IEICE TRANSACTIONS on Fundamentals
The Optimum Approximate Restoration of Multi-Dimensional Signals Using the Prescribed Analysis or Synthesis Filter Bank
Summary :
We present a systematic theory for the optimum sub-band interpolation using a given analysis or synthesis filter bank with the prescribed coefficient bit length. Recently, similar treatment is presented by Kida and quantization for decimated sample values is contained partly in this discussion [13]. However, in his previous treatment, measures of error are defined abstractly and no discussion for concrete functional forms of measures of error is provided. Further, in the previous discussion, quantization is neglected in the proof of the reciprocal theorem. In this paper, linear quantization for decimated sample values is included also and, under some conditions, we will present concrete functional forms of worst case measures of error or a pair of upper bound and lower limit of those measures of error in the variable domain. These measures of error are defined in Rn, although the measure of error in the literature [13] is more general but must be defined in each limited block separately. Based on a concrete expression of measure of error, we will present similar reciprocal theorem for a filter bank nevertheless the quantization for the decimated sample values is contained in the discussion. Examples are given for QMF banks and cosine-modulated FIR filter banks. It will be shown that favorable linear phase FIR filter banks are easily realized from cosine-modulated FIR filter banks by using reciprocal relation and new transformation called cosine-sine modulation in the design of filter banks.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.6 pp.845-863
- Publication Date
- 1996/06/25
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- Online ISSN
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- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
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Takuro KIDA, Yi ZHOU, "The Optimum Approximate Restoration of Multi-Dimensional Signals Using the Prescribed Analysis or Synthesis Filter Bank" in IEICE TRANSACTIONS on Fundamentals,
vol. E79-A, no. 6, pp. 845-863, June 1996, doi: .
Abstract: We present a systematic theory for the optimum sub-band interpolation using a given analysis or synthesis filter bank with the prescribed coefficient bit length. Recently, similar treatment is presented by Kida and quantization for decimated sample values is contained partly in this discussion [13]. However, in his previous treatment, measures of error are defined abstractly and no discussion for concrete functional forms of measures of error is provided. Further, in the previous discussion, quantization is neglected in the proof of the reciprocal theorem. In this paper, linear quantization for decimated sample values is included also and, under some conditions, we will present concrete functional forms of worst case measures of error or a pair of upper bound and lower limit of those measures of error in the variable domain. These measures of error are defined in Rn, although the measure of error in the literature [13] is more general but must be defined in each limited block separately. Based on a concrete expression of measure of error, we will present similar reciprocal theorem for a filter bank nevertheless the quantization for the decimated sample values is contained in the discussion. Examples are given for QMF banks and cosine-modulated FIR filter banks. It will be shown that favorable linear phase FIR filter banks are easily realized from cosine-modulated FIR filter banks by using reciprocal relation and new transformation called cosine-sine modulation in the design of filter banks.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_6_845/_p
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@ARTICLE{e79-a_6_845,
author={Takuro KIDA, Yi ZHOU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Optimum Approximate Restoration of Multi-Dimensional Signals Using the Prescribed Analysis or Synthesis Filter Bank},
year={1996},
volume={E79-A},
number={6},
pages={845-863},
abstract={We present a systematic theory for the optimum sub-band interpolation using a given analysis or synthesis filter bank with the prescribed coefficient bit length. Recently, similar treatment is presented by Kida and quantization for decimated sample values is contained partly in this discussion [13]. However, in his previous treatment, measures of error are defined abstractly and no discussion for concrete functional forms of measures of error is provided. Further, in the previous discussion, quantization is neglected in the proof of the reciprocal theorem. In this paper, linear quantization for decimated sample values is included also and, under some conditions, we will present concrete functional forms of worst case measures of error or a pair of upper bound and lower limit of those measures of error in the variable domain. These measures of error are defined in Rn, although the measure of error in the literature [13] is more general but must be defined in each limited block separately. Based on a concrete expression of measure of error, we will present similar reciprocal theorem for a filter bank nevertheless the quantization for the decimated sample values is contained in the discussion. Examples are given for QMF banks and cosine-modulated FIR filter banks. It will be shown that favorable linear phase FIR filter banks are easily realized from cosine-modulated FIR filter banks by using reciprocal relation and new transformation called cosine-sine modulation in the design of filter banks.},
keywords={},
doi={},
ISSN={},
month={June},}
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TY - JOUR
TI - The Optimum Approximate Restoration of Multi-Dimensional Signals Using the Prescribed Analysis or Synthesis Filter Bank
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 845
EP - 863
AU - Takuro KIDA
AU - Yi ZHOU
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1996
AB - We present a systematic theory for the optimum sub-band interpolation using a given analysis or synthesis filter bank with the prescribed coefficient bit length. Recently, similar treatment is presented by Kida and quantization for decimated sample values is contained partly in this discussion [13]. However, in his previous treatment, measures of error are defined abstractly and no discussion for concrete functional forms of measures of error is provided. Further, in the previous discussion, quantization is neglected in the proof of the reciprocal theorem. In this paper, linear quantization for decimated sample values is included also and, under some conditions, we will present concrete functional forms of worst case measures of error or a pair of upper bound and lower limit of those measures of error in the variable domain. These measures of error are defined in Rn, although the measure of error in the literature [13] is more general but must be defined in each limited block separately. Based on a concrete expression of measure of error, we will present similar reciprocal theorem for a filter bank nevertheless the quantization for the decimated sample values is contained in the discussion. Examples are given for QMF banks and cosine-modulated FIR filter banks. It will be shown that favorable linear phase FIR filter banks are easily realized from cosine-modulated FIR filter banks by using reciprocal relation and new transformation called cosine-sine modulation in the design of filter banks.
ER -
English
