SSP'05 -- Proceedings

	IEEE/SP 13th workshop on Statistical Signal Processing July, 17-20, 2005 - Bordeaux - France

Information regarding the paper

Title

An Efficient Finite Positivity Test Algorithm for Statistical Signal Processing

Author(s)

Swaminathan Ganesan	Qualcomm Inc.
Issa Panahi	University of Texas at Dallas

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Abstract

A real finite sequence r[0,M] is positive if and only if its Fourier Transform is positive over the entire frequency range [1-4]. Testing positivity of r[0,M] using its Fourier transform or its autocorrelation matrix requires an infinite or very lengthy algorithm. As an alternative, an efficient finite algorithm to test positivity, non-negativity or negativity of the real finite sequence r[0,M] is presented. The need to test the positivity of a real sequence arises in many practical situations. For instance, though theoretically non-negative, practical considerations (or missing data) result in a non-positive spectral estimate, e.g. unbiased autocorrelation lag estimates [6]. The algorithm described in this paper is a finite algorithm based on Sturm’s theorem from the classical theory of equations. Performance analysis of the algorithm is presented together with simulation results for different positive and non-positive test cases.