Introduces techniques of digital signal processing for deterministic signals. Covers discrete-time and linear time-invariant systems, difference equation description, the Z-transform, and advanced applications such as FIR filter design.

Students gain a working knowledge of discrete-time signals and systems, using a formalism that is natural to those systems. The paper covers discrete-time, linear time-invariant systems, the impulse response and system function, the frequency response, the Nyquist-Shannon sampling theorem, BIBO stability, difference equation description, the Z-transform and its connection to the discrete Fourier transform, and advanced applications.

Prerequisites:
None

This paper consists of 15 lectures and 6 tutorials. There are 3 assignments.

Assesment:
Final Exam 70%, Assignments 30%

Important information about assessment for ELEC442

Course Coordinator:
Associate Professor Colin Fox

After completing this paper students are expected to have achieved the following major learning objectives:

• Understand the consequences of the sampling theorem.
• Convert between continuous-time and discrete-time signals by using sampling theorem.
• Classify discrete-time signals and linear time-invariant systems using difference equations description.
• Apply the Z–transform to discrete-time signals and systems .
• Perform simple manipulations on Z-transforms, in particular find solutions to some simple systems given by their difference equations or their block diagrams.
• Determine the stability of a linear time-invariant system based on its poles and zeros structure.
• Design elementary infinite impulse response (IIR) and finite impulse response (FIR) filters.
• Construct Matlab functions, using the built-in DSP toolbox, corresponding to FIR filter specifications.

Additional outcomes:

• An overall goal is to provide each student with confidence in their ability to describe linear time-invariant systems and discrete-time signals over the time-domain and over the frequency domain.
• Confidence in interpreting block diagram representation of a linear time-invariant system.

Topics:

• Classification of signals/systems
• Sampled waveforms
• Common waveforms
• Sampling theorem
• Signal reconstruction, Quantisation
• Introductions of the Z-transform
• Consequences of the sampling theorem
• Properties of the Z-transform
• Introduction of the system function
• Analysis of a linear time-invariant system over the z domain
• Manipulating the Z-transforms
• Block-diagram representation of linear time-invariant systems
• Causality and stability
• Introduction of digital filters and the two big classes: IIR and FIR filters
• Interpretation of a typical filter specification
• Four classes of linear phase digital filters
• Filter design by windowing technique