PDF versionCourse Leader
Lecturer
Timing and Structure
Lent Term: 7 lectures Weeks 1-3, 2 lectures, week 4, 1 lecture
Aims
The aims of the course are to:
- Introduce the Fourier Transform as an extension of Fourier techniques on periodic functions and to see how the Fourier Transform is applied to real problems
- Introduce discrete Fourier methods and to develop skills in analysing discrete data.
Objectives
As specific objectives, by the end of the course students should be able to:
- develop the ability to discuss and manipulate signals in terms of their frequency content.
- relate properties of signals in the time domain to those in the frequency domain.
- be familiar with the difference in behaviour/properties of continuous signals compared to sampled signals, and the basic rules that apply to the latter.
Content
Introduction and preliminaries
- Motivation for signal analysis. Examples of typical datasets.
- Power and energy
- Revision and extension of delta functions
- Revision of Fourier series
The Fourier Transform (FT)
- Mathematical formulation of the FT
- Interpretation of the FT
- The inverse Fourier transform (IFT)
- Some important Fourier transforms
Properties of the Fourier Transform
- Linearity and scaling
- Time and frequency shifts (modulation)
- Duality, Parseval's Theorem, convolution
- Relationship to Laplace transforms
Sampling Theory
- The sampling theorem and aliasing
- The discrete time Fourier transform
- Signal reconstruction and the Nyquist frequency
The Discrete Fourier Transform
- Derivation of DFT and inverse DFT
- Examples of using the DFT
- The spectrogram
Booklists
Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
Last modified: 26/08/2020 09:25