[Numpy-tickets] [NumPy] #748: Ifft pads incorrectly

[NumPy]

#748: Ifft pads incorrectly
-----------------------+----------------------------------------------------
 Reporter:  stefan     |        Owner:  somebody
     Type:  defect     |       Status:  new     
 Priority:  normal     |    Milestone:  1.1.0   
Component:  numpy.fft  |      Version:  devel   
 Severity:  major      |   Resolution:          
 Keywords:             |  
-----------------------+----------------------------------------------------
Comment (by charris):

 When the input to the fft is complex and has high frequencies. The middle
 padding is what you get when the upper half of the transform are aliases
 of negative frequencies, i.e., you want low frequency interpolation. In
 that case you should also split the value at the nyquist frequency and put
 half at each end of the middle padding, using one less zero in the
 padding. But what bugs me most is that the scaling is screwed up. If you
 are padding for interpolation, then you should divide by the original
 number of points, not the padded number of points. Note the factor of two
 I had to insert below in the inverse fft.

 Example of high frequency interpolation:

 {{{
 In [13]: x = exp(1j*pi*arange(8))

 In [14]: xt = numpy.fft.fft(x)

 In [15]: xi = numpy.fft.ifft(xt, n=16)*2

 In [16]: xi
 Out[16]:
 array([  1.00000000e+00 +0.00000000e+00j,
         -6.45783293e-17 +1.00000000e+00j,
         -1.00000000e+00 +1.22460635e-16j,
         -2.41157599e-16 -1.00000000e+00j,
          1.00000000e+00 -2.44921271e-16j,
          2.81792654e-16 +1.00000000e+00j,
         -1.00000000e+00 +3.67381906e-16j,
         -4.28612224e-16 -1.00000000e+00j,
          1.00000000e+00 -4.89842542e-16j,
          5.75431794e-16 +1.00000000e+00j,
         -1.00000000e+00 +6.12303177e-16j,
         -6.16066849e-16 -1.00000000e+00j,
          1.00000000e+00 -7.34763812e-16j,
          9.21802777e-16 +1.00000000e+00j,
         -1.00000000e+00 +8.57224448e-16j,  -4.28612224e-16
 -1.00000000e+00j])

 In [17]: xtrue = exp(.5j*pi*arange(16))

 In [18]: xtrue
 Out[18]:
 array([  1.00000000e+00 +0.00000000e+00j,
          6.12303177e-17 +1.00000000e+00j,
         -1.00000000e+00 +1.22460635e-16j,
         -1.83690953e-16 -1.00000000e+00j,
          1.00000000e+00 -2.44921271e-16j,
          3.06151588e-16 +1.00000000e+00j,
         -1.00000000e+00 +3.67381906e-16j,
         -4.28612224e-16 -1.00000000e+00j,
          1.00000000e+00 -4.89842542e-16j,
          5.51072859e-16 +1.00000000e+00j,
         -1.00000000e+00 +6.12303177e-16j,
         -2.44989033e-15 -1.00000000e+00j,
          1.00000000e+00 -7.34763812e-16j,
         -9.80362709e-16 +1.00000000e+00j,
         -1.00000000e+00 +8.57224448e-16j,  -2.69481160e-15
 -1.00000000e+00j])
 }}}

-- 
Ticket URL: <http://scipy.org/scipy/numpy/ticket/748#comment:3>
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