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Frequency domain analysis

Created: 20/7/2005
Fourier analysis is the mathematical analysis of waves, discovered by the French mathematician Fourier (1768-1830). The raw EEG can be processed by fast Fourier transformation into its component sine waves. These can be further analysed with respect to three features:

1. Frequency distribution
2. Power contained within different frequencies (a function of wave amplitude)
3. Phase relationships between waves of different frequencies.

Traditional power spectral analysis investigates the relationship between power and frequency over a short time period (epoch). A graph of power versus frequency forms a spectral array. The spectral arrays from successive epochs can be superimposed upon each other to build up a composite display of changes in the location of power within different frequencies over time. Such rolling visual summaries effectively display raw EEG data that have been transformed with minimal loss of information. They are compact, indicate trends and, because different frequency bands are considered independently, changes occurring in one part of the frequency spectrum are immediately apparent. This is in contrast to cerebral function monitoring (CFM), where they can be cancelled out by changes in other parts of the spectrum. So, for example, in a CFM trace generated by EEG waves of 6 Hz, 9 Hz and 12 Hz, an increase in the amplitude (power) of the 6 Hz wave, coupled with a decrease in that of the 12 Hz wave, might produce no net change in overall voltage and hence no change in the trace. In a spectral array, both the decrease in 12 Hz power and the increase in the 6 Hz power would be obvious.

Fourier analysis is the mathematical analysis of waves, discovered by the French mathematician Jean Baptiste Joseph Fourier (1768-1830).

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