Detection, classification, and estimation in the (t, f ) domain

Several studies involving real-life applications have shown that methods for the detection, estimation, and classification of nonstationary signals can be enhanced by utilizing the time-frequency ((t,f)) characteristics of such signals. Such (t,f) formulations are described in this chapter and include (t,f) matched filtering for detection and extraction of (t,f) features for classification. The topic is covered in six sections with appropriate internal cross-referencing to this and other chapters.

The structure of (t,f) methods is suitable for designing and implementing optimal detectors. Several approaches exist, such as decomposition of TFDs into sets of spectrograms (Section 12.1). For both analysis and classification, a successful (t,f) methodology requires matching of TFDs with the structure of the signal. This can be achieved by a matching pursuit algorithm using (t,f) atoms adapted to the analyzed signals (Section 12.2). We can perform system identification by exciting linear systems with a linear FM signal and relating TFDs of the input and output using (t,f) filtering techniques (Section 12.3). Methods for (t,f) signal estimation and detection can be carried out using time-varying Wiener filters (Section 12.4). Then, advanced formulations and methods for (t,f) matched filtering are described and applied to abnormality detection (Section 12.5). Finally, the formulation of (t,f) features for classification (Section 12.6) is derived and applied to a serious medical problem as an illustration of the performance gained.