Answer to Question #95928 in Electrical Engineering for Utibe Ettebong

Question

Determine the z-transform of x(n)= 3Cos2wnSinwn

Answer 1

The Z-transform of the sequence $[a_n=3\text{cos}(2\omega n)\text{sin}(\omega n)]$ with frequency variable z is

$$Z_n[3\text{cos}(2\omega n)\text{sin}(\omega n)](z)=\sum_{n=-\infty}^\infty a_nz^{-n}=\\ \space\\ =-\frac{3i(-1+e^{2\omega i})e^{\omega i}z(z^2+e^{4\omega i}(z^2+1)-2e^{3\omega i}z-2e^{\omega i}z+1)}{4(-z+e^{\omega i})(-z+e^{3\omega i})(-1+e^{\omega i}z)(-1+e^{3\omega i})}.$$