Time-frequency processing: Tutorial on principles and practice

The area of signal processing is founded on a rigorous mathematical exposition that is important for a profound understanding of the subject. The application of these mathematical concepts and techniques is necessitated by the continuous developments in many technologically advanced fields that require the processing of signals to extract important information. Signals convey information to represent measured streams of real-world application-dependent data such as remote-sensing satellite waveforms or seismic waves. For a practical application, a signal can be processed in a multitude of ways to extract specific information that cannot easily be obtained in the time domain. The processing of such signals forms the basis of many applications including analysis, synthesis, filtering, characterization or modeling, modulation, detection, estimation, classification, suppression, cancellation, equalization, coding and synchronization. A classical tool to accommodate this processing is the Fourier transform (FT)* that is widely used to extract frequency information from the time domain signal. However, although successful in a wide range of applications, Fourier theory often possesses intrinsic limitations that depend on the signal to be processed. 1.1.1 Demand for time-frequency processing techniques The purpose of this tutorial is to aid many signal processing practitioners to comprehend, utilize, conjecture and prove useful the theory on extracting information from signals that are nonstationary or time varying (TV). These signals have frequency content and properties that change with time. This class of signals is very common in real-world occurrences and, as such, it is very important to be able to process the signals as accurately as possible. TV signals include the following: the impulse response of a wireless communications channel, radar and sonar acoustic waves, seismic acoustic waves, biomedical signals such as the electrocardiogram (ECG) or neonatal seizures, biological signals such as bat or dolphin echolocation sounds, vocals in speech, notes in music, engine noise, shock waves in fault structures and jamming interference signals.