Fourier Methods, 5 cr

Tampere University

Description
Completion options

Teaching periods

Course code

MATH.APP.240

Language of instruction

English, Finnish

Academic years

2024–2025, 2025–2026, 2026–2027

Level of study

Basic studies

Grading scale

General scale, 0-5

Persons responsible

Responsible teacher:

Merja Laaksonen, Teacher responsible for the Finnish implementation

Responsible teacher:

Petteri Laakkonen, Teacher responsible for the English implementation

Responsible organisation

Faculty of Information Technology and Communication Sciences 100 %

Coordinating organisation

Computing Sciences Studies 100 %

Core content

Real Fourier series for periodic function and determining its coefficients, even and odd functions as special cases, Gibbs phenomenon.
Complex Fourier series, Parseval's theroem, series as frequency decomposition.
Discrete Fourier transform and its properties.
Fourier transform of non-periodic functions: definition and basic properties, Fourier transform as frequency decomposition.

Complementary knowledge

Dirichlet conditions for fourier series convergence, expanding a function defined on a bounded interval to a periodic function.
Significance of the fast Fourier transform
Dirac delta function, Convolution, Parseval's theorem

Learning outcomes

Prerequisites

Compulsory prerequisites

Further information

Learning material

Equivalences

Kokonaisuudet, joihin opintojakso kuuluu

Completion option 1

This is only in Finnish.

Completion of all options is required.

Participation in teaching

Lectures (Finnish)

07.01.2025 – 23.02.2025

Exam

No scheduled teaching

Completion option 2

This is only in english

Completion of all options is required.

Participation in teaching

Lectures (English)

21.10.2024 – 08.12.2024

Exam

No scheduled teaching