Multitapering

Multitapering is a method in spectral analysis that improves the estimation of a signal’s power spectrum by using multiple orthogonal window functions, or tapers, instead of a single window. Each taper localizes the data differently in time, reducing spectral leakage caused by finite sample length. The spectra obtained with the different tapers are combined, typically by averaging, to produce a final estimate with lower variance than a single-taper approach.

The most common tapers are discrete prolate spheroidal sequences (DPSS), also known as Slepian tapers. They are designed to concentrate as much energy as possible within a specified bandwidth, defined by the time-bandwidth product NW. For a data record of length N, the number of effectively usable tapers K is approximately 2NW−1. Each taper h_k yields a tapered data sequence, whose Fourier transform provides a spectral estimate S_k(f). The multitaper spectral estimate is formed by averaging these S_k(f) with weights that may be equal or adaptively chosen based on the eigenvalues or the estimated spectrum.

Adaptive multitapering weights can be used to further reduce bias, especially in the presence of colored noise. The method also extends to cross-spectral density and coherence estimation by applying the same tapers and then combining cross-spectra across tapers.

Applications span geophysics, seismology, climatology, and neuroscience (EEG/MEG), where reliable spectral estimates are critical under limited data length or noisy conditions. Practical considerations include choosing the time-bandwidth product NW and the number of tapers K, balancing bias and variance for the specific signal and noise characteristics.