Usually the mel-frequency cepstral coefficients are estimated either from a periodogram or from a windowed periodogram. We state a general estimator which also includes multitaper estimators. We propose approximations of the variance and bias of the estimate of each coefficient. By using Monte Carlo computations, we demonstrate that the approximations are accurate. Using the proposed formulas, the peak matched multitaper estimator is shown to have low mean square error (squared bias + variance) on speech-like processes. It is also shown to perform slightly better in the NIST 2006 speaker verification task as compared to the Hamming window conventionally used in this context.

The instantaneous frequency (IF) of a non-stationary signal is usually estimated from a time-frequency distribution (TFD). The IF of heart rate variability (HRV) is an important parameter because the power in a frequency band around the IF can be used for the interpretation and analysis of the respiratory rate but also for a more accurate analysis of heart rate (HR) signals. In this study, we compare the performance of five states of the art kernel-based time-frequency distributions (TFDs) in terms of their ability to accurately estimate the IF of HR signals. The selected TFDs include three widely used fixed kernel methods: the modified B distribution, the S-method and the spectrogram; and two adaptive kernel methods: the adaptive optimal kernel TFD and the recently developed adaptive directional TFD. The IF of the respiratory signal, which is usually easier to estimate as the respiratory signal is a mono-component with small amplitude variations with time, is used as a reference to examine the accuracy of the HRV IF estimates. Experimental results indicate that the most reliable estimates are obtained using the adaptive directional TFD in comparison to other commonly used methods such as the adaptive optimal kernel TFD and the modified B distribution.

This paper investigates the time-discrete multitapers that give a mean square error optimal Wigner spectrum estimate for a class of locally stationary processes (LSPs). The accuracy in the estimation of the time-variable Wigner spectrum of the LSP is evaluated and compared with other frequently used methods. The optimal multitapers are also approximated by Hermite functions, which is computationally more efficient, and the errors introduced by this approximation are studied. Additionally, the number of windows included in a multitaper spectrum estimate is often crucial and an investigation of the error caused by limiting this number is made. Finally, the same optimal set of weights can be stored and utilized for different window lengths. As a result, the optimal multitapers are shown to be well approximated by Hermite functions, and a limited number of windows can be used for a mean square error optimal spectrogram estimate.