TABLE OF CONTENTS To investigate cell responses, we test with sine gratings. We would like to optimize over spatial frequency, angle of orientation, and phase. We could use a Fast Fourier Transform (FFT) procedure to get the spatial frequency by simply looking at the peak in frequency space of the weight vector. Unfortunately, this is very sensitive to noise. What we do in practice is to use a spatial frequency, k, determined empirically, for all BCM simulations of 4.4 ?/(rf diameter).
Optimizing over angle requires a programming loop [*], but the optimization over phase can be done in the linear region, using the following trick.
We first introduce rotated coordinates
Now we maximize with respect to ?.
We then use this phase in Equations 6A.4 and 6A.5 in order to find the maximum response (over phase), at a particular angle. We then need only to calculate the response of the cell to a sine grating (zero phase) and a cosine grating (zero phase).
For direction selectivity, in a two channel model, we follow a similar procedure.
The cell is tested with gratings of spatial frequency, k, and temporal frequency, ?. The two channels are offset by a delay, ?. Thus the response is
Since we are maximizing with respect to time and temporal frequency, we can treat the problem as follows. We find the phase which maximizes each term independently using Equation 6A.10,
This gives...
