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SYSC3501 Communication Theory Assignment #1 Solution Set (Winter 2012), Assignments of Signals and Systems Theory

Carleton UniversitySignals and Systems Theory

Solutions is assignment 3 for SYSC 3501

Typology: Assignments

2019/2020

Uploaded on 07/14/2020

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SYSC3501 Communication Theory
Assignment #1
Solution Set
(Winter 2012)
Problem 1 : Determine the Fourier transform of the signal:
||
5)2000cos(3)( t
etts
There are 2 approaches to answer this question. Both yield equivalent answers.
1st approach:
2nd approach:
Directly from the Fourier Transform Pair table:
Let
s(t) = s1(t) + s2(t)
pf3
pf4
pf5

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SYSC3501 Communication Theory

Assignment

Solution Set

(Winter 201 2 )

Problem 1 : Determine the Fourier transform of the signal:

s ( t ) 3 cos( 2000  t )  5 e | t |

There are 2 approaches to answer this question. Both yield equivalent answers.

1st approach:

2nd approach:

Directly from the Fourier Transform Pair table:

Let s(t) = s 1 (t) + s 2 (t)

where

s 1 ( t ) 3 cos( 2000  t )

Using the property of linearity:

S(f) = S 1 (f) + S 2 (f)

Problem 2 : Determine the complex Fourier coefficients for the following periodic waveform.

t

s (t)

1st approach:

2nd approach:

Directly from the Fourier Transform Pair table:

H(n =

Problem 4 : If w(t) has the Fourier transform:

Find X(f) for the following waveforms:

a) x(t) = w(2t+2) b) x(t) = e-jt^ w(t-1)