Chapter 3Phase Estimation Fundamentals

Josef Kulmer and Pejman Mowlaee

Graz University of Technology, Graz, Austria

3.1 Chapter Organization

In this chapter, we will present the fundamentals of phase estimation and its potential with regard to phase-aware speech processing. We start with key examples demonstrating the influence of the applied window function on estimating the phase of one sinusoid. The influence of window functions on phase estimation performance is examined. We extend this example to multiple harmonics in noise. The detailed analysis reveals that the phase estimation error variance is affected by the choice of the analysis window and the frequency distance, as well as the interaction of amplitude and phase between the underlying harmonics. We continue with a detailed presentation of the existing methods for phase estimation available in the literature. Through experiments we demonstrate the usefulness of the phase estimation methods for speech enhancement applications. The chapter concludes with a comparative study, evaluating the effectiveness of the state-of-the-art phase estimation methods in speech enhancement.

3.2 Phase Estimation Fundamentals

3.2.1 Background and Fundamentals

The problem of interest in many signal processing applications, including radar, spectrum estimation, and signal enhancement, is to detect a signal of interest in a noisy observation. The signal of interest is often represented as a sum of sinusoids characterized by their amplitude, ...

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