Minor script for padding in 1D

padding.py

from numpy import *

N = 8
x = sin(4*pi*arange(N)/N)+sin(6*pi*arange(N)/N)

x_hat_c = fft.fft(x)       # Use regular fft
x_hat_r = fft.rfft(x)      # Use rfft. Should be same

M = 3*N//2
x_hat_c_pad = zeros(M, complex)
x_hat_r_pad = zeros(M//2+1, complex)

c_indices = fft.fftfreq(N, 1./N).astype(int)
r_indices = fft.rfftfreq(N, 1./N).astype(int)

x_hat_c_pad[c_indices] = x_hat_c
x_hat_r_pad[r_indices] = x_hat_r

x_c_pad = fft.ifft(x_hat_c_pad)
x_r_pad = fft.irfft(x_hat_r_pad)

# Alternative
x_c_pad2 = fft.ifft(x_hat_c, n=M)       # Not ok because of ordering (fftfreq)
x_r_pad2 = fft.irfft(x_hat_r, n=M)      # Ok because of 0,1,2,...N/2 ordering (rfftfreq)

assert allclose(x_r_pad, x_r_pad2)
assert allclose(x_c_pad, x_c_pad2) == False
assert allclose(x_c_pad, x_r_pad)

x_hat_c2 = fft.fft(x_c_pad)[c_indices]
x_hat_r2 = fft.rfft(x_r_pad)[r_indices]

x_hat_r3 = fft.rfft(x_r_pad2, n=N)      # Not ok because input is cropped, not output

assert allclose(x_hat_c2, x_hat_c)
assert allclose(x_hat_r2, x_hat_r)
assert allclose(x_hat_r2, x_hat_r3) == False