Topic: Electronics Engineering
Consider a low pass random process with a white noise power spectral density $S_{x}(\omega)=N/2$ where $-2\pi B\le\omega\le2\pi B$ elsewhere $=0$. The auto-correlation function $R_{x}(\tau)$ is
- A. $2NB sinc(2\pi B\tau)$
- B. $\pi NBsinc(2\pi B\tau)$
- C. $NBsinc(2\pi B\tau)$
- D. None of these
Answer: D. None of these
Explanation: $A_{x}(\tau)=\int_{-\infty}^{+\infty}S_{x}(\omega)e^{j\omega\tau}d\omega = \int_{-2\pi B}^{2\pi B}\frac{N}{2}\cdot e^{i\omega\tau}d\omega = 2\pi BN~sinc(2\pi B\tau)$