An Introduction to the Mathematics of Linear Predictive Filtering as Applied to Speech Analysis and Synthesis

Abstract

A MINIMUM-MEAN-SQUARED-ERROR TECHNIQUE FOR ESTIMATING THE COEFFICIENTS OF THIS FILTER FROM SPEECH DATA IS PRESENTED. This technique leads to a set of equations for the coefficient estimates which can be solved by a computationally efficient recursive technique known as Levinson's method. The filter derived by the above mentioned technique can be realized by any standard technique; however, a particularly interesting realization is in terms of a digital simulation of a non-uniform acoustic tube. It is shown that any stable all-pole filter can be realized as an acoustic tube and, moreover, that the Levinson recursion produces as a by-product exactly the reflection coefficients needed for such a realization. The report concludes by showing how the classical theory of orthogonal polynomials can be applied to the speech analysis/synthesis problem and used to derive many of the results obtained above by other means.

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Document Details

Document Type
Technical Report
Publication Date
Jul 12, 1973
Accession Number
AD0765176

Entities

People

  • Edward M. Hofstetter

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Autocorrelation
  • Coefficients
  • Equations
  • Filters
  • Filtration
  • Integrals
  • Mathematics
  • Noise
  • Polynomials
  • Reflection
  • Speech Analysis
  • Square Roots
  • Standards
  • Transfer Functions
  • Weighting Functions
  • White Noise

Fields of Study

  • Engineering

Readers

  • Approximation Theory.
  • Linear Algebra
  • Speech Processing/Speech Recognition.