Linear Prediction of Speech (Communication and Cybernetics)
During the past ten years a new area in speech processing, generally referred to as linear prediction, has evolved. As with all scientific research, results did not always get published in a logical order and terminology was not always con sistent. In mid-1974, we decided to begin an extra hours and weekends project of organizing the literature in linear prediction of speech and developing it into a unified presentation in terms of content and terminology. This effort was completed in November, 1975, with the contents presented herein. If there are two words which describe our goals in this book, they are unifica tion and depth. Considerable effort has been spent on showing the interrelation ships among various linear prediction formulations and solutions, and in develop ing extensions such as acoustic tube models and synthesis filter structures in a unified manner with consistent terminology. Topics are presented in such a manner that derivations and theoretical details are covered, along with Fortran sub routines and practical considerations. Using this approach we hope to have made the material useful for a wide range of backgrounds and interests.
Why Read This Book
You should read this book if you want a rigorous, unified treatment of linear predictive techniques for speech — from theory to practical algorithms — written by a careful synthesizer of the scattered literature. You will learn both the mathematical foundations (AR modelling, autocorrelation/covariance formulations) and the efficient solution methods (Levinson–Durbin, lattice structures) needed to build LPC-based analyzers, coders, and spectral estimators.
Who Will Benefit
Graduate students, researchers, and DSP engineers working on speech/audio processing, speech coding, or spectral estimation who need a deep, mathematically coherent foundation for linear prediction methods.
Level: Advanced — Prerequisites: Undergraduate-level signals and systems, linear algebra (matrix equations, eigenvalues), basic probability/statistics, Fourier transforms, and familiarity with discrete-time filters and z-transform.
Key Takeaways
- Derive and interpret the linear prediction (AR) model for speech and understand its connection to the source-filter model of speech production.
- Formulate and solve the normal equations for LPC using autocorrelation and covariance approaches.
- Implement efficient algorithms such as Levinson–Durbin and lattice (reflection coefficient) structures for real-time LPC computation.
- Apply LPC to spectral analysis and formant estimation, and evaluate model order selection and stability issues.
- Design analysis-by-synthesis systems: perform inverse filtering, residual analysis, and basic LPC-based coding/synthesis.
- Extend linear prediction concepts to time-varying/adaptive contexts and understand their statistical underpinnings for noisy/real-world signals.
Topics Covered
- Introduction and historical perspective on linear prediction
- Mathematical preliminaries: signals, systems, and stochastic processes
- Speech production model and the autoregressive representation
- Formulation of the linear prediction problem: autocorrelation and covariance methods
- Normal equations and properties of the prediction-error filter
- Efficient solution methods: Levinson–Durbin recursion
- Lattice structures and reflection coefficients
- Spectral analysis, formant estimation, and model-order selection
- Inverse filtering, excitation (residual) analysis, and synthesis
- Applications to speech coding and low-bit-rate representations
- Adaptive and time-varying linear prediction methods
- Extensions, practical considerations, and implementation notes
- Appendices: useful transforms, proofs, and numerical considerations
Languages, Platforms & Tools
How It Compares
Compared with Makhoul's 1975 tutorial review and Rabiner & Gold's practical treatments, Markel's book emphasizes unification and mathematical depth across formulations and solution methods rather than a purely tutorial or implementation-focused approach.
