I need to do a Fourier transform of a map in Python. Fast Fourier Transforms expect periodic boundary conditions, but the input map is not periodic. So I need to apply an input filter/weight slowly tapering the map toward zero at the edges. Are there libraries for doing this in python?
2 Answers
Such tapering is often referred to as a "window".
Scipy has many window functions.
You can use numpy.expand_dims to create the 2D window you want.
Regarding Stefan's comment, apparently the numpy team thinks that including more than arrays was a mistake. I would stick to using scipy for signal processing. Watch out, as they moved quite a bit of functions around in their 1.0 release so older documentation is, well, quite old.
As a final note: a "filter" is typically reserved for multiplications you apply in the Frequency domain, not spatial domain.
My favorite function to apodize a map is the generalized Gaussian (also called 'Super-Gaussian' which is a Gaussian whose exponent is raised to a power P. By setting P to, say, 4 or 6 you get a flat-top pulse which falls off smoothly, which is good for FFT applications where sharp edges always create ripples in conjugate space.
The generalized Gaussian is available on Scipy. Here is a minimal code (Python 3) to apodize a 2D array with a generalized Gaussian. As noted in previous comments, there are dozens of functions which would work just as well.
import numpy as np
from scipy.signal import general_gaussian
# A 128x128 array
array = np.random.rand(128,128)
# Define a general Gaussian in 2D as outer product of the function with itself
window = np.outer(general_gaussian(128,6,50),general_gaussian(128,6,50))
# Multiply
ap_array = window*array
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