Chapter 2Fundamentals of Phase-Based Signal Processing

Pejman Mowlaee

Graz University of Technology, Graz, Austria

2.1 Chapter Organization

In this chapter, the objective is to provide a compilation of practical concepts and useful analysis tools for phase-based signal processing. The aim is to make spectral phase accessible for researchers working on speech signal processing. Further, this knowledge will be useful in understanding the phase-based signal processing ideas explained in the following chapters. In particular, knowledge from this chapter is required to fully understand the phase-aware processing solutions discussed for the applications in the second part of the book. The major problem in phase signal processing is the phase wrapping in the spectral Fourier analysis. Examples are given in order to visualize the phase wrapping problem and further to demonstrate how phase unwrapping works. To reveal this in more detail, several phase unwrapping methods will be discussed, with a comparative study demonstrating their effectiveness.

Due to the wrapping, the Fourier phase spectrum will not produce an accessible or useful presentation. As analysis tools, the chapter explains several useful representations to display the phase information in a signal. These tools include: group delay (GD), instantaneous frequency (IF), phase variance, harmonic unwrapped phase, phase distortion, baseband phase difference (BPD), and relative phase shift (RPS). Through computer simulations, ...

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