GATE ECE 2002 | Question: 17

Question

A DSBSC modulated signal $s(t)=10 \cos \left(2 \pi \times 10^{b} t\right. +\phi) m\left(t^{-}\right)$is corrupted by an additive white Gaussian noise of power spectral density $10^{-4} \mathrm{~W} /$ Hz. The message power spectral density $S_{max}(f)$ is as shown in the figure and $\phi$ is uniformly distributed over the range 0 to $2 \pi$.

• A. Express the signal autocorrelation function Rss(T) in terms of the message autocorrelation function $R_{\operatorname{max}}(T)$. Clearly state the necessary assumptions.
• B. Delermine the signal power spectral density $\mathrm{S}_{ss}(f)$.
• C. Find the power of the modulated signal and the noise power in the transmission bandwidth.