Duality theory of composite sinusoidal modeling and linear prediction

@article{Sagayama1986DualityTO,
  title={Duality theory of composite sinusoidal modeling and linear prediction},
  author={Shigeki Sagayama and Fumitada Itakura},
  journal={ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing},
  year={1986},
  volume={11},
  pages={1261-1264}
}
  • S. Sagayama, F. Itakura
  • Published 7 April 1986
  • Engineering
  • ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing
This paper reveals that an elegant duality exists between Linear Prediction (LPC) and Composite Sinusoidal Modeling (CSM) from the viewpoint of orthogonal polynomial theory. Both LPC and CSM are formulated as orthogonal polynomial theory with variablesz = e^{j\omega}(LPC) andx = \cos\omega(CSM) where the "inner product" is defined by the integral of a pair of functions of frequency ω weighted by the spectral density function of the signal. This viewpoint leads to the duality of LPC and CSM and… 

Figures and Tables from this paper

Inverse unitary eigenproblems and related orthogonal functions
Summary.This paper explores the relationship between certain inverse unitary eigenvalue problems and orthogonal functions. In particular, the inverse eigenvalue problems for unitary Hessenberg
On a Sturm Sequence of Polynomials for Unitary Hessenberg Matrices
TLDR
A unitary analogue of the bisection method for symmetric tridiagonal matrices is presented, motivated by the Cayley transformation, and a sequence of modified unitary submatrices are introduced.
Sinusoidal parameters estimation in speech sinusoidal model
Sinusoidal model is efficient for low bit-rate audio coding. A novel sinusoidal parameters extraction algorithm based on narrow band spectrum is described in this paper to improve sinusoidal
On a general time-varying model for speech signals
  • Yi-Teh Lee, H. Silverman
  • Physics
    ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing
  • 1988
The authors show that the solutions of time-dependent difference equations represent a very general class of time-varying models for speech. Kamen's definition of time-dependent poles is introduced.
Beyond bandlimited sampling of speech spectral envelope imposed by the harmonic structure of voiced sounds
A new spectral envelope estimation procedure is proposed to recover details beyond band limitation imposed by the Shannon’s sampling theory when interpreting periodic excitation of voiced sounds as
Aliasing-free implementation of discrete-time glottal source models and their applications to speech synthesis and F0 extractor evaluation
TLDR
A closed-form representation of anti-aliased L-F model is derived for a LPF function family based on cosine series that provides virtually aliasing-free source signal, which is applicable to speech synthesis and F0 extractor evaluation.
Error bounds in the isometric
TLDR
Error bounds for the eigenvalues computed in the isometric Arnoldi method are derived and an upper bound for the distance between each individual eigenvalue of H k and one of U are given.
On the Perturbation Theory for Unitary Eigenvalue Problems
TLDR
Some aspects of the perturbation theory for eigenvalues of unitary matrices are considered and an inclusion theorem analogous to the Kahan theorem for Hermitian matrices is presented.
...
1
2
...

References

SHOWING 1-5 OF 5 REFERENCES
A composite sinusoidal model applied to spectral analysis of speech
A new technique of speech analysis based on a composite sinusoidal model is proposed. In this model, parameters (frequency and intensity of each sinusoid) are determined such that the lower-order
Speech modelling and the trigonometric moment problem
It is shown that the partial trigonometrie moment problem provides an appropriate unifying framework for some speech modelling techniques like the line spectral pairs and composite sinusoidal wave
On the role of the partial trigonometric moment problem in AR speech modelling
The partial trigonometric moment problem is shown to provide a unifying framework for several speech modelling techniques, such as the classical LPC antoregressive model, the line spectral pairs and
The factorial linear modelling: A Karhumen-Loeve approach to speech analysis
TLDR
A modified linear prediction method based on the Karhumen-Loeve expansion of the correlation matrix of the speech samples, obtained via a new normalization of the parameters, which shows that, due to some important properties of Toeplitz matrices, the poles of the A. R. model lie on the unit circle.
The Retrieval of Harmonics from a Covariance Function
Summary A new method for retrieving harmonics from a covariance function is introduced. The method is based on a theorem of Caratheodory about the trigonometrical moment problem. The relation