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Proceedings Paper

Design of distributed sub-band networks having the minimum total weighted energy based on the concept of generating function of networks
Author(s): Yuichi Kida; Takuro Kida
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Paper Abstract

We present two topics in this paper. First topic is the optimum running approximation of signals by a FIR filter bank minimizing various worst-case continuous measures of error, simultaneously. As a direct application, we obtain a favorable sub-band multi-input multi-output transmission system that is useful to multi-path sensor network with transmission paths having the minimum transmission power and error of approximation at the same time at each channel independently. We assume that a Fourier transform F(ω) of a signal f(t) is band-limited approximately under a Nyquist frequency but its side-lobes over the Nyquist frequency are small. We introduce a positive low-pass weight function and we define a set of signals Ξ such that a weighted-square-integral of F(ω) by this weight function is bounded by a given positive constant A. Firstly, we consider a finite number of signals densely scattered in the initial set of signals and present one-to-one correspondences between a signal and its running approximation or the error of approximation in a certain small segment in the time domain. Based on this one-to-one correspondence, we show that any continuous worstcase measures of error in any time-limited interval can be expressed by the corresponding measures of error in the small segment in the time axis. Combining this one-to-one correspondence with the optimum approximation proved by Kida, we present a running approximation minimizing various continuous worst-case measures of error and continuous upper-limit of many measures of the approximation formula, at the same time.

Paper Details

Date Published: 3 September 2009
PDF: 12 pages
Proc. SPIE 7444, Mathematics for Signal and Information Processing, 74440B (3 September 2009); doi: 10.1117/12.825790
Show Author Affiliations
Yuichi Kida, Ohu Univ. (Japan)
Takuro Kida, Tokyo Institute of Technology (Japan)
Nihon Univ. (Japan)


Published in SPIE Proceedings Vol. 7444:
Mathematics for Signal and Information Processing
Franklin T. Luk; Mark S. Schmalz; Gerhard X. Ritter; Junior Barrera; Jaakko T. Astola, Editor(s)

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