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Appl. Sci. 2016, 6(10), 306; doi:10.3390/app6100306

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Center for Computer Research in Music and Acoustics (CCRMA), Department of Music, Stanford University, 660 Lomita Drive, Stanford, CA 94305-8180, USA
This paper is an extended version of our paper published in the 41st International Computer Music Conference (ICMC), Denton, TX, USA, 25 September–1 October 2015, entitled “The XQIFFT: Increasing the accuracy of quadratic interpolation of spectral peaks via exponential magnitude spectrum weighting.”.
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Academic Editor: Vesa Valimaki
Received: 16 March 2016 / Accepted: 11 October 2016 / Published: 21 October 2016
(This article belongs to the Special Issue Audio Signal Processing)
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Abstract

The magnitude of the Discrete Fourier Transform (DFT) of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude) of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions. View Full-Text
Keywords: acoustics; discrete Fourier transforms; frequency estimation; interpolation; signal analysis; sinusoidal modeling acoustics; discrete Fourier transforms; frequency estimation; interpolation; signal analysis; sinusoidal modeling
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Werner, K.J.; Germain, F.G. Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks. Appl. Sci. 2016, 6, 306.

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