Signals and Systems
Available in 2012
|Callaghan Campus||Semester 2|
|UoN Singapore||Trimester 2, Trimester 3|
Previously offered in 2013, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004
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.
Not to count for credit with the subject PHYS2010
1. Students should be able to intuitively infer the qualitative response of a linear system to any input merely by knowledge of its Laplace Transform transfer function description.
2. Students should have an intuitive understanding of 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.
3. Students should have a thorough understanding of 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. Students should be able calculate appropriate sampling rates for signals by employing the Nyquist Sampling Criterion.
5. Students should be able to interpret the DFT or FFT of a signal in terms of the underlying continuous time sinusoidal frequencies and magnitudes. As well, given specifications of maximum bandwidth and minimum spectral resolution, students should be able to specify sampling periods and observation durations of DFT analysis.
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.
Modes of Delivery
Lecture: for 4 hour(s) per Week for Full Term
Tutorial: for 2 hour(s) per Week for Full Term