###### Learning Outcomes:

On successful completion of this subject the student will be able to:

1. Explain the mathematical basis for the frequency content of a signal with particular reference to the Fourier series and the Fourier transform.

2. Explain the mathematical basis of the frequency response of a linear, time-invariant system, continuous-time (analog) or discrete-time.

3. Derive mathematical models for and analyse the response of linear, time-invariant systems, continuous-time (analog) or discrete-time.

4. Effectively solve linear, constant coefficient ordinary differential and difference equations.

5. Effectively employ MATLAB, Python or both in the analysis of signals and systems.

###### Indicative Module Content:

The topics outlined in the content will be complemented with examples. Computer-based simulations and experiments will complement the learning.

Lec. 0: Background Mathematics: calculus and algebra of complex numbers.

Lec. 1 – Lec. 3: Introduction, linearisation and motivation.

Lec. 4: Introduction to frequency response and partial sample report.

Lec. 5: Linear, Time-invariant Systems.

Lec. 6: Dirac Delta function, Convolution Integral and Impulse Response.

Lec. 7: Definition of Laplace Transform.

Lec. 8 – Lec. 13: Laplace Transform and solution of linear, constant coefficient ordinary differential equations.

Lec. 14: Laplace Transform and Frequency Response.

Lec. 15 – Lec. 17: Fourier Series.

Lec. 18 – Lec. 19: Fourier Series and Numerical Fourier Series.

Lec. 20: Fourier Analysis.

Lec. 21: Fourier Transform.

Lec. 22: Numerical Fourier Transform

Lec. 23 : Discrete-time Linear, Time-invariant Systems.

Lec. 24 – Lec. 25: Z-Transform.

Lec. 26: Discrete-time Fourier Series.

Lec. 27: Discrete-time Fourier Transform.

Lec. 28: Discrete-time Fourier Analysis.

Week 1: Practical Computer Laboratory: introduction to MATLAB/Python

Week 2: Practical Computer Laboratory: specialised MATLAB/Python for Signals and Systems

Week 5: Practical Computer Laboratory: Laplace Transform

Week 8: Practical Computer Laboratory: Fourier Theory

Week 11: Practical Computer Laboratory: Discrete-time systems