Variability of responses to sinusoidal modulation

Many studies of visual neurons make use of stimuli that are sinusoidally modulated in time, and take as the response the fundamental Fourier component of the firing. This is a study of the variability of the fundamental sinusoidal components. A theoretical analysis shows that the variance of sinusoidal components should be nearly independent of their amplitudes; this is expected despite the observation that variance of firing rate increases with increasing firing rate. However, this result applies only to the variance of the complex amplitude, defined as the complex Fourier amplitude in response to each stimulus cycle. This variance is called the complex variance. The variance of the scalar amplitude, which is simply the amplitude in response to each stimulus cycle disregarding phase (scalar variance) is expected to shrink by a factor of up to 2 1/3 as the response magnitude approaches zero. If the relationship between variance of rate and rate is linear, complex variance should be independent of amplitude. If the relationship between variance of rate and rate is characterized by a compressive nonlinearity (as has been observed), the complex variance should very slightly decrease with increased amplitude, despite the main trend of increased variance of rate with increased rate. Data from cat ganglion cells stimulated with sinusoidally modulated lights of various contrasts agree with the theory, although some individual cases show trends that may be indicative of nonlinearity in the relationship between variance of rate and rate.