## Description

1. [40 points] 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. [30 points] 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. [30 points] 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.