The Optimum Discrete Approximation of Band-Limited Signals with an Application to Signal Processing on Internet

Yuichi KIDA  Takuro KIDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.8   pp.1592-1607
Publication Date: 1999/08/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
digital signal processing,  optimum interpolation,  filter Banks,  

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In the literature [9], the optimum discrete interpolation of one-dimensional signals is presented which minimizes various measures of approximation error simultaneously. In the discussion, the ratio λ of the weighted norm of the approximation error and that of the corresponding input signal plays an essential role to determine the structure of the set of signals. However, only the upper bound of λ is provided in [9]. In this paper, we will present more exact and systematic discussion of the optimum discrete interpolation of one-dimensional signals which minimizes various measures of approximation error at the same time. In this discussion, we will prove that the exact value of λ is identical with the upper limit, for ω (|ω| π), of the largest eigen value of a matrix including the weighting function W(ω) and the Fourier transforms of the optimum interpolation functions. Further, we will give a sufficient condition for W(ω) under which the ratio λ is equal to one, where the approximation error, if it is interpolated by sinc, is included in the set of band-limited signals defined by W(ω). Finally, as application of the presented approximation, we will propose a direction to interactive signal processing on Internet and a transmultiplexer system included in it. The transmultiplexer system included in this discussion can realize flexible arrangement of sub-bands which is inevitable in realizing the above proposal on interactive signal processing.