Distortion Geodesic Lines and Their Application to Spectral Interpolation

Masahide SUGIYAMA

Distortion Geodesic Lines and Their Application to Spectral Interpolation

Masahide SUGIYAMA

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In this paper, we propose a spectral interpolation method using a distortion geodesic line, which is defined as the curve with minimal accumulated distortion. We apply the distortion geodesic line to interpolation of two given spectra (vectors). The first part of this paper describes the definition of the distortion geodesic line. It is shown that a geodesic line is characterized by the Riemannian metric which is introduced as a bilinear form of the second partial derivatives of a given distortion measure. The second part describes an inequality for the WLR measure on several interpolating curves. This inequality guarantees that the accumulated WLR distortion value for any two given spectra, ƒ⁽⁰⁾ and ƒ⁽¹⁾, on the correlation interpolation curve, is always smaller than the direct WLR value d_WLR(ƒ⁽⁰⁾, ƒ⁽¹⁾). This property is easily extended to a category of several distortion measures. The third part describes an application of the distortion geodesic line to spectral interpolation, and numerically shows that the interpolation line on the correlation parameter is the best of several kinds of LPC based parameters.

Publication: IEICE TRANSACTIONS on Information Vol.E74-D No.3 pp.609-614

Publication Date: 1991/03/25

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Type of Manuscript: PAPER

Category: Speech Processing

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Masahide SUGIYAMA

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Masahide SUGIYAMA, "Distortion Geodesic Lines and Their Application to Spectral Interpolation" in IEICE TRANSACTIONS on Information, vol. E74-D, no. 3, pp. 609-614, March 1991, doi: .
Abstract: In this paper, we propose a spectral interpolation method using a distortion geodesic line, which is defined as the curve with minimal accumulated distortion. We apply the distortion geodesic line to interpolation of two given spectra (vectors). The first part of this paper describes the definition of the distortion geodesic line. It is shown that a geodesic line is characterized by the Riemannian metric which is introduced as a bilinear form of the second partial derivatives of a given distortion measure. The second part describes an inequality for the WLR measure on several interpolating curves. This inequality guarantees that the accumulated WLR distortion value for any two given spectra, ƒ⁽⁰⁾ and ƒ⁽¹⁾, on the correlation interpolation curve, is always smaller than the direct WLR value d_WLR(ƒ⁽⁰⁾, ƒ⁽¹⁾). This property is easily extended to a category of several distortion measures. The third part describes an application of the distortion geodesic line to spectral interpolation, and numerically shows that the interpolation line on the correlation parameter is the best of several kinds of LPC based parameters.
URL: https://global.ieice.org/en_transactions/information/10.1587/e74-d_3_609/_p

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@ARTICLE{e74-d_3_609,
author={Masahide SUGIYAMA, },
journal={IEICE TRANSACTIONS on Information},
title={Distortion Geodesic Lines and Their Application to Spectral Interpolation},
year={1991},
volume={E74-D},
number={3},
pages={609-614},
abstract={In this paper, we propose a spectral interpolation method using a distortion geodesic line, which is defined as the curve with minimal accumulated distortion. We apply the distortion geodesic line to interpolation of two given spectra (vectors). The first part of this paper describes the definition of the distortion geodesic line. It is shown that a geodesic line is characterized by the Riemannian metric which is introduced as a bilinear form of the second partial derivatives of a given distortion measure. The second part describes an inequality for the WLR measure on several interpolating curves. This inequality guarantees that the accumulated WLR distortion value for any two given spectra, ƒ⁽⁰⁾ and ƒ⁽¹⁾, on the correlation interpolation curve, is always smaller than the direct WLR value d_WLR(ƒ⁽⁰⁾, ƒ⁽¹⁾). This property is easily extended to a category of several distortion measures. The third part describes an application of the distortion geodesic line to spectral interpolation, and numerically shows that the interpolation line on the correlation parameter is the best of several kinds of LPC based parameters.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - Distortion Geodesic Lines and Their Application to Spectral Interpolation
T2 - IEICE TRANSACTIONS on Information
SP - 609
EP - 614
AU - Masahide SUGIYAMA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E74-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 1991
AB - In this paper, we propose a spectral interpolation method using a distortion geodesic line, which is defined as the curve with minimal accumulated distortion. We apply the distortion geodesic line to interpolation of two given spectra (vectors). The first part of this paper describes the definition of the distortion geodesic line. It is shown that a geodesic line is characterized by the Riemannian metric which is introduced as a bilinear form of the second partial derivatives of a given distortion measure. The second part describes an inequality for the WLR measure on several interpolating curves. This inequality guarantees that the accumulated WLR distortion value for any two given spectra, ƒ⁽⁰⁾ and ƒ⁽¹⁾, on the correlation interpolation curve, is always smaller than the direct WLR value d_WLR(ƒ⁽⁰⁾, ƒ⁽¹⁾). This property is easily extended to a category of several distortion measures. The third part describes an application of the distortion geodesic line to spectral interpolation, and numerically shows that the interpolation line on the correlation parameter is the best of several kinds of LPC based parameters.
ER -