# ELEC441 Linear Systems and Noise

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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 ELEC441 Electronics 0.0833 10 points First Semester \$666.57 \$2,895.09
Limited to
BSc(Hons), PGDipSci, MSc, MAppSc
Contact

Teaching staff

Textbooks

Textbooks are not required for this paper.

Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
Learning Outcomes

After completing this paper students are expected to:

1. 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.
2. Understand the convolution integral and its relation to the delta function and the superposition principle.
3. 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.
4. Find the Fourier transform of generalised functions from the definition.
5. 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.
6. Understand the effect of causality on a system transfer function, the Hilbert transform and the Kramers-Kronig relation.
7. 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.
8. Be introduced to stationary stochastic processes and be able to calculate the effect of a linear system on the power spectrum of a signal.
9. Be able to use matched filtering to optimally find signals in noise.

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None

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 ELEC441 Electronics 0.0833 10 points First Semester Tuition Fees for 2021 have not yet been set Tuition Fees for international students are elsewhere on this website.
Limited to
BSc(Hons), PGDipSci, MSc, MAppSc
Contact

Teaching staff

Textbooks

Textbooks are not required for this paper.

Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
Learning Outcomes

After completing this paper students are expected to:

1. 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.
2. Understand the convolution integral and its relation to the delta function and the superposition principle.
3. 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.
4. Find the Fourier transform of generalised functions from the definition.
5. 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.
6. Understand the effect of causality on a system transfer function, the Hilbert transform and the Kramers-Kronig relation.
7. 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.
8. Be introduced to stationary stochastic processes and be able to calculate the effect of a linear system on the power spectrum of a signal.
9. Be able to use matched filtering to optimally find signals in noise.

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None