Topic: Electronics Engineering
Auto-correlation of a sinusoid $s(t)=A~sin(\omega t)$ is
- A. $(A^{2}/2)$ sin(\omega\tau)
- B. $(A/2)$ sin(\omega t)
- C. $(A^{2}/2)cos(cor)$
- D. $(A/2)$ cos(\omega\tau)
Answer: C. $(A^{2}/2)cos(cor)$
Explanation: $s(t)=A~sin(\omega t)$
$R_{x}(\tau)=E[x(t+\tau)x(t)] = E[A^{2}sin(\omega t+\omega\tau)sin(\omega t)]$
$= E[\frac{A^{2}}{2}cos(\omega\tau)-\frac{A^{2}}{2}cos(2\omega t+\omega\tau)] = \frac{A^{2}}{2}cos(\omega\tau)$