Signals and Systems

Description

Introduces students to the analysis of signals and dynamic systems. Topics include: differential equation modelling, impulse response and convolution, Laplace transforms, stability, frequency response, Fourier transforms, sampling theory.

Availability

UoN Singapore

  • Trimester 2 - 2015 (Singapore)

Callaghan Campus

  • Semester 2 - 2015

Learning Outcomes

1. Understand the nature of the Fourier Transform of a signal in such a way that they could, without calculation, predict the general nature of a signal in the time domain, via knowledge of the spectrum.

2. Infer the qualitative response of a linear system to any input merely by knowledge of its Laplace Transform transfer function description.

3. Understand the fundamental limitation of continuous time system design in terms of how ideal phase or magnitude performances are disallowed by the restriction of maintaining a real valued and causal impulse response.

4. Calculate appropriate sampling rates for signals by employing the Nyquist Sampling Criterion

5. Interpret the DFT or FFT of a signal in terms of the underlying continuous time sinusoidal frequencies and magnitudes.

Content

  1. Differential equation modelling - a review with emphasis on electrical circuit examples.
  2. Relationship of differential equation models of linear systems to solution via ideas of impulse response and convolution.
  3. State space modelling and its relationship to linear systems modelling via convolution and impulse response. Solution of differential equations in state space form.
  4. Relationship of differential equation models of linear systems to solution via Laplace Transform and the idea of a transfer function. Relationship of transfer function to impulse response.
  5. The idea of stability and instability of linear systems and how it can be inferred from the transfer function description of the linear system.
  6. Frequency response of linear systems and the relationship to Laplace transforms and transfer functions.
  7. The Fourier transform of a signal and its relationship to its Laplace Transform.
  8. Sampling of continuous signals in order to provide discrete time sample streams. This includes coverage of the Nyquist Sampling theorem and the Shannon Reconstruction Theorem.
  9. Inferring the spectrum of an underlying continuous time signal from samples of that signal. This includes discussion of the Discrete Fourier Transform, the Fast Fourier Transform, and the relationship of these transforms to the continuous time Fourier Transform.
  10. MATLAB, programming particular to the study of signals and systems, such as system modelling, frequency response analysis, and spectral analysis.

Assumed Knowledge

MATH1120

Assessment Items

Quiz: Quiz

Report: Assignments

Tutorial / Laboratory Exercises: Lab Exercises

Formal Examination: Formal Examination

Contact Hours

Lecture

Face to Face On Campus 4 hour(s) per Week for Full Term

PSB students enrolled in the part-time evening program at UoN Singapore will receive equivalent instruction delivered in a block mode of 7 teaching weeks.

Tutorial

Face to Face On Campus 2 hour(s) per Week for Full Term