A bandlimited signal $x(t)$ with $a^{\prime}$ spectrum $X(f)$ as shown in first figure is processed as shown in second figure is $p(t)$ is a periodic train of impulses as in third figure. The ideal bandpass filter has a passband from $26 \; \mathrm{kHz}$ to $34 \; \mathrm{kHz}$.
- Calculate the Fourier series coefficients $C_{n}$ in the Fourier expansion of $p(t)$ in the form \[p(t)=\sum_{n=-\infty}^{+\infty} C_{n} \text{exp } (j n 2 \pi t / T)\]
- .Find the Fourier Transform of $p(t)$.
- Obtain and sketch the spectrum of $x_{s}(t)$.
- Obtain and sketch the spectrum of $y(t)$.