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**Spectrum-oriented source coding theory.**
*(English)*
Zbl 0658.94007

Author’s abstract: In this paper we present rigorous mathematical foundations of source coding theory with spectral distances at the place of distortion measures. Such a theory is applicable e.g. in speech coding. We prove a new general joint source/channel coding theorem which is of theoretical as well as of practical importance. We also establish correctness of some frequently used conclusions and procedures for which semirigorous “proofs” are known to the authors only, or the rigorous proofs are too scattered in the literature. The theory presented in this paper is oriented not only to recipients of speech signals but to all users concerned about the spectral structure of signals rather than about signals as such.

Reviewer: A.Sgarro

### MSC:

94A29 | Source coding |

94A34 | Rate-distortion theory in information and communication theory |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

### Keywords:

source coding theory with spectral distances; distortion measures; speech coding; channel coding; speech signals; spectral structure of signals
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\textit{O. Šefl} and \textit{I. Vajda}, Kybernetika 23, 458--475 (1987; Zbl 0658.94007)

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### References:

[1] | P. R. Halmos: Measure Theory. Van Nostrand, Princeton 1964. |

[2] | J. Le Roux, G. Geuguen: Fixed point computation of partial correlation coefficients. IEEE Trans. Acoust. Speech Signal Process. ASSP-25 (1977), 257-259. · Zbl 0376.93012 |

[3] | J. D. Markel, A. H. Gray, Jr.: Linear Prediction of Speech. Springer-Verlag, Berlin 1976. · Zbl 0443.94002 |

[4] | L. Prouza: Introduction to the Theory and Applications of Linear Pulse Systems (in Czech). Academia, Praha 1967. |

[5] | I. Vajda: Alphabet-oriented and user-oriented source coding theories. Kybernetika 23 (1987), 5, 388-406. · Zbl 0637.94006 |

[6] | I. Vajda: Theory of Statistical Inference and Information. Reidel Publishing Company · Zbl 0711.62002 |

[7] | J. Kadlec: Moving Probabilistic Identification of Autoregressive Models of Unknown Order by Means of Lattice Structures. Res. Rept. No. 1313, UTIA - CSAV, Prague 1985. |

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