Basis functions to include

[billbrod]

(can create separate issues for these as needed, just link from here)

Following is an incomplete list of basis functions to include, we can add more as needed:

• [ ] Fourier basis
• [x] 2d basis
  • [ ] for position
  • [ ] for visual input. separate for e.g., retina and V1?
• [ ] circular (head position, orientation, etc)
• [x] allow for Cartesian product of basis: accept two bases and generically take their product. Could be used to cross position in space and head direction or to generate the simpler 2d bases above

[BalzaniEdoardo]

generalize to N-dimensional basis function

[BalzaniEdoardo]

I am coding up the Fourier basis, still working on a PR for it. A couple of considerations:

• Should we enforce equi-spaced sampling when generating the basis? this would make it easy to check for aliasing, and would enforce the evaluated basis to be sinusoidal.
• Convolving with this basis is equivalent of using a sliding window FFT as a predictor. would this estimate be robust enough (without multi-tapering or similar robust estimation procedures)?

[ahwillia]

We should also include Bernstein Polynomial Basis Functions