Analysis of split-spectrum algorithms in an automatic detection framework

In this paper we study the problem of automatic detection of ultrasonic echo pulses in a grain noise background considering split-spectrum (SS) algorithms as sub-optimum solutions. First, SS algorithms are reformulated following an algebraic approach which is more appropriate from the perspective of automatic detection. Then, recombination methods will be modified according to the previous reformulation. We will consider some of the popular methods based in the phase observation (Polarity Thresholding and Scaled Polarity Thresholding) and in the order statistics (Minimization, Normalized Minimization and Frequency Multiplication). Different experiments with simulated and real data will support our theoretical analysis, and will show the advantages of the Frequency Multiplication method. Derivation of the formulas of the probability of detection and the probability of false alarm in every detector are included in the paper.

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