The fast Hartley transform
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Cites background from "The fast Hartley transform"
...Therefore, the real-valued discrete cosine or discrete Hartley transforms [124], [125] may be more convenient from an implementational point of view....
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1,251 citations
Cites methods from "The fast Hartley transform"
...2 The Fast Hartley Transform method of spectral analysis is conceptuilly analogous to the Fast Founer Transform, provides identical output, and IS computationally more efficient 3 Asymmetry scores are used because they can control for nonneurogemc sources of mdividual differences (e g, skull thickness) in power density values (see Wheeler et al, 1993, for further details) 206 VOL 8, NO 3, MAY 1997 RCSULIS Tlu^crrehuon l ....
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...…Adjacent chunks were overlapped 50% in order to minimize the loss of data due to Hamming window extraction For each chunk, a Fast Hartley Transform (Bracewell, 1984) was used to denve esUmates of spectral power ((xV^) m different 1-Hz frequency bins for each electrode site ^ Spectral power values…...
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...Each subject partiapated individually m the first baseline EEG session between the 3rd and 6th weeks of the fall 1994 semester Electrodes were placed and checked within the first 50 min of the subject's amval While the expenmenter momtored the recording equipment from an adjacent room, computer instnicuons led the subject through a senes of eight l-mm basebnes dunng which EEG was recorded while the subject sat quietly with eyes opened and closed m counterbalanced tnals The eight baselines were usually completed m less than 15 min Following the removal of electrodes, the subject completed a set of selfreport lnventones, including the general version of the PANAS The second EEG session was completed exactly 6 weeks later It was identical to the first session with two exceptions A different counterbalanced order of eyes-opened and eyes-closed tnals was used, and the BIS/BAS scales (Carver & White, 1994) were administered at this session, in place of the PANAS Approximately 3 months following participation m the second EEG session, each subject was invited to participate in a twosession study dunng which a battery of cognitive and behavioral tasks was administered The second non-EEG session was completed between 4 and 6 months following the second baseline EEG session Near the end of this 2-hr session, the subject completed the PANAS and BIS/BAS scales for a second time Data Reduction and Analysis EEGs from 29 sites (13 homologous pairs and 3 midline sites) of the 10-20 electrode system were recorded using a Lycra stretchable cap (Electro-Cap International, Inc, Eaton, Ohio) positioned according to standard anatomical landmarks All electrode impedances were less than 5,000 ohms, and impedances for homologous sites were within 2,000 ohms All EEG signals were referenced to an electrode placed on the left ear lobe (Al) An electrode was also placed on the nght ear lobe (A2, referenced to Al) so that a denved averaged-ears reference could be used in analyses For the purposes of artifact sconng, vertical and horizontal eye movements (electro-oculograms) were also recorded Electrode pairs were placed at the supra- and suborbit of one eye (randomly selected), and at the external canthi of each eye EEGs were amplified with Grass Model 12 Neurodata System amplifiers after passing through Model 12A5 preamplifiers with bandpass filters set at 1 and 300 Hz and the 60-Hz notch filter I, and passing through antialiasing, low-pass, 36-dB/octave rolloff filters set at 200 Hz (MF6, National Semiconductor Corp, Santa Qara, Cahfomia) Electro-oculograms were processed in a similar manner, with the exception that there was no antialiasing filtenng and amphficaUon was occasionally lowered to 20,000 ohms All EEG and electro-oculogram signals were digitized at 500 Hz using SnapStream (HEM Data Corp, Spnngfield, Michigan) and a 486 DX2-66 computer Digitized EEG signals were calibrated using 25-n.V and 50- ' 10-Hz signals recorded unmediately before and after each ision These signals were visually reviewed off-hne by a trained assistant Portions of each 1-min baselme containing eye movement, muscle movement, or other sources of artifact were removed pnor to further analysis The designation of artifact in any one channel resulted m the removal of data in all channels ensure that data preserved in all channels were denved from the identical Ume penods Then, 1 024-s chunks of artifact-fret EEG were used for spectral analysis If fewer than 10 chunks o artifact-free data were available m a given 1-min baseline, the basehne was dropped from further processing and analysis (1 6% of baselines) TTie denved averaged-ears reference was used for all further data reduction Chunks of artifact-free EEG were extracted through a Hamming window in order to reduce spunous esUmates of spectral power Adjacent chunks were overlapped 50% in order to minimize the loss of data due to Hamming window extraction For each chunk, a Fast Hartley Transform (Bracewell, 1984) was used to denve esUmates of spectral power ((xV^) m different 1-Hz frequency bins for each electrode site ^ Spectral power values were then averaged across all chunks within a smgle baselme Power values were then converted to power density values (ftVV Hz) for the standard EEG bands Analyses focused on the alpha band (8-13 Hz) because previous data indicated that power m the alpha band is inversely related to activation (e g, Shagass, 1972) and is more strongly related to behavior than power m other frequency bands (Davidson, Chapman, Chapman, & Hennques, 1990) Power density values were normalized via log-transformation An asymmetry score was calculated for each of the 13 homologous electrode pairs by subtracting the log-transformed power density value in the alpha band for the left site from that for the nght site (e g , log F4 - log F3) ' Positive asymmetry scores reflect greater left-side activation (greater alpha band power density on nght than on left) In order to assess internal consistency reliability, we calculated an asymmetry score for each 1-min basehne Weighted averages (weighted by the number of artifact-free chunks in a tnal) across the eight 1-min baseline penods within Sessions 1 and 2 were calculated in order to assess test-retest reliability A simple mean based on weighted averages for Sessions 1 and 2 was calculated as the final, aggregate estimate of EEG asymmetry used to assess relations with the self-report mea- Carver and White's (1994) 24-item BIS/BAS scales inventory was used to measure strengths of the BIS and BAS Scores for the 13-item BAS scale and 7-item BIS scale were calculated following Carver and White (l e , summing 4-point Likert scale responses) In order to obtain a self-report metnc conceptually similar to EEG asymmetry (l e , relative strength), we calculated a BAS-BIS difference score by subtracting the z-transformed BIS scale score from the z-transformed BAS scale score Positive BAS-BIS difference scores reflect relatively greater BAS activity The general version of the 20-item PANAS (Watson et al, 1988) self-reported dispositional levels of jwsitive affect (PA) and negative affect (NA) The PA and NA measures were calculated following Watson et al (1988) As with the BIS/ BAS scales, a PA-NA difference score was calculated by subtracting the z-transformed NA score from the z-transformed PA of relations among the vanous measures....
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Cites methods or result from "The fast Hartley transform"
...The Hartley transform [3], [4] is shown in [34] to have properties similar to those of the DFT....
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...Another recent scheme [19] uses a prime factor map, but computes the modules using the Hartley transform [3], [34]....
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References
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