Multi-Resolution Fourier Analysis Part I: Fundamentals

Multi-Resolution Fourier Analysis Part I: Fundamentals

In the first paper of this series, we propose a multi-resolution theory of Fourier spectral estimates of finite duration signals. It is shown that multi-resolution capability, achieved without further observation, is obtained by constructing multi-resolution signals from the only observed finite duration signal. Achieved resolutions meet bounds of the uncertainty principle (Heisenberg inequalit...

Part I Fundamentals

FUNDAMENTALS Part I of our book lays the physical and conceptual foundations of hydrologic optics, the quantitative study of the interactions of light with the earth's oceans, estuaries, lakes, rivers and other water bodies. Radiative transfer theory is the physical and mathematical framework for hydrologic optics. Chapter 1 begins with a few comments upon the nature of light itself and upon th...

Part I Fundamentals and Concepts

Multi-Resolution Fourier Analysis Part II: Missing Signal Recovery and Observation Results

In this paper, we report application procedures and observed results of multi-resolution Fourier analysis proposed in the first part of this series. Missing signal recovery derived from multi-resolution theory is developed. It is shown that multi-resolution Fourier analysis enhances dramatically performances of Fourier spectra suffering limitations traced to implicit time windowing. Observed fr...

PARALLEL TREE CONTRACTION ' PART I : FUNDAMENTALS Gary

This paper introduces parallel tree contraction: a new bottom-up technique for constructing parallel algorithms on trees. Contraction can be used to solve a wide variety of problems. Two examples included in this article are expression evaluation and subexpression elimination. In this paper we show these applications only require O(1ogn) time and O(n/logn) processors on a Q-sided randomized PRA...