High resolution time-frequency representations
ABSTRACTNon-stationary signals are very common in nature, e.g. sound waves such as human speech, bird song and music. It is usually meaningful to describe a signal in terms of time and frequency. Methods for doing so exist and are well defined. From the time representation it is possible to see the oscillations or waves of the signal and if the signal changes over time. From the frequency representation, obtained from the Fourier transform, the frequency decomposition of the signal can be seen, i.e. which frequencies the signal contains. However the time and frequency representations are not unique for any given signal, i.e. the transformation from time to frequency is not injective. It is therefore, especially for non-stationary and multi-component signals, important to study a joint time-frequency (TF) representation, which shows how the frequency content of the signal varies with time. This is done in the field of time-frequency analysis, which is the topic of this thesis. There exist many different joint TF representations for any given signal and choosing an appropriate representation is most often not straight forward. Unfortunately there exist no optimal TF representation for all signals and finding good representations, especially for multi-component signals is a complex problem. In this thesis, methods for obtaining good TF representations, for two types of non-stationary and multi-component signals, and for extracting meaningful information from these representations, are developed. The two types of signals are long, frequency modulated signals and short, transient signals. Even though the types of signals are very different and require very different TF representations, the aim is to resolve components that are close in time, frequency or both. This requires TF representations with high resolution. For the long, frequency modulated signals, a signal adaptive method, which enables automatic comparison between different TF representations, is proposed. For the short, transient signals, a method which finds the TF centres of transient pulses and counts the number of pulses in a signal is presented. An approach for determining the (time) shape of transient pulses is also given.