Phase-Based Speech Processing

The following sections are included:

• Contents

The following sections are included:

• Motivation

• The Meaning of Phase

• Dual Microphone Speech Processing, or Why Two Ears Are Better Than One

• The Microphone From the 22nd Century - The Human Ear

• Why Smart Computers Are Hard To Find

• The Bigger Picture

• Book Overview

The following sections are included:

• Continuous and Discrete Time Signals

• Continuous Time Fourier Transform
  • Useful Mathematical Identities

• Sampling

• Spectral Analysis of Discrete Time Signals
  • The Effect of Sampling on the Fourier Transform of a Signal
  • The Reconstruction Theorem
  • The Discrete Time Fourier Transform (DTFT)
  • Sampling in the Frequency Domain
  • The Discrete Fourier Transform (DFT)

• Windowing

• Delaying Discrete Time Signals by Non-Integer Amounts

The following sections are included:

• Introduction

• Background

• The Role of Phase in Speech Enhancement

• The Role of Phase in Speech Recognition
  • The Fundamentals of HMM Based ASR
  • Performance Overview of ASR Systems

• Phase Estimation from Magnitude
  • Signal Estimation from the Modified STFT
  • Signal Estimation from the STFT Magnitude

• Recent Developments in Phase Utilization

• Summary

The following sections are included:

• Anatomy of the Ear
  • External Ear
  • Middle Ear
  • Inner Ear

• Physiology of the Ear
  • Transmission of Sound Through the Middle Ear
  • Physiology of the Cochlea
  • Inner Ear Performs Super Fast Fourier Transform
  • The “Place” Principle
  • Action Potential and Determination of Loudness
  • Detection of the Change in the Loudness and the Power Law
  • Threshold for Hearing and Frequency Range of Hearing

• Hearing in the Central Nervous System
  • Parallel Processing of Sound in the Cerebral Cortex
  • Importance of the Cerebral Cortex in Hearing

• The Importance of Phase in Human Speech Processing

• Experimental Setup

• Experimental Results

• Modeling the Effect of Phase

• Speech Recognition Experiments Incorporating Phase Restoration
  • Experimental Setup
  • Experimental Results

• Conclusions

The following sections are included:

• Introduction
  • Dual Microphone Sound Model
  • Frequency Dependent Nature of Phase Wrapping

• Delay-and-sum Beamforming
  • Two-microphone Sum Beamforming
  • Multi-element Sum Beamforming
  • Steering the Array

• Sound Localization Using a Delay-and-sum Beamformer

• TDOA Based Sound Localization
  • TDOA Estimation

• A Detailed Look at the Phase Error

• The Relationship Between Phase-Error and SNR

• Probabilistic constraints on the SNRs

• Phase-Based Time-Varying Filters

• Beamforming as a Phase-Error Filter

The following sections are included:

• Summary (i.e. things you would have known if you had read the book)

• Directions for Future Research

• Where Does it End?

• Disclaimer

The following sections are included:

• Bibliography