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Consideration on the Optimum Interpolation and Design of Linear Phase Filterbanks with High Attenuation in Stop Bands
Takuro KIDA Yuichi KIDA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E81A
No.2
pp.275287 Publication Date: 1998/02/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword: digital signal processing, the optimum interpolation, filter banks,
Full Text: PDF(985.6KB)>>
Summary:
In the literatures [5] and [10], a systematic discussion is presented with respect to the optimum interpolation of multidimensional 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 timelimited interpolation functions ψ_{m}(t) (m=0,1,. . . ,M1) 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 piecewise 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 timelimited, 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 onedimensional linear phase M channel FIR filter bank with high attenuation characteristic in each stop band. In this design, we adopt the cosinesine modulation initially, and then, use the iterative approximation based on the reciprocal property.

