1. Consider the following periodic signal x(t) shown below.
a. Find the compact trigonometric Fourier series and sketch the amplitude and phase spectra.
b. Find the exponential Fourier series and sketch the corresponding spectra.
2. Consider the following LTIC system:
(D2+3D+2)y(t)=(D+3)f(t),
Find the zero-state response if the input f(t) is e-3tu(t) using Fourier Transform.
3. A TV signal (video and audio) has a bandwidth of 4.5 MHz. This signal is sampled, quantized, and binary-coded to obtain a PCM (pulse code modulated) signal.
a. Determine the sampling rate if the signal is to be sampled at a rate 20% above the Nyquist rate.
b. Determine the number of binary pulses required to encode each sample if the quantization level is 1024.
c. Determine the binary pulse rate (bits/second) of the binary coded signal.
