Assignment 1.pdf - ELEC242 CT Signal and Systems Assignment 1 Overview of Signals and Systems Due Date 1 2 Sketch the following signals over the

# Assignment 1.pdf - ELEC242 CT Signal and Systems Assignment...

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ELEC242: CT Signal and Systems Assignment # 1: Overview of Signals and Systems Due Date: May 10, 2016 1. Sketch the following signals over the specified range i) ( ) ). 2 1 ( for 2 8 3 sin ) ( π + π = t t t x ii) ). 2 2 ( for 3 5 ) ( + = t e t t x t iii) ( ) ( ) ). 3 2 ( for 2 sin 4 3 cos ) ( π + π = t t t t x iv) ( ) ). 3 2 ( for 2 exp ) ( = t t t t x 2. Determine if the following signals are periodic. If yes, calculate the fundamental period for the signals. i) ) 2 8 / 5 sin( ) ( π + π = t t x ii) ( ) ( ) 5 3 cos 2 7 6 sin ) ( t t t x + π = iii) ( ) ( ) 6 8 exp 8 3 exp ) ( t t j t x π + π = 3. Show that the average power of the DT periodic signal x [ k ] = A cos( Ω k ) is given by A 2 /2. 4. Determine if the following signals are even, odd, or neither-even-nor-odd. In the later case, evaluate and sketch the even and odd components of the CT signals. i) ( ) ( ) ( ) [ ] t t t x π + π = 4 cos 2 2 sin 2 ii) ( ) ( ) t t t x 3 cos 2 + = iii) ࠵? t = 3࠵? 0 ≤ ࠵? ≤ 2 6 2 ≤ ࠵? ≤ 4 3(−࠵? + 6) 4 ≤ ࠵? ≤ 6 0 elsewhere 5. Determine if the following signals are energy or power signals or neither. Calculate the energy and power

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