Answer to Question #95928 in Electrical Engineering for Utibe Ettebong

Question #95928
Determine the z-transform of x(n)= 3Cos2wnSinwn
1
Expert's answer
2019-10-07T08:33:05-0400

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


Zn[3cos(2ωn)sin(ωn)](z)=n=anzn= =3i(1+e2ωi)eωiz(z2+e4ωi(z2+1)2e3ωiz2eωiz+1)4(z+eωi)(z+e3ωi)(1+eωiz)(1+e3ωi).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})}.


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