Modern methods for signal analysis and its applications

Abstract

One of the objectives of signal processing is to extract features of the data which is considered as the first step toward data analysis. Number of oscillating components, the rate at which it oscillates, starting and ending time of the oscillation, duration of the oscillation, and strength of the oscillation are some of the features that help to make the decision for different problems such as classification, fault analysis, complex systems modeling, pattern recognition, condition monitoring etc. Many signals from natural or man-made dynamical systems are often composed of many different oscillations (or modes), with complex waveforms, time-varying amplitudes and frequencies. They carry valuable information about the originating system and are therefore worthy to conduct careful investigation. In this chapter, we look at signals with several components whose frequency varies with respect to time around a central frequency. We intend to explore various methods such as empirical mode decomposition (EMD), empirical wavelet transform (EWT), variational mode decomposition (VMD), synchrosqueezing transform (SST) for the analysis of signals such as electrocardiogram (ECG), electroencephalogram (EEG), phonocardiogram (PCG), machine vibrations etc. The most important keywords of this chapter are Hilbert transform, analytic signal, amplitude and frequency modulated signal and variational calculus. The code samples use the original authors packages for the methods.