On fast implementation of harmonic MUSIC for known and unknown model orders

This paper presents a fast implementation of the MUltiple SIgnal Classification (MUSIC) estimation criterion for fundamental frequency estimation of harmonic signals with known or unknown model orders. First, we reformulate the MUSIC estimator such that the MUSIC estimate can be computed directly from the signal subspace or just an arbitrary basis thereof. We also discuss the selection of a subspace tracker based on the known or unknown rank of the signal and noise subspaces. Second, we introduce an implementation of the MUSIC estimator that only involves one FFT for known model orders, and we extend it to the case of unknown model orders. The performance gain in terms of computation times obtained by the efficient implementation is significant which is demonstrated through simulations.