帰納的生成法による多重正弦波の周波数検出アルゴリズム

概要

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The Pronys method is an approximation approach to decomposing a function into sum of exponents, and thus, is applicable to unknown frequencies estimation of signals. The concrete algorithms for estimating pure sine-wave, triple-tone, and quadruple-tone have already been derived and presented. This paper aims at deriving the estimating algorithm for multi-sine signals which consist of unknown sine-waves.The new method of generating algebraic algorithm for detecting unknown frequencies in the signals is derived by mathematical induction. The crux of the generation is depending on the integer matrices induction. A handy method for generating the matrices is shown as well. Algorithms for the triple-tone, quadruple-tone and the higher order tone are generated and verified. As a result, they are shown to be identical with the ordinary algorithms.Subjects on the application of the induced algorithm to practical frequency detection are discussed. The algorithm has both instantaneity in time domain and higher resolution in frequency domain, that is, the signal analysis by the algorithm can be performed without constraint of the uncertainty principle. Iterative solution for algebraic equation is dominant for calculation in the algorithm. Techniques for detecting frequencies in a multi-sine of unknown order are also discussed.
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