Example 6.4 Find the z-transform of the following signal with the help of linearity and ...