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Detection of Sinusoids Using Statistical Goodness-of-Fit Test

Detection of tonal components from magnitude spectrum is an important initial step in several speech and audio processing applications. In this paper we present an approach for detecting sinusoidal components from the magnitude spectrum using “goodness-of-fit” test. The key idea is to test the null-hypothesis that the region of spectrum under observation is drawn from the magnitude spectrum of an ideal windowed-sinusoid. This hypothesis is tested with a chi-square “goodness-of-fit” test. The outcome of this hypothesis test is a decision about the presence of sinusoid in the observed region of magnitude spectrum. We have evaluated the performance of the proposed approach using synthetically generated samples containing steady and modulated harmonics in clean and noisy conditions.

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