Question

Determine the z-transform of the signal \[ x(n)=a^n(\sin\omega_0 n)u(n) \]

• A. \[ \frac{az^{-1}\cos\omega_0} {1-2az^{-1}\sin\omega_0-a^2z^{-2}} ,\quad |z|>|a| \]
• B. \[ \frac{az^{-1}\cos\omega_0} {1+2az^{-1}\cos\omega_0-a^2z^{-2}} ,\quad |z|<|a| \]
• C. \[ \frac{az^{-1}\sin\omega_0} {1-2az^{-1}\cos\omega_0+a^2z^{-2}} ,\quad |z|>|a| \]
• D. \[ \frac{az^{-1}\sin\omega_0} {1-2az^{-1}\cos\omega_0-a^2z^{-2}} ,\quad |z|<|a| \]

Hint:

Memorize the standard z-transform pairs of \[ a^n\cos(\omega_0 n)u(n) \] and \[ a^n\sin(\omega_0 n)u(n). \] They appear frequently in competitive examinations.

Answer 1

The Correct Option is C