File:Spectra computation.png: Difference between revisions
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 in the time-domain on each block. The colored lines are the same spectra but obtained using an alternate spectral averaging strategy. The purple has 58 degrees of freedom. |
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== Summary == | == 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 in the time-domain | 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>\chi_2</math> distributed. | ||
The purple | |||
Latest revision as of 14:31, 11 July 2022
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.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:31, 11 July 2022 |  | 1,200 × 600 (78 KB) | CynthiaBluteau (talk | contribs) | Added labels for the fft-length, degrees of freedom and nyquist frequency <math>f_N</math> |
| 02:11, 11 July 2022 |  | 1,200 × 600 (69 KB) | CynthiaBluteau (talk | contribs) | 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 in the time-domain on each block. The colored lines are the same spectra but obtained using an alternate spectral averaging strategy. The purple has 58 degrees of freedom. |
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