Real-time fundamental frequency estimation by least-square fitting

The real-time performance of a fundamental frequency estimation algorithm depends not only on its computational eeciency but also on its ability to obtain accurate estimates from short signal segments. Previous frequency-domain algorithms make use of spectral analysis algorithms that require the application of a window function, which cause them to fail when signal segments are short and their fundamental frequencies are low. A new spectral analysis algorithm based on least-square tting, which does not require the application of a window function, is introduced. This algorithm operates by minimizing the square error of tting a sinusoid to the signal segment. Special properties of the shape of the error function allow the spectrum of the signal segment to be deduced from it and the algorithm to be implemented eeciently. The proofs of these properties are given. A fundamental frequency estimation algorithm based on this spectral analysis algorithm is then described. Its computation time is analyzed and we demonstrate its real-time performance by a set of experiments using actual sound data.