GATE ECE 1999 | Question 19

Question

The power spectral density $\text{(PSD)}$ of a noise process is given by

$\mathrm{S}_{\mathrm{N}}(f)=\left\{\begin{array}{cc}10^{-8}\left(1+\frac{|f|-10^8}{10^8}\right) & f \mid<10^8 \\ 0 & f \mid>10^8\end{array}\right.$

The noise is passed through a unity-gain ideal band pass filter, centered at $50 \; \mathrm{MHz}$ and having a bandwidth of $2 \; \mathrm{MHz}$.

1. Sketch neatly the $\text{PSD}$ of the output noise. process.
2. Determine the output noise power.
3. Using the bandpass representation for the output noise process, sketch the $\text{PSD}$ of the inphase and quadrature noise components, and determine their respective powers.