Fluctuations in the discharge of impulses were studied in eccentric cells of the compound eye of the horseshoe crab, Limulus polyphemus. A theory is presented which accounts for the variability in the response of the eccentric cell to light. The main idea of this theory is that the source of randomness in the impulse rate is "noise" in the generator potential. Another essential aspect of the theory is that the process which transforms the generator potential "noise" into the impulse rate fluctuations may be treated as a linear filter. These ideas lead directly to Fourier analysis of the fluctuations. Experimental verification of theoretical predictions was obtained by calculation of the variance spectrum of the impulse rate. The variance spectrum of the impulse rate is shown to be the filtered variance spectrum of the generator potential.

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