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CSE 351 – Signals and Systems Homework # 3 solved

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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.