Hartley transforms and narrow Bessel bandpass filters produce similar power spectra of multiple frequency oscillators and all-night EEG

Abstract

Frequency specific power obtained from time and frequency domain analyses are explored in simulated signals and all-night electroencephalogram (EEG). Signals were subjected to a fast Hartley transformation (FHT) and to digital sixth-order Bessel bandpass filters (BDF) of the infinite impulse response type. Numeric values of FHT, BDF and, if suited, authentic frequency specific power were subjected to a Pearson correlation. Frequency bins at 1.6-2.4 Hz (delta), 4.75-5.9 Hz (theta), 9.3-11.5 Hz (alpha), 12.5-14.9 Hz (sigma) and 16.6-19.5 Hz (beta) were investigated. When compared with true power of single frequency oscillators (256-sample windows), frequency specific power of the FHT correlated functionally (1.0) and BDF correlated highly (0.85, delta; 0.99, other bins). For analyses of 'white noise', a multiple frequency oscillator and all-night EEG, four rectangular window sizes were applied (256, 512, 1,024 or 2,048 samples). The FHT power correlated better with authentic frequency specific power of 'white noise' (256-sample windows) (0.61-0.98) than BDF power (0.67-0.89). With 512-sample windows of 'white noise', the estimate of both the FHT (0.69-0.99) and BDF (0.71-0.93) improved. Direct comparison between FHT and BDF frequency specific power obtained from 'white noise' or all-night EEG revealed a high degree of compliance between methods for all frequency bins (up to 0.99). For delta, the accord was relatively low for the 256-sample window (EEG, 0.68; 'white noise', 0.72), but increased with lengthening window size (2,048-sample: 0.97; 0.99). Averaging of multiple EEG 256-sample windows also increased the agreement between methods. It is concluded that both the frequency domain analysis and the time domain bandpass filtering produce similar frequency specific power of the EEG. Long window sizes or window averaging guarantees close to equivalent frequency specific power quantitations by the two methods. Thus, frequency specific power assessments of the EEG are practically justified, despite problems inherent to both methods.