File:Spectra computation.png

Summary

Velocity spectra estimated from a 128-s long segment of observations. The original spectra (black) were estimated using 7 fft blocks, each 32 s long with a 50% overlap and Hanning window applied on each block in the time-domain (21 degrees of freedom). The colored lines are the same spectra but obtained using an alternate spectral averaging strategy. The fft-length was halved to 16 s in red (43 degrees of freedom), while the third example (purple) uses a combination of block and band avegaring. The blocks were the same as the first example (32-s long) but three adjacent frequencies were averaged together in the frequency domain increasing the degrees of freedom to 58. The degrees of freedom and statistical significance were estimated using the methods described in Priestly 1981 (Priestley, M. B. 1981. Spectral analysis and time series: Multi- variate series prediction and control. Academic Press) and section 5.6.8.1 of Emery, W. J., and R. E. Thomson. 2001. Data analysis methods in physical oceanography, 2nd ed. Elsevier Science, which assumes the spectra observations are [math]\displaystyle{ \chi_2 }[/math] distributed.