Course Outline

This introductory course on geophysical digital signal processing covers a lot of fundamental mathematical and numerical topics that you will need in your career as a geophysicist or more broadly when playing a quantitative role in the physical sciences.

Module 01 - Introduction

The purpose of this module is to emphasize how fundamental DSP has been to your instructor in his career, and to highlight the key topics that will be investigated in this course.

Module 02 - Terminology of Digital Signal Processing

This short module introduces some key tems used DSP.

Module 03 - Complex Numbers

This module provides a refresher on the manipulation of complex numbers and functions, which are fundamental building blocks for the material developed later on in the course.

Module 04 - Fourier Series

This module starts to build up the Fourier machinary by examining continuous, periodic time series. We calculate Fourier spectra that are a very helpful tool for examining signals in a different light.

Module 05 - 1D Fourier Transforms

In this module we examine both the analytical and numerical properties of the 1D Fourier transform of continuous (non-periodic) time series. We also look at Fourier transform of a number of important analytic signals as well as that of instrument, earthquakes and seismic data.

Module 06 - 2D Fourier Transforms

This module extends the 1D Fourier analysis presented in Module 5 to 2D images. Concepts of 2D spatial filtering are introduced. We investigate the wavenumber structure of 2D magnetic and gravity data sets.

Module 07 - Linear Time Invariant (LTI) systems

This module introduces the concepts of linear time-invariant (LTI) systems, including the operations of convolution, correlation, autocorrelation and deconvolution.

Module 08 - Applications of Singular Value Decompositions (SVD)

This module introduces concepts of SVD and presents some applications involving their denoising capabilities.

Module 09 - Discrete Time Signals

This module introduces a number of important concepts regarding discrete time series including: continuous vs discrete vs digital signals; deterministic vs stochastic signals; and characteristics of LTI systems.

Module 10 - Digital Sampling and Reconstruction

This module explores the key consequences of performing digital sampling (i.e., aliasing), discusses strategies to avoid aliasing, and how to reconstruct analog signals from properly sampled time series.

Module 11 - Discrete Fourier Transform

This module looks at how we can take 1D/2D Fourier transforms that we defined in a continuous fashion in the modules above and looks at how they can be posed in discrete systems.

Module 12 - Windows and Spectrograms

This module looks at how we can go beyond Fourier transforms that span the entire time series to those that provide more information on the "local" frequency information.

Module 13 - Wavelet Transforms

This module extends the module's work on time-frequency analysis by examining 1D and 2D wavelet transformations and their use in denoising and compressions algorithms.

Module 14 - Z Transforms

This module looks at how we can generalize Discrete Fourier Transforms to more generalized and abstract spaces.

Module 15 - Practical Filtering

We finish the course by looking how Z-Transforms can be use to set up FIR and IIR filters that can be used to do a whole bunch of useful things such as lowpass, highpass, bandpass and bandreject filtering of 1D signals.