leID1. Time-frequency analysis: Theory and applications

Time-varying spectra are one of the most primitive sensations we experience, since we are surrounded by light of changing color, by sounds of varying pitch, and by many other phenomena whose periodicities change. The development of the physical and mathematical ideas needed to explain and understand time-varying spectra has evolved into the field now called “time-frequency analysis.” Among the many signals whose frequency content has been shown to vary in time are speech and other animal sounds, biomedical signals (e.g., heart sounds, heart rate, the electroencephalogram (EEG), the electromyogram (EMG), and others), music, radar and sonar signals, and machine vibrations, among others. In this tutorial, we give an overview of time-frequency analysis, with a focus on its applications. We describe how these methods impinge on and clarify issues in biomedical and biological signal analysis, wave propagation, random systems, non-linear systems, and other areas. Of particular interest is the application of time-frequency analysis to pulse propagation in dispersive media. We show that time-frequency considerations lead to new approximation methods for dynamic systems and wave propagation. We describe how to transform wave equations into phase-space, where the resulting equation is often more revealing than the original wave equation. We also discuss the applications to random systems and in particular to the propagation of noise fields.Time-varying spectra are one of the most primitive sensations we experience, since we are surrounded by light of changing color, by sounds of varying pitch, and by many other phenomena whose periodicities change. The development of the physical and mathematical ideas needed to explain and understand time-varying spectra has evolved into the field now called “time-frequency analysis.” Among the many signals whose frequency content has been shown to vary in time are speech and other animal sounds, biomedical signals (e.g., heart sounds, heart rate, the electroencephalogram (EEG), the electromyogram (EMG), and others), music, radar and sonar signals, and machine vibrations, among others. In this tutorial, we give an overview of time-frequency analysis, with a focus on its applications. We describe how these methods impinge on and clarify issues in biomedical and biological signal analysis, wave propagation, random systems, non-linear systems, and other areas. Of particular interest is the application of time...