SIGNALS & SYSTEMS
5CCS2SAS

COURSEWORK 2
M. R. Nakhai, Department of Engineering, March
2021
There are 4 Questions, answer 4 questions.
Detailed answers and sketches with accurate and careful
labelling are required.

Submit clearly scanned copies of your written answers by the
deadline of Wednesday 24 March 2021, 11 pm.
1
Question 1:
The impulse response of a discrete-time linear time invariant (LTI)
system is given by
ℎ[] = 2 [
sin(

4 )

] cos(

2
)

a) Plot the discrete-time Fourier transform of ℎ[] over
– < < .
[15 marks]

b) Find the output [] of this system to the input

[] =
1
2


6 +

3 +

2 +
2
3 +
1
2

5
6 −
1
2
−

6 − −

3
− −

2 − −
2
3 −
1
2
−
5
6

[10 marks]



Question 2:
Consider the continuous-time signal

() =
sin(10)

+
sin(20)




a) Draw the Fourier transform of (). [15 marks]

b) Find and draw the Fourier transform of () = () cos(30).

[10 marks]








2
Question 3:
The impulse response ℎ() of a linear-time invariant (LTI) system and a
signal () are given as:

ℎ() = {
1, − 5 ≤ ≤ 5
0, otherwise



() = {
1, 0 ≤ ≤ 10
0, otherwise



a) Using convolution in time domain find and sketch the output of
this system to the input signal () = ( + 5).
Note: Details and calculations leading to the final result must be
written.
[15 marks]

b) Find and sketch the output of this LTI system to the input ().
[5 marks]

c) Is this system causal? Why?
[5 marks]



Question 4:
In a causal discrete-time linear-time invariant system the relation
between the input [] and the output [] is given by the following
difference equation:
[] −
1
4
[ − 1] = []

Find the Fourier series representation of the output [] for the input:
[] = cos (

4
) + 2cos (

2
)

[25 marks]











































































































































































































































































































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