8000 Make forward/inverse Fourier transforms consistent by ojdf · Pull Request #68 · AOtools/aotools · GitHub
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Make forward/inverse Fourier transforms consistent #68

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Merged
merged 2 commits into from
Nov 3, 2021
Merged

Make forward/inverse Fourier transforms consistent #68

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d9d74d4
make inverse fts consistent with forward fts
ojdf Sep 7, 2021
b98260f
further fix to inverse fourier transforms
ojdf Sep 10, 2021
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52 changes: 28 additions & 24 deletions aotools/fouriertransform.py
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Original file line number Diff line number Diff line change
Expand Up @@ -21,24 +21,24 @@ def ft(data, delta):
axes=(-1)) * delta
return DATA

def ift(DATA, delta_f):
def ift(data, delta_f):
"""
Scaled inverse 1-D FFT

Parameters:
DATA (ndarray): Data in Fourier Space to transform
data (ndarray): Data in Fourier Space to transform
delta_f (ndarray): Frequency spacing of grid

Returns:
ndarray: Scaled data in real space
"""

data = numpy.fft.ifftshift(
DATA = numpy.fft.ifftshift(
numpy.fft.ifft(
numpy.fft.ifftshift(DATA, axes=(-1))),
axes=(-1)) * len(DATA) * delta_f
axes=(-1)) * data.shape[-1] * delta_f

return data
return DATA


def ft2(data, delta):
Expand All @@ -61,23 +61,25 @@ def ft2(data, delta):

return DATA

def ift2(DATA, delta_f):
def ift2(data, delta_f):
"""
Scaled inverse 2-D FFT

Parameters:
DATA (ndarray): Data in Fourier Space to transform
data (ndarray): Data in Fourier Space to transform
delta_f (ndarray): Frequency spacing of grid

Returns:
ndarray: Scaled data in real space
"""
N = DATA.shape[0]
g = numpy.fft.ifftshift(
N = data.shape[-1]
DATA = numpy.fft.ifftshift(
numpy.fft.ifft2(
numpy.fft.ifftshift(DATA))) * (N * delta_f)**2
numpy.fft.ifftshift(data, axes=(-1,-2)
), axes=(-1,-2))
, axes=(-1,-2)) * (N * delta_f)**2

return g
return DATA

def rft(data, delta):
"""
Expand All @@ -96,24 +98,24 @@ def rft(data, delta):
axes=(-1)) * delta
return DATA

def irft(DATA, delta_f):
def irft(data, delta_f):
"""
Scaled real inverse 1-D FFT

Parameters:
DATA (ndarray): Data in Fourier Space to transform
data (ndarray): Data in Fourier Space to transform
delta_f (ndarray): Frequency spacing of grid

Returns:
ndarray: Scaled data in real space
"""

data = numpy.fft.ifftshift(
DATA = numpy.fft.ifftshift(
numpy.fft.irfft(
numpy.fft.ifftshift(DATA, axes=(-1))),
axes=(-1)) * len(DATA) * delta_f
numpy.fft.ifftshift(data, axes=(-1))),
axes=(-1)) * data.shape[-1] * delta_f

return data
return DATA

def rft2(data, delta):
"""
Expand All @@ -134,20 +136,22 @@ def rft2(data, delta):

return DATA

def irft2(DATA, delta_f):
def irft2(data, delta_f):
"""
Scaled inverse real 2-D FFT

Parameters:
DATA (ndarray): Data in Fourier Space to transform
data (ndarray): Data in Fourier Space to transform
delta_f (ndarray): Frequency spacing of grid

Returns:
ndarray: Scaled data in real space
"""
data = numpy.fft.ifftshift(
N = data.shape[-1]
DATA = numpy.fft.ifftshift(
numpy.fft.irfft2(
numpy.fft.ifft2(DATA), s=(-1,-2)
)
) * (DATA.shape[0]*delta_f)**2
return data
numpy.fft.ifftshift(data, axes=(-1,-2)),
axes=(-1,-2)
),
axes=(-1,-2)) * (N * delta_f)**2
return DATA
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