Figure 27

Animated simulations: SS compared with QSD. Herein you can access 6 simulations, 3 each for SS and for QSD. There are three ranges of mean repetition-rate:

A = 0.3 – 2.4 S/s.

B = 3 – 11 S/s.

C = 11 – 25 S/s. Each of these rates can be seen for either SS or QSD from the following Demonstration files:"Fig. 27_SS_A" [see Additional file 13]"Fig. 27_SS_B" [see Additional file 14]"Fig. 27_SS_C" [see Additional file 15]"Fig. 27 QSD_A" [see Additional file 9]"Fig. 27 QSD_B" [see Additional file 10]"Fig. 27 QSD_C" [see Additional file 11]

SS Animations These animations contain simulations of SS responses based upon an actual brain response waveform, also seen in Fig. 4, 30 S/s. That response is shown as a red trace in the lower left-hand side of all the steady-state animations. Above that is shown a 500 ms SS response in black, this is the same epoch length as used by Herrmann [16] and is equivalent to his averaged SS responses. The long blue trace shows the convolution of the brain response shown in the lower left, with a periodic sequence at the rate shown by the number in the top left. The first five seconds of our simulated convolved response are shown in the upper blue trace. In the bottom right hand corner there is a box that contains information plotted in the frequency domain. This box contains the frequencies from 0 Hz to 26 Hz with a mark below the horizontal axis showing 10 Hz. The red trace in the box is the magnitude of the Fourier coefficients of the time-domain brain response shown in the bottom left red trace. The blue dots are the Fourier coefficients of the blue trace above. The black vertical lines are the Fourier magnitudes of the periodic sequence (comb filter) with which the brain response is convolved. NOTE: All of the traces in these animations may have been scaled, and/or cropped for demonstrative purposes.

QSD Animations These animations contain simulations of QSD responses based upon an actual brain response wave form recovered with the QSD method, also seen in Fig.4, 30 S/s. This response is shown in red at the bottom left. The long blue trace in the middle of the animation is the convolution of the brain response shown, with a QSD sequence at the mean repetition rate shown by the number in the top left. This trace is equivalent to our data-averages when stimulating with a QSD sequence. It is 5 sec long (longer than we have ever used) in order to show, in the simulation of the lowest stimulus repetition-rates the gradual overlap of the individual responses. In the bottom left, above the red trace is shown, in black, the corresponding waveform deconvolved from the upper blue trace (after random noise had been added). If we had not added noise here there would be no changes in the deconvolved trace during the animation. (Each of the three animations was based upon a different QSD sequence. QSD sequences for these simulations were produced by taking a QSD sequence used in this paper (see Table 1 [see Additional file 16]) and using it for multiple stimulus repetition-rates. To accomplish this author MO changed the sampling rate used during the simulation. (The frequencies are thinning as the repetition-rate goes faster in the animation because we did not want to find so many good q-sequences. So in the simulation, the use of one q-sequence over multiple frequencies led to automatic change in the length of the convolved data with every change in stimulus repetition-rate. This had the consequence that the number of frequencies analyzed changed, and this appears as changing q-sequence frequencies during the animation. In actual practice, since the SL is often the same length even though the repetition-rate is changed, the frequencies in the deconvolution waveform are the same.) In the bottom right hand corner there is a box that contains information plotted in the frequency-domain. This box contains the frequencies from 0 Hz to 26 Hz with a mark below the horizontal axis showing 10 Hz. The red trace here is the magnitude of the Fourier coefficients of the brain's response shown in the red trace at the bottom left. The blue dots are the Fourier coefficients of the convolution shown as the blue trace above. The black vertical lines are the Fourier magnitudes of the q-sequence (i.e., Q-magnitudes) with which the brain's response is convolved (see QSD paper for further details) [14]. The tick marks on the vertical axis show the Q-magnitudes 1 and 5 of the q-sequence (cropped above 5). NOTE: All of the other traces in these animations may have been scaled, and/or cropped for demonstrative purposes.