An introduction to the "systems" approach to solving physical problems: generalised functions, the Fourier transform, sampling and the FFT, causality and the Kramers-Kronig relations, noise processes and matched filtering.
|Paper title||Linear Systems and Noise|
|Teaching period||Semester 1 (On campus)|
|Domestic Tuition Fees (NZD)||$704.22|
|International Tuition Fees||Tuition Fees for international students are elsewhere on this website.|
- Limited to
- BSc(Hons), PGDipSci, MSc
- Teaching staff
Textbooks are not required for this paper.
- Graduate Attributes Emphasised
- Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship,
Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
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- Learning Outcomes
After completing this paper students are expected to:
- Have a good understanding of the delta function and generalised functions in general and be able to use the formal definition of generalised functions for doing calculus on generalised functions
- Understand the convolution integral and its relation to the delta function and the superposition principle
- Be familiar with the Fourier transform and its properties and be comfortable finding Fourier transforms using the properties of the Fourier transform and the Fourier transforms for a base set of functions
- Find the Fourier transform of generalised functions from the definition
- Understand sampling and its effects in the Fourier domain and be able to derive the sampling theorem and show the relationship between the discrete and continuous Fourier transforms
- Understand the effect of causality on a system transfer function, the Hilbert transform and the Kramers-Kronig relation
- Be able to solve problems related to the one dimensional propagation of a signal through a dispersive and for the narrow bandwidth approximation derive expressions for the group and phase velocities
- Be introduced to stationary stochastic processes and be able to calculate the effect of a linear system on the power spectrum of a signal
- Be able to use matched filtering to optimally find signals in noise