Share Email Print

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
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

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)

© SPIE. Terms of Use
Back to Top