Figure 8
LNP model: Stimulus whitening and filter estimation by spike-triggered averaging. (a) Example segment of the original stimulus in grey, and the corresponding segment of the whitened stimulus in black. (b) Power spectral density (PSD) of the original (grey) and whitened (black) stimulus. While the PSD of the original stimulus declines at frequencies \( > \)100 Hz due to filtering, this effect is undone by whitening. (c) The autocorrelation function of the original (grey) and the whitened (black) stimulus at time lags of up to \(20\) ms. The temporal extent of the autocorrelation of the whitened stimulus is much reduced compared to the original. (d) For every spike of a RGC (black vertical lines), a segment of the whitened version of the stimulus, spanning 20 ms before and 10 ms after the spike, is added to the spike-triggered ensemble (STE). (e) The spike-triggered average (black trace) is computed by averaging across all elements of the STE (the STE elements from panel (a) are shown as thin gray lines). Gray shaded area indicates \(\pm 1\) standard deviation of the STE. Vertical black line indicates time of spike. (f) The elements of the full stimulus ensemble, consisting of all 300 sample long stimulus snippets taken 10 samples apart, are projected onto the linear filter of a cell and binned to yield a histogram (empty bars). The same is done for the elements of the STE (black histogram). (g) The nonlinearity (black dots) is estimated as the ratio between the histogram of the projected elements of the spike-triggered ensemble to the histogram of the projected elements of the full stimulus ensemble (black and the empty histograms from panel (f), respectively) and fit by a sigmoidal (Eq. (14)) or exponential (Eq. (15)) function (black trace, here sigmoidal).
