Signals and Systems

This course covers the fundamental concepts of signals and systems, including the mathematical representation of signals and systems, linear time-invariant (LTI) systems and their responses to input signals, time-domain and frequency-domain analysis, and transform-based methods such as the Fourier, Laplace, and Z-transforms. It provides an introduction to analog and digital signal processing, which is a core component of engineering systems across diverse fields, including telecommunications and wireless communications, audio and speech processing, image and video processing, control systems, biomedical engineering, radar and sonar systems, and power systems.

The course begins with an overview of continuous-time and discrete-time signals, energy and power signals, and fundamental signal operations such as time shifting, scaling, and time reversal. It then introduces LTI systems and their key properties, including linearity, stability, causality, time invariance, and convolution. The course subsequently explores Fourier analysis in depth, covering Fourier series, the Fourier transform, the discrete-time Fourier transform, and the sampling theorem. Additional topics include Laplace and Z-transform analysis, as well as the design and analysis of basic filters, such as low-pass, high-pass, and band-pass filters.

This course introduces the mathematical foundations required to analyse continuous-time and discrete-time signals and systems. Students study Linear Time-Invariant (LTI) systems, convolution, Fourier analysis, Laplace and Z-transforms, and sampling theory while developing the analytical skills needed to understand signal behaviour in both time and frequency domains. The course concludes with the analysis of basic filters and their applications in engineering systems.

By the end of this course, students will be able to:

• Understand the mathematical representation of continuous-time and discrete-time signals and systems.
• Analyse the behaviour and properties of Linear Time-Invariant (LTI) systems.
• Apply convolution techniques for analysing system responses.
• Analyse signals using Fourier series, Fourier transforms, Laplace transforms, and Z-transforms.
• Understand sampling theory and the analysis of basic analog and digital filters.

Upon successful completion of this course, students will be able to:

• Demonstrate mathematical proficiency in analysing signals and systems.
• Apply concepts of signals and systems to analyse engineering problems theoretically.
• Analyse the response of Linear Time-Invariant (LTI) systems to input signals.
• Analyse signals and systems in the time domain using convolution techniques.
• Analyse signals in the frequency domain using Fourier, Laplace, and Z-transform methods.

• Signals and Systems – Alan V. Oppenheim, Alan S. Willsky and S. Hamid Nawab (2nd Edition, Pearson).
• Linear Systems and Signals – B. P. Lathi (3rd Edition, Oxford University Press).

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