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Fundamentals of Digital Signal Processing

Coursework Assignment 1

1. Consider the sequence

a) What is the Fourier transform of ?

b) Using MATLAB, or your favourite software, plot the Fourier transform of sequences

for and and in the range with the step 

2. The frequency response of an LTI system is

Determine the output of the system to Express your answer in as simple form as you can.

3. What can you say about the periodicity of the output of an LTI system when its input is a periodic sequence of period Prove your answer.

4. When the input to an LTI system is

the output is

a) Find the transfer function of the system, i.e. the z-transform of its impulse response.

b) Find the impulse response of the system.

c) Determine whether the system stable.

5. Consider the system in the figure below with for and the discrete-time system a squarer, i.e. What is the largest value of such that ?