The XQIFFT: Increasing the Accuracy of Quadratic Interpolation of Spectral Peaks via Exponential Magnitude Spectrum Weighting

In spectral audio, accurate estimation of the frequency and magnitude of spectral peaks is a central task. One particularly attractive method for increasing the interpolation density of a spectrum is both inexpensive and accurate: quadratic interpolation over magnitude spectrum peaks (MQIFFT). Although it is known that using this method on a logarithmicallyweighted magnitude spectrum (LQIFFT) can increase its accuracy, other weighting functions are under-explored. In this paper, we introduce an exponentially-weighted version of the QIFFT: the XQIFFT. The accuracy of each method is estimated experimentally; for estimation of stationary sinusoid parameters, the XQIFFT is much more accurate than other known QIFFT-derived methods. This increased accuracy is not accompanied by an increase in runtime computational cost, but it does require a one-time tuning procedure which chooses the best exponent by brute-force evaluation of a range of candidates. Correction functions (CQIFFT) are know to unbias some of the systematic errors of these methods. We apply similar functions to improve XQIFFT estimation. We informally study noise sensitivity properties of the XQIFFT and CXQIFFT; they are more sensitive to noise than known QIFFT-derived methods, but still perform better across a wide range of noise levels.