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This unit will cover the following:

Part I: Continuous-time domain

• Mathematical definition of signals
• Energy and spectral density of deterministic signals.
• Correlation and autocorrelation, white noise signals.
• Mathematical definition of a system as an input/output mapping
• Fundamental properties of a system: memoryless, causality, invertibility, stability, linearity and time-invariance
• Convolution operator
• Impulse response of a linear time-invariant (LTI) system
• Fourier transform and its properties
• Signal spectrum, Fourier analysis, PSD, ESD and Wiener-Kitchen relationship, Parseval’s theorem, linear time invariant channels, and equalisation.
• Frequency domain response of an LTI system
• Introduction to analogue filters
• Laplace transform and its properties
• Transfer function of a causal LTI system
• Transients of circuits based on their transfer function 

Part II: Discrete-time domain

• Mathematical definition of signals, elementary signals, and signal properties
• Sampling theorem and pulse shaping theorem.
• Mathematical definition of a system as an input/output mapping
• Fundamental properties of a system: memoryless, causality, invertibility, stability, linearity and time-invariance
• Convolution operator
• Impulse response of a linear time-invariant (LTI) system
• Numerical integration and differentiation
• Fourier transform and its properties
• Frequency domain response of an LTI system
• Introduction to digital filters
• z-transform and its properties
• Transfer function of a causal LTI system 

Part III: Laboratories

The laboratories will focus on Matlab and Simulink

The course unit aims to: Introduce the mathematical tools for analysing signals and systems in the time and frequency domains, and provide a basis for applying these techniques in control and communications engineering.

ILO1: Analyse and develop simple mathematical models for representing signals and systems.

ILO2: Convert time domain models into frequency, Laplace and Z domain models of signals and linear time-invariant systems (continues and discrete) and vice versa.

ILO3: Analyse and calculate system impulse responses and system responses for given inputs of linear time-invariant systems using convolution (time domain), system transfer function (frequency, Laplace and Z domains)

ILO4: Design of analogue and digital filters based on their frequency domain response.

ILO5: Explain the signal and system properties and relationship between continous-time and discrete-time signals and systems. 

ILO6: Analyse the transient of electrical circuits using their transfer function.

ILO7: Apply basic Matlab and Simulink tools for analysis and simulation of continuous and discrete-time systems.

Coursework:

Laboratories (9 hours).

Form of assessment: quiz and report

Exam: feedback is provided after exam board.

Laboratories: feedback is provided two weeks after report submission.

Chaparro, L.F. and Akan, A. (2024). Signals and Systems Using MATLAB. 4th edn. Academic Press. ISBN: 9780443157097. 

Oppenheim, A.V. and Willsky, A.S. (1997). Signals and Systems. 2nd edn. Prentice Hall. ISBN: 9780138147571.

Haykin, S. and Van Veen, B. (2003). Signals and Systems. 2nd edn. Wiley. ISBN: 9780471164746.

Hossain, E. (2022). MATLAB and Simulink Crash Course for Engineers. Springer. ISBN: 9783030897611.