Cofounder of Flying Frog Consultancy Ltd., Dr Jon Harrop, did his PhD at the University of Cambridge on the "Structural properties of Amorphous Materials" in the department of chemistry. A large part of this work was on the application of time-frequency analysis to the study of the diffraction data of amorphous materials. The complete PhD thesis is now freely available for download as a PDF here.
In the process, Dr Harrop developed a new approach to time-frequency analysis that is based upon the continuous wavelet transform (CWT). This method of analysis is applicable to a wide variety of signals that arise in many different areas of study including biology, physics, finance, engineering, and bioinformatics.
Chapter 2 introduces the method of time-frequency analysis and discusses various different approaches that have been invented over the years. In particular, the beneficial charactistics of the continuous wavelet transform are described in detail, along with the mathematics behind Delprat's time-frequency interpretation of the CWT.
Chapter 3 describes the evolution of a new approach to time-frequency analysis that avoids the problems of the existing methods. The new framework consists of an objective and quantitative measure of the suitability of a wavelet and the derivation of a wavelet that improves upon all others in the general case. The properties of the wavelet are then determined such that a more accurate time-frequency interpretation can be constructed, allowing the continuous wavelet transform with the new wavelet to be used as an accurate quantitative method of time-frequency analysis.
Creating a computational implementation that is fast, accurate and reliable requires considerable attention to detail. The software developed by Dr Harrop for the analysis of diffraction data has since been developed into a commercial Mathematica add-on package for general-purpose signal analysis.