Linear Prediction of Speech
J D. Markel, A. H. Gray, Jr., 1976

Chapter 1. Introduction

1.1 Basic Physical Principles

1.2 Acoustical Waveform Examples

1.3 Speech Analysis and Synthesis Models

1.4 The Linear Prediction Method

1.5 Organization of the Book

Chapter 2. Formulations

2.1 Historical Perspective

2.2 Maximum Likelihood

2.3 Minimum Variance

2.4 Prony's Method

2.5 Correlation Matching

2.6 PARCOR (Partial Correlation)

2.6.1 Inner Products and an Orthogonality Principle

2.6.2 The PARCOR Lattice Structure

Chapter 3. Solutions and Properties

3.1 Introduction

3.2 Vector Spaces and Inner Products

3.2.1 Filter or Polynomial Norms

3.2.2 Properties of Inner Products

3.2.3 Orthogonality Relations

3.3 Solution Algorithms

3.3.1 Correlation Matrix

3.3.2 Initialization

3.3.3 Gram-Schmidt Orthogonalization

3.3.4 Levinson Recursion

3.3.5 Updating Am(z)

3.3.6 A Test Example

3.4 Matrix Forms

Chapter 4. Acoustic Tube Modeling

4.1 Introduction

4.2 Acoustic Tube Derivation

4.2.1 Single Section Derivation

4.2.2 Continuity Conditions

4.2.3 Boundary Conditions

4.3 Relationship between Acoustic Tube and Linear Prediction

4.4 An Algorithm, Examples, and Evaluation

4.4.1 An Algorithm

4.4.2 Examples

4.4.3 Evaluation of the Procedure

4.5 Estimation of Lip Impedance

4.5.1 Lip Impedance Derivation

4.6 Further Topics

4.6.1 Losses in the Acoustic Tube Model

4.6.2 Acoustic Tube Stability

Chapter 5. Speech Synthesis Structures

5.1 Introduction

5.2 Stability

5.2.1 Step-Up Procedure

5.2.2 Step-Down Procedure

5.2.3 Polynomial Properties

5.2.4 A Bound on |Fm(z)|

5.2.5 Necessary and Sufficient Stability Conditions

5.2.6 Application of Results

5.3 Recursive Parameter Evaluation

5.3.1 Inner Product Properties

5.3.2 Equation Summary with Program

5.4 A General Synthesis Structure

5.5 Specific Speech Synthesis Structures

5.5.1 The Direct Form

5.5.2 Two-Multiplier Lattice Model

5.5.3 Kelly-Lochbaum Model

5.5.4 One-Multiplier Models

5.5.5 Normalized Filter Model

5.5.6 A Test Example

Chapter 6. Spectral Analysis

6.1 Introduction

6.2 Spectral Properties

6.2.1 Zero Mean All-Pole Model

6.2.2 Gain Factor for Spectral Matching

6.2.3 Limiting Spectral Match

6.2.4 Non-umiform Spectral Weighting

6.2.5 Minimax Spectral Matching

6.3 A Spectral Flatness Model

6.3.1 A Spectral Flatness Measure

6.3.2 Spectral Flatness Transformations

6.3.3 Numerical Evaluation

6.3.4 Experimental Results

6.3.5 Driving Function Models

6.4 Selective Linear Prediction

6.4.1 Selective Linear Prediction (SLP) Algorithm

6.4.2 A Selective Linear Prediction Program

6.4.3 Computational Considerations

6.5 Considerations in Choice of Analysis Conditions

6.5.1 Choice of Method

6.5.2 Sampling Rates

6.5.3 Order of Filter

6.5.4 Choice of Analysis Interval

6.5.5 Windowing

6.5.6 Pre-emphasis

6.6 Spectral Evaluation Techniques

6.7 Pole Enhancement

Chapter 7. Automatic Formant Trajectory Estimation

7.1 Introduction

7.2 Formant Trajectory Estimation Procedure

7.2.1 Introduction

7.2.2 Raw Data from A(z)

7.2.3 Examples of Raw Data

7.3 Comparison of Raw Data from Linear Prediction and Cepstral Smoothing

7.4 Algorithm 1

7.5 Algorithm 2

7.5.1 Definition of Anchor Points

7.5.2 Processing of Each Voiced Segment

7.5.3 Final Smoothing

7.5.4 Results and Discussion

7.6 Formant Estimation Accuracy

7.6.1 An Example of Synthetic Speech Analysis

7.6.2 An Example of Real Speech Analysis

7.6.3 Influence of Voice Periodicity

Chapter 8. Fundamental Frequency Estimation

8.1 Introduction

8.2 Preprocessing by Spectral Flattening

8.2.1 Analysis of Voiced Speech with Spectral Regularity

8.2.2 Analysis of Voiced Speech with Spectral Irregularities

8.2.3 The STREAK Algorithm

8.3 Correlation Techniques

8.3.1 Autocorrelation Analysis

8.3.2 Modified Autocorrelation Analysis

8.3.3 Filtered Error Signal Autocorrelation Analysis

8.3.4 Practical Considerations

8.3.5 The SIFT Algorithm

Chapter 9. Computation Considerations in Analysis

9.1 Introduction

9.2 Ill-Conditioning

9.2.1 A Measure of Ill-Conditioning

9.2.2 Pre-emphasis of Speech Data

9.2.3 Prefiltering before Sampling

9.3 Implementing Linear Prediction Analysis

9.3.1 Autocorrelation Method

9.3.2 Covariance Method

9.3.3 Computational Comparison

9.4 Finite Word Length Considerations

9.4.1 Finite Word Length Coefficient Computation

9.4.2 Finite Word Length Solution of Equations

9.4.3 Overall Finite Word Length Implementation

Chapter 10. Vocoders

10.1 Introduction

10.2 Techniques

10.2.1 Coefficient Transformations

10.2.2 Encoding and Decoding

10.2.3 Variable Frame Rate Transmission

10.2.4 Excitation and Synthesis Gain Matching

10.2.5 A Linear Prediction Synthesizer Program

10.3 Low Bit Rate Excited Vocoders

10.3.1 Maximum Likelihood and PARCOR Vocoders

10.3.2 Autocorrelation Method Vocoders

10.3.3 Covariance Method Vocoders

10.4 Base-Band Excited Vocoders

Chapter 11. Further Topics

11.1 Speaker Identification and Verification

11.2 Isolated Word Recognition

11.3 Acoustical Detection of Laryngeal Pathology

11.4 Pole-Zero Estimation

11.5 Summary and Future Directions


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