TY - JOUR

T1 - Supporting Information Text

AU - Hardenberg, Jost Von

AU - Kletter, Assaf Y

AU - Yizhaq, Hezi

AU - Nathan, Jonathan

AU - Meron, Ehud

PY - 2007

Y1 - 2007

N2 - Validation on artificial models of the artifact removal algorithm. We tested the algorithm to remove artifacts on artificial signals by using different rearranging procedures. In particular, we used both the " Mean Method " with three different values of N = 1, 3, 5 and " Minimum Method " (see S2 Text) . The signals were generated by using models for which the value of a specific measure (power band, cross correlation, mutual information, granger causality) can be computed analitically. Thus, we could estimate the effects of adding a large number of artifact recordings (N a = 100) to the artificial model, as well as the efficiency of the method to remove them. To test the performance of the algorithm on spectral bands (see Spectral Analysis section in the Main Manuscript) we considered the following autoregressive model x n+1 = a 1 x n + σξ n , (1) where ξ n is a gaussian white noise with zero mean and unit variance. It can be shown that the variance of x is σ 2 x = σ 2 /(1 − a 2 1) and its autocorrelation is proportional to e −λk with λ = − log a 1 . In particular, the power spectrum has the form P (f) = 1 √ 2π (σ 1 − a 2 1 − 2a 1 cos(2πf)) . (2) For fixed initial condition x 0 = 1 and parameters a 1 = 1/2, σ = 0.1, we considered ten realizations of the autoregressive model with independent noise realizations. Each realization had a length of N = 3 × 10 5 data points (the first 500 data points were neglected) and the spectrum was estimated using the Welch method of modified periodograms. The length of the windowing was set equal to N p = 4096. As can be seen in the panel A of S2 Fig, the artifacts strongly affected the values of the power of spectral bands δ, θ, α, β, γ and after the application of the artifact removing algorithm PLOS 1/4

AB - Validation on artificial models of the artifact removal algorithm. We tested the algorithm to remove artifacts on artificial signals by using different rearranging procedures. In particular, we used both the " Mean Method " with three different values of N = 1, 3, 5 and " Minimum Method " (see S2 Text) . The signals were generated by using models for which the value of a specific measure (power band, cross correlation, mutual information, granger causality) can be computed analitically. Thus, we could estimate the effects of adding a large number of artifact recordings (N a = 100) to the artificial model, as well as the efficiency of the method to remove them. To test the performance of the algorithm on spectral bands (see Spectral Analysis section in the Main Manuscript) we considered the following autoregressive model x n+1 = a 1 x n + σξ n , (1) where ξ n is a gaussian white noise with zero mean and unit variance. It can be shown that the variance of x is σ 2 x = σ 2 /(1 − a 2 1) and its autocorrelation is proportional to e −λk with λ = − log a 1 . In particular, the power spectrum has the form P (f) = 1 √ 2π (σ 1 − a 2 1 − 2a 1 cos(2πf)) . (2) For fixed initial condition x 0 = 1 and parameters a 1 = 1/2, σ = 0.1, we considered ten realizations of the autoregressive model with independent noise realizations. Each realization had a length of N = 3 × 10 5 data points (the first 500 data points were neglected) and the spectrum was estimated using the Welch method of modified periodograms. The length of the windowing was set equal to N p = 4096. As can be seen in the panel A of S2 Fig, the artifacts strongly affected the values of the power of spectral bands δ, θ, α, β, γ and after the application of the artifact removing algorithm PLOS 1/4

UR - https://www.mendeley.com/catalogue/9c9a9a2e-d658-35d1-8f60-13ae85840868/

M3 - Article

SN - 0027-8424

VL - I

SP - 2007

EP - 2007

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 1

ER -