Multitaper spectral analysis

In traditional spectral estimation, the data are often “windowed” (multiplied with a bell-shaped function) in order to reduce spectral leakage. In the multitaper method, several different (orthogonal) window functions are applied, and the results combined. The resulting spectrum has low leakage, low variance, and retains information contained in the beginning and end of the time series. In addition, statistical testing can take advantage of the multiple spectral estimates. One possible disadvantage is reduced spectral resolution.

The multitaper method requires evenly spaced data, given in one column.

The implementation in Past is based on the code of Lees & Park (1995). The multitaper spectrum can be compared with a simple periodogram (FFT with a 10% cosine window) and a smoothed periodogram. The number of tapers (NWIN) can be set to 3, 4 or 5, for different tradeoffs between variance reduction and resolution. The “time-bandwidth product” p is fixed at 3.0.

The F test for significance of periodicity follows Lees & Park (1995). The 0.05 and 0.01 significance levels are shown as horizontal lines, based on 2 and 2*NWIN-2 degrees of freedom.

The data are zero-padded to the second lowest power of 2 above the length of the sequence. This is required to reproduce the test results given by Lees & Park (1995).

Reference

Lees, J.M. & J. Park. 1995. Multiple-taper spectral analysis: a stand-alone C-subroutine. Computers & Geosciences 21:199-236.

Published Aug. 31, 2020 9:02 PM - Last modified Aug. 31, 2020 9:02 PM