Prof. Stewart Greenhalgh



What should I know?

mathematic basics like complex numbers, polynomials, matrix algebra,...

What will I learn?

You will learn the basic concepts of geophysical signal analysis: signal classification and noise, linear system theory for continuous functions, sampled data and the Z-transform, correlation and spectral analysis, the fast Fourier transform, and digital filtering. The course will emphasise the theoretical aspects, in preparation for later courses on the more practical aspects, especially the courses of the IDEA League Joint Master Programme in Applied Geophysics.



In this chapter we will examine linear versus non-linear systems and analysis methods, look at various means of classifying signals and review some special functions with singularities , such as the Dirac delta function and the Heaviside function.

Linear System Theory for Contiuous Function:

This section of the course is concerned with Fourier and Laplace transforms, transfer function and impulse response of linear systems, and the convolution theorem.

Sampled Data and the Z Transform:

The subject matter covered here is  a mathematcial description of the sampling process, the concept of aliasing, the forward and inverse z transforms of sampled functions and system transfer function for digital signals and wavelets.

Correlation and Spectral Analysis:

This chapter is concerned with auto-correlation and cross correlation functions, their uses and relationship to spectral density functions and how to compute them, along with considerations of windowing and tapering of signals and spectra.

The Fast Fourier Transform:

Here we will look at the forward and inverse discrete Fourier transforms, cover the theory of the Fast Fourier Transform , its applications and practical considerations in using the FFT.

Digital Filters:

This chapter is concerned with analysis and synthesis of digital filters of various types (realizable and non-realizable, non-feedback and recursive filters), their design in terms of zero and pole location in the complex z-plane, how to apply digital filters to a signal, and finally we treat inverse and shaping filters after a  consideration of minimum phase.