def createPreWhiteningFilter(**kwargs):
'''
Creates a pre-whitening filter in 3D. Fits a polynomial to the spectrum
beyond the "elbowAngstrom" frequency. Returns a whitening filter that
can be adjusted using the "rampWeight." (Alp Kucukelbir, 2013)
'''
epsilon = 1e-10
spectrum = kwargs.get('spectrum', 0)
elbowAngstrom = kwargs.get('elbowAngstrom', 0)
rampWeight = kwargs.get('rampWeight', 1.0)
vxSize = kwargs.get('vxSize', 0)
n = kwargs.get('n', 0)
# Create radius matrix
R = createRmatrix(n)
# Create the x and y variables for the polynomial regression
xpoly = np.array(range(1, spectrum.size + 1))
ypoly = np.log(np.sqrt(spectrum))
# Create the index of frequencies (depends on vxSize)
Fs = 1 / vxSize
Findex = 1 / (Fs / 2 * np.linspace(epsilon, 1, xpoly.size))
# Find the points of interest
indexElbow = np.argmin((Findex - elbowAngstrom)**2)
indexStart = np.argmin((Findex - (1.05 * elbowAngstrom))**2)
indexNyquist = xpoly[-1]
# Create the weighting function to do a weighted fit
wpoly = np.array(np.bitwise_and(xpoly > indexElbow, xpoly < indexNyquist),
dtype='float32')
wpoly += 0.5 * np.array(np.bitwise_and(xpoly > indexStart,
xpoly <= indexElbow),
dtype='float32')
# Do the polynomial fit
pcoef = np.polynomial.polynomial.polyfit(xpoly, ypoly, 2, w=wpoly)
peval = np.polynomial.polynomial.polyval(xpoly, pcoef)
# Don't change any frequencies outside of indexStart to indexNyquist
R[R < indexStart] = indexStart
R[R > indexNyquist] = indexNyquist
# Create the pre-whitening filter
pWfilter = np.exp(
np.polynomial.polynomial.polyval(R, -1.0 * rampWeight * pcoef))
del R
return {'peval': peval, 'pcoef': pcoef, 'pWfilter': pWfilter}
def createPreWhiteningFilter(**kwargs):
'''
Creates a pre-whitening filter in 3D. Fits a polynomial to the spectrum
beyond the "elbowAngstrom" frequency. Returns a whitening filter that
can be adjusted using the "rampWeight." (Alp Kucukelbir, 2013)
'''
epsilon = 1e-10
spectrum = kwargs.get('spectrum', 0)
elbowAngstrom = kwargs.get('elbowAngstrom', 0)
rampWeight = kwargs.get('rampWeight',1.0)
vxSize = kwargs.get('vxSize', 0)
n = kwargs.get('n', 0)
# Create radius matrix
R = createRmatrix(n)
# Create the x and y variables for the polynomial regression
xpoly = np.array(range(1,spectrum.size + 1))
ypoly = np.log(np.sqrt(spectrum))
# Create the index of frequencies (depends on vxSize)
Fs = 1/vxSize
Findex = 1/( Fs/2 * np.linspace(epsilon, 1, xpoly.size) )
# Find the points of interest
indexElbow = np.argmin((Findex-elbowAngstrom)**2)
indexStart = np.argmin((Findex-(1.05*elbowAngstrom))**2)
indexNyquist = xpoly[-1]
# Create the weighting function to do a weighted fit
wpoly = np.array(np.bitwise_and(xpoly>indexElbow, xpoly<indexNyquist), dtype='float32')
wpoly += 0.5*np.array(np.bitwise_and(xpoly>indexStart, xpoly<=indexElbow), dtype='float32')
# Do the polynomial fit
pcoef = np.polynomial.polynomial.polyfit(xpoly, ypoly, 2, w=wpoly)
peval = np.polynomial.polynomial.polyval(xpoly, pcoef)
# Don't change any frequencies outside of indexStart to indexNyquist
R[R<indexStart] = indexStart
R[R>indexNyquist] = indexNyquist
# Create the pre-whitening filter
pWfilter = np.exp(np.polynomial.polynomial.polyval(R,-1.0*rampWeight*pcoef))
del R
return {'peval':peval, 'pcoef':pcoef, 'pWfilter': pWfilter}
def createPreWhiteningFilterFinal(**kwargs):
'''
Creates a pre-whitening filter in 3D. Expects a fitted polynomial
defined by its "pcoef". Returns a whitening filter that
can be adjusted using the "rampWeight." (Alp Kucukelbir, 2013)
'''
epsilon = 1e-10
spectrum = kwargs.get('spectrum', 0)
pcoef = kwargs.get('pcoef', 0)
elbowAngstrom = kwargs.get('elbowAngstrom', 0)
rampWeight = kwargs.get('rampWeight', 1.0)
vxSize = kwargs.get('vxSize', 0)
n = kwargs.get('n', 0)
cubeSize = kwargs.get('cubeSize', 0)
# Create radius matrix
R = createRmatrix(n)
# Create the x and y variables for the polynomial regression
xpoly = np.array(range(1, spectrum.size + 1))
# Create the index of frequencies (depends on vxSize)
Fs = 1 / vxSize
Findex = 1 / (Fs / 2 * np.linspace(epsilon, 1, xpoly.size))
# Find the points of interest
indexStart = np.argmin((Findex - (1.05 * elbowAngstrom))**2)
indexNyquist = xpoly[-1]
# Don't change any frequencies outside of indexStart to indexNyquist
R[R < indexStart] = indexStart
R[R > indexNyquist] = indexNyquist
# Rescale R such that the polynomial from the cube fit makes sense
R = R / (float(n) / (cubeSize - 1))
# Create the pre-whitening filter
pWfilter = np.exp(
np.polynomial.polynomial.polyval(R, -1.0 * rampWeight * pcoef))
del R
return {'pWfilter': pWfilter}
def createPreWhiteningFilterFinal(**kwargs):
'''
Creates a pre-whitening filter in 3D. Expects a fitted polynomial
defined by its "pcoef". Returns a whitening filter that
can be adjusted using the "rampWeight." (Alp Kucukelbir, 2013)
'''
epsilon = 1e-10
spectrum = kwargs.get('spectrum', 0)
pcoef = kwargs.get('pcoef', 0)
elbowAngstrom = kwargs.get('elbowAngstrom', 0)
rampWeight = kwargs.get('rampWeight',1.0)
vxSize = kwargs.get('vxSize', 0)
n = kwargs.get('n', 0)
cubeSize = kwargs.get('cubeSize', 0)
# Create radius matrix
R = createRmatrix(n)
# Create the x and y variables for the polynomial regression
xpoly = np.array(range(1,spectrum.size + 1))
# Create the index of frequencies (depends on vxSize)
Fs = 1/vxSize
Findex = 1/( Fs/2 * np.linspace(epsilon, 1, xpoly.size) )
# Find the points of interest
indexStart = np.argmin((Findex-(1.05*elbowAngstrom))**2)
indexNyquist = xpoly[-1]
# Don't change any frequencies outside of indexStart to indexNyquist
R[R<indexStart] = indexStart
R[R>indexNyquist] = indexNyquist
# Rescale R such that the polynomial from the cube fit makes sense
R = R/(float(n)/(cubeSize-1))
# Create the pre-whitening filter
pWfilter = np.exp(np.polynomial.polynomial.polyval(R,-1.0*rampWeight*pcoef))
del R
return {'pWfilter': pWfilter}
