def PSD2(image, image2=None, oned=False,
fft_pad=False, real=False, imag=False,
binsize=1.0, radbins=1, azbins=1, radial=False, hanning=False,
wavnum_scale=False, twopi_scale=False, **kwargs):
"""
Two-dimensional Power Spectral Density.
NAN values are treated as zero.
image2 - can specify a second image if you want to see the cross-power-spectrum instead of the
power spectrum.
oned - return radial profile of 2D PSD (i.e. mean power as a function of spatial frequency)
freq,zz = PSD2(image); plot(freq,zz) is a power spectrum
fft_pad - Add zeros to the edge of the image before FFTing for a speed
boost? (the edge padding will be removed afterwards)
real - Only compute the real part of the PSD (Default is absolute value)
imag - Only compute the complex part of the PSD (Default is absolute value)
hanning - Multiply the image to be PSD'd by a 2D Hanning window before performing the FTs.
Reduces edge effects. This idea courtesy Paul Ricchiazzia (May 1993), author of the
IDL astrolib psd.pro
wavnum_scale - multiply the FFT^2 by the wavenumber when computing the PSD?
twopi_scale - multiply the FFT^2 by 2pi?
azbins - Number of azimuthal (angular) bins to include. Default is 1, or
all 360 degrees. If azbins>1, the data will be split into [azbins]
equally sized pie pieces. Azbins can also be a numpy array. See
AG_image_tools.azimuthalAverageBins for details
radial - An option to return the *azimuthal* power spectrum (i.e., the spectral power as a function
of angle). Not commonly used.
radbins - number of radial bins (you can compute the azimuthal power spectrum in different annuli)
"""
# prevent modification of input image (i.e., the next two lines of active code)
image = image.copy()
# remove NANs (but not inf's)
image[image!=image] = 0
if hanning:
image = hanning2d(*image.shape) * image
if image2 is None:
image2 = image
else:
image2 = image2.copy()
image2[image2!=image2] = 0
if hanning:
image2 = hanning2d(*image2.shape) * image2
if real:
psd2 = numpy.real( correlate2d(image,image2,return_fft=True,fft_pad=fft_pad) )
elif imag:
psd2 = numpy.imag( correlate2d(image,image2,return_fft=True,fft_pad=fft_pad) )
else: # default is absolute value
psd2 = numpy.abs( correlate2d(image,image2,return_fft=True,fft_pad=fft_pad) )
# normalization is approximately (numpy.abs(image).sum()*numpy.abs(image2).sum())
if wavnum_scale:
wx = numpy.concatenate([ numpy.arange(image.shape[0]/2,dtype='float') , image.shape[0]/2 - numpy.arange(image.shape[0]/2,dtype='float') -1 ]) / (image.shape[0]/2.)
wy = numpy.concatenate([ numpy.arange(image.shape[1]/2,dtype='float') , image.shape[1]/2 - numpy.arange(image.shape[1]/2,dtype='float') -1 ]) / (image.shape[1]/2.)
wx/=wx.max()
wy/=wy.max()
wavnum = numpy.sqrt( numpy.outer(wx,numpy.ones(wx.shape))**2 + numpy.outer(numpy.ones(wy.shape),wx)**2 )
psd2 *= wavnum
if twopi_scale:
psd2 *= numpy.pi * 2
if radial:
azbins,az,zz = radialAverageBins(psd2,radbins=radbins, interpnan=True, binsize=binsize, **kwargs)
if len(zz) == 1:
return az,zz[0]
else:
return az,zz
if oned:
return pspec(psd2, azbins=azbins, binsize=binsize, **kwargs)
# else...
return psd2
def PSD2(image,
image2=None,
oned=False,
fft_pad=False,
real=False,
imag=False,
binsize=1.0,
radbins=1,
azbins=1,
radial=False,
hanning=False,
wavnum_scale=False,
twopi_scale=False,
**kwargs):
"""
Two-dimensional Power Spectral Density.
NAN values are treated as zero.
image2 - can specify a second image if you want to see the cross-power-spectrum instead of the
power spectrum.
oned - return radial profile of 2D PSD (i.e. mean power as a function of spatial frequency)
freq,zz = PSD2(image); plot(freq,zz) is a power spectrum
fft_pad - Add zeros to the edge of the image before FFTing for a speed
boost? (the edge padding will be removed afterwards)
real - Only compute the real part of the PSD (Default is absolute value)
imag - Only compute the complex part of the PSD (Default is absolute value)
hanning - Multiply the image to be PSD'd by a 2D Hanning window before performing the FTs.
Reduces edge effects. This idea courtesy Paul Ricchiazzia (May 1993), author of the
IDL astrolib psd.pro
wavnum_scale - multiply the FFT^2 by the wavenumber when computing the PSD?
twopi_scale - multiply the FFT^2 by 2pi?
azbins - Number of azimuthal (angular) bins to include. Default is 1, or
all 360 degrees. If azbins>1, the data will be split into [azbins]
equally sized pie pieces. Azbins can also be a numpy array. See
AG_image_tools.azimuthalAverageBins for details
radial - An option to return the *azimuthal* power spectrum (i.e., the spectral power as a function
of angle). Not commonly used.
radbins - number of radial bins (you can compute the azimuthal power spectrum in different annuli)
"""
# prevent modification of input image (i.e., the next two lines of active code)
image = image.copy()
# remove NANs (but not inf's)
image[image != image] = 0
if hanning:
image = hanning2d(*image.shape) * image
if image2 is None:
image2 = image
else:
image2 = image2.copy()
image2[image2 != image2] = 0
if hanning:
image2 = hanning2d(*image2.shape) * image2
if real:
psd2 = numpy.real(
correlate2d(image, image2, return_fft=True, fft_pad=fft_pad))
elif imag:
psd2 = numpy.imag(
correlate2d(image, image2, return_fft=True, fft_pad=fft_pad))
else: # default is absolute value
psd2 = numpy.abs(
correlate2d(image, image2, return_fft=True, fft_pad=fft_pad))
# normalization is approximately (numpy.abs(image).sum()*numpy.abs(image2).sum())
if wavnum_scale:
wx = numpy.concatenate([
numpy.arange(image.shape[0] / 2, dtype='float'), image.shape[0] / 2
- numpy.arange(image.shape[0] / 2, dtype='float') - 1
]) / (image.shape[0] / 2.)
wy = numpy.concatenate([
numpy.arange(image.shape[1] / 2, dtype='float'), image.shape[1] / 2
- numpy.arange(image.shape[1] / 2, dtype='float') - 1
]) / (image.shape[1] / 2.)
wx /= wx.max()
wy /= wy.max()
wavnum = numpy.sqrt(
numpy.outer(wx, numpy.ones(wx.shape))**2 +
numpy.outer(numpy.ones(wy.shape), wx)**2)
psd2 *= wavnum
if twopi_scale:
psd2 *= numpy.pi * 2
if radial:
azbins, az, zz = radialAverageBins(psd2,
radbins=radbins,
interpnan=True,
binsize=binsize,
**kwargs)
if len(zz) == 1:
return az, zz[0]
else:
return az, zz
if oned:
return pspec(psd2, azbins=azbins, binsize=binsize, **kwargs)
# else...
return psd2