Design of distributed sub-band networks having the minimum total weighted energy based on the concept of generating function of networks

Yuichi Kida; Takuro Kida

doi:10.1117/12.825790

3 September 2009 Design of distributed sub-band networks having the minimum total weighted energy based on the concept of generating function of networks

Yuichi Kida, Takuro Kida

Author Affiliations +

Proceedings Volume 7444, Mathematics for Signal and Information Processing; 74440B (2009) https://doi.org/10.1117/12.825790
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

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.

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Yuichi Kida and Takuro Kida "Design of distributed sub-band networks having the minimum total weighted energy based on the concept of generating function of networks", Proc. SPIE 7444, Mathematics for Signal and Information Processing, 74440B (3 September 2009); https://doi.org/10.1117/12.825790

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KEYWORDS

Sensor networks

Finite impulse response filters

Fourier transforms

Fermium

Electronic filtering

Linear filtering

Optical filters

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