The exponential Fourier series for someperiodic signal is given by v(t)=\sum_{n=-\infty}^{\infty} \frac{5|n|}{n^{2}+1} \cdot e^{j 2 \pi 6000 n t} n=-00if this signal is passed through a band-pass filter with cutoff frequencies fa =10000 \mathrm{HZ} \text { and } f_{C U}=20000 \mathrm{HZ} \text {. } Plot the spectrum of the input signal from -20000 HZ to 20000 HZ. b. Write down the equation for the output signal and plot the spectrum of the output signal. c. How much power is contained in the input signal between -20000 HZand 20000 HZ and how much power is contained in the output signal? d. What is the output signal bandwidth?