# Time Series Analysis of Geophysical Data

5 credits

Syllabus, Bachelor's level, 1GE066

Code
1GE066
Education cycle
First cycle
Main field(s) of study and in-depth level
Earth Science G2F, Physics G2F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 27 February 2023
Responsible department
Department of Earth Sciences

## Entry requirements

90 credits including 75 credits in physics and mathematics. Introduction to Scientific Computing, 5 credits, is recommended. Proficiency in English equivalent to the Swedish upper secondary course English 6.

## Learning outcomes

On completion of the course, the student should be able to:

• represent time series with linear functions, polynomials or splines,
• analyse time series for deterministic or statistical behaviour,
• transform time series to spectra with Fourier transformation,
• understand the processes leading to aliasing and spectral leakage and design filters to prevent aliasing and leakage,
• compare the performance of different filters in time and frequency domain.

## Content

Least-squares approximations: linear functions, polynomial functions, splines. Deterministic and statistical time series. Fourier expansion: sampling theorem; finite record length, leakage and windowing. Practical estimation of spectra: discrete and Fast Fourier transform; convolution, covariance and correlation; covariance of power spectral estimates. Time and frequency filtering: convolution and deconvolution; shaping filters; spiking filters; matched filters; prediction filters. Z-transform, wavelets and applications as filters.

## Instruction

Lectures, homework, problem solving and computer exercises.

## Assessment

Take-home examination (3 credits) and homework assignments (2 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.