gain

why would a process vary with the square root of wavelength?

with constant bandwidth, e.g. receptive field area will vary with the square of frequency (of wavelength). the linear size (radius) of the r.f. will vary directly with wavelength. a process in volume would vary with the cube of wavelength. how do you go backwards from here?

okay, so the inhibitory inputs are all squared. i want the weights on these inputs to be proportional to the square root of filter wavelength. i could get a step closer by making the linear inputs proportional to wavelength before the squaring, which changes the question to:

why would a process vary with the inverse of spatial frequency? in my mind, the weights are still tied to the size of the r.f., so that the bigger it is, the more inhibitory connections it has. strictly speaking, this would make inhibition vary with the square of wavelength.

a bigger r.f. would have more inhibition, then. i am just making this up. so, an r.f. that's twice as big would have four times the inhibition. fine, but then why wouldn't it have four times the excitation? they would balance out. but maybe the excitation isn't balanced. maybe excitatory inputs are sparser and sparser for larger r.f.s. is that true?

if it's true, then effectively the gain for different wavelength r.f.s should increase with frequency, because the density of excitatory inputs should increase with frequency.


i feel like this is getting somewhere... atick and redlich, brady and field... somewhere in there...