Bias, Variance, and Threshold Level of the Least Squares Pitch Estimator with Windowed Data

Estimating the pitch of a periodic signal, also referred to as fundamental frequency, plays an important role in many signal processing applications, e.g. [1]–[3] and the references therein. The approximate nonlinear least squares ( ANLS) pitch estimator is of great practical importance since it is asymptotically unbiased and attains the Cram ´er-Rao lower bound (CRLB) for additive white Gaussian noise (AWGN) under certain assumptions. Furthermore, it allows for a low-complex fast Fourier transform (FFT)-based implementation. Similar to other spectral estimators, the ANLS pitch estimator suffers from side lobe interference in the spectrum, especially in presence of interferences or for large amplitude differences of the harmonic signal components. Windowing the data for side lobe suppression can therefore be useful in practice. In this paper we provide an expression for the asymptotic bias and variance of this estimator for windowed data. Furthermore, the influence of windowing on the threshold effect is investigated.