Consideration on the Optimum Interpolation and Design of Linear Phase Filterbanks with High Attenuation in Stop Bands

Takuro KIDA; Yuichi KIDA

Consideration on the Optimum Interpolation and Design of Linear Phase Filterbanks with High Attenuation in Stop Bands

Takuro KIDA, Yuichi KIDA

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In the literatures [5] and [10], a systematic discussion is presented with respect to the optimum interpolation of multi-dimensional signals. However, the measures of error in these literatures are defined only in each limited block separately. Further, in these literatures, most of the discussion is limited to theoretical treatment and, for example, realization of higher order linear phase FIR filter bank is not considered. In this paper, we will present the optimum interpolation functions minimizing various measures of approximation error simultaneously. Firstly, we outline necessary formulation for the time-limited interpolation functions ψ_m(t) (m=0,1,. . . ,M-1) realizing the optimum approximation in each limited block separately, where m are the index numbers for analysis filters. Secondly, under some assumptions, we will present analytic or piece-wise analytic interpolation functions φ_m(t) minimizing various measures of approximation error defined at discrete time samples n=0, 1, 2,. . . . In this discussion, φ_m(n) are equal to ψ_m(n) n=0, 1, 2,. . . . Since ψ_m(t) are time-limited, φ_m(n) vanish outside of finite set of n. Hence, in designing discrete filter bank, one can use FIR filters if one wants to realize discrete synthesis filters which impulse responses are φ_m(n). Finally, we will present one-dimensional linear phase M channel FIR filter bank with high attenuation characteristic in each stop band. In this design, we adopt the cosine-sine modulation initially, and then, use the iterative approximation based on the reciprocal property.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.2 pp.275-287

Publication Date: 1998/02/25

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Category: Digital Signal Processing

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Takuro KIDA, Yuichi KIDA, "Consideration on the Optimum Interpolation and Design of Linear Phase Filterbanks with High Attenuation in Stop Bands" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 2, pp. 275-287, February 1998, doi: .
Abstract: In the literatures [5] and [10], a systematic discussion is presented with respect to the optimum interpolation of multi-dimensional signals. However, the measures of error in these literatures are defined only in each limited block separately. Further, in these literatures, most of the discussion is limited to theoretical treatment and, for example, realization of higher order linear phase FIR filter bank is not considered. In this paper, we will present the optimum interpolation functions minimizing various measures of approximation error simultaneously. Firstly, we outline necessary formulation for the time-limited interpolation functions ψ_m(t) (m=0,1,. . . ,M-1) realizing the optimum approximation in each limited block separately, where m are the index numbers for analysis filters. Secondly, under some assumptions, we will present analytic or piece-wise analytic interpolation functions φ_m(t) minimizing various measures of approximation error defined at discrete time samples n=0, 1, 2,. . . . In this discussion, φ_m(n) are equal to ψ_m(n) n=0, 1, 2,. . . . Since ψ_m(t) are time-limited, φ_m(n) vanish outside of finite set of n. Hence, in designing discrete filter bank, one can use FIR filters if one wants to realize discrete synthesis filters which impulse responses are φ_m(n). Finally, we will present one-dimensional linear phase M channel FIR filter bank with high attenuation characteristic in each stop band. In this design, we adopt the cosine-sine modulation initially, and then, use the iterative approximation based on the reciprocal property.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_2_275/_p

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@ARTICLE{e81-a_2_275,
author={Takuro KIDA, Yuichi KIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Consideration on the Optimum Interpolation and Design of Linear Phase Filterbanks with High Attenuation in Stop Bands},
year={1998},
volume={E81-A},
number={2},
pages={275-287},
abstract={In the literatures [5] and [10], a systematic discussion is presented with respect to the optimum interpolation of multi-dimensional signals. However, the measures of error in these literatures are defined only in each limited block separately. Further, in these literatures, most of the discussion is limited to theoretical treatment and, for example, realization of higher order linear phase FIR filter bank is not considered. In this paper, we will present the optimum interpolation functions minimizing various measures of approximation error simultaneously. Firstly, we outline necessary formulation for the time-limited interpolation functions ψ_m(t) (m=0,1,. . . ,M-1) realizing the optimum approximation in each limited block separately, where m are the index numbers for analysis filters. Secondly, under some assumptions, we will present analytic or piece-wise analytic interpolation functions φ_m(t) minimizing various measures of approximation error defined at discrete time samples n=0, 1, 2,. . . . In this discussion, φ_m(n) are equal to ψ_m(n) n=0, 1, 2,. . . . Since ψ_m(t) are time-limited, φ_m(n) vanish outside of finite set of n. Hence, in designing discrete filter bank, one can use FIR filters if one wants to realize discrete synthesis filters which impulse responses are φ_m(n). Finally, we will present one-dimensional linear phase M channel FIR filter bank with high attenuation characteristic in each stop band. In this design, we adopt the cosine-sine modulation initially, and then, use the iterative approximation based on the reciprocal property.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Consideration on the Optimum Interpolation and Design of Linear Phase Filterbanks with High Attenuation in Stop Bands
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 275
EP - 287
AU - Takuro KIDA
AU - Yuichi KIDA
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 1998
AB - In the literatures [5] and [10], a systematic discussion is presented with respect to the optimum interpolation of multi-dimensional signals. However, the measures of error in these literatures are defined only in each limited block separately. Further, in these literatures, most of the discussion is limited to theoretical treatment and, for example, realization of higher order linear phase FIR filter bank is not considered. In this paper, we will present the optimum interpolation functions minimizing various measures of approximation error simultaneously. Firstly, we outline necessary formulation for the time-limited interpolation functions ψ_m(t) (m=0,1,. . . ,M-1) realizing the optimum approximation in each limited block separately, where m are the index numbers for analysis filters. Secondly, under some assumptions, we will present analytic or piece-wise analytic interpolation functions φ_m(t) minimizing various measures of approximation error defined at discrete time samples n=0, 1, 2,. . . . In this discussion, φ_m(n) are equal to ψ_m(n) n=0, 1, 2,. . . . Since ψ_m(t) are time-limited, φ_m(n) vanish outside of finite set of n. Hence, in designing discrete filter bank, one can use FIR filters if one wants to realize discrete synthesis filters which impulse responses are φ_m(n). Finally, we will present one-dimensional linear phase M channel FIR filter bank with high attenuation characteristic in each stop band. In this design, we adopt the cosine-sine modulation initially, and then, use the iterative approximation based on the reciprocal property.
ER -