How to zero-pad nicely symmetric vectors for FFT, so FFT of real symmetric inputs is (to machine precision) real

Fsympad.py

def Fsympad(h, m=None, inputOriginMiddle=True):
  if inputOriginMiddle:
    h = fft.ifftshift(np.array(h))
  else:
    h = np.array(h)
  if not m:
    return fft.fftshift(fft.fft(h))
  n = h.size
  assert m >= n
  # odd-length case: just insert zeros
  if n % 2 == 1:
    nfirst = int(np.ceil(n / 2))
    padded = np.hstack((h[:nfirst], np.zeros(m - n), h[nfirst:]))
    return fft.fftshift(fft.fft(padded))
  # even-length input: split the anti-DC component in half
  if m == n:
    padded = h
  else:
    ncut = int(n / 2)
    padded = np.hstack((h[:ncut], [h[ncut] / 2], np.zeros(m - n - 1), [h[ncut] / 2], h[ncut + 1:]))
  return fft.fftshift(fft.fft(padded))