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The Optimum Approximate Restoration of MultiDimensional Signals Using the Prescribed Analysis or Synthesis Filter Bank
Takuro KIDA Yi ZHOU
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E79A
No.6
pp.845863 Publication Date: 1996/06/25
Online ISSN:
DOI:
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword: digital signal processing, the optimum approximation, interpolation, filter bank, linear phase filter bank,
Full Text: PDF>>
Summary:
We present a systematic theory for the optimum subband 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 R^{n}, 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 cosinemodulated FIR filter banks. It will be shown that favorable linear phase FIR filter banks are easily realized from cosinemodulated FIR filter banks by using reciprocal relation and new transformation called cosinesine modulation in the design of filter banks.

