def matchedFilter(template, noiseSpectrum, nTaps=50):
'''
Make a matched filter using a template and noise PSD. Rolls off template above 250kHz.
(same as 250 roll off Wiener filter but calculated with the covariance matrix)
INPUTS:
template - array containing pulse template
noiseSpectrum - noise PSD
nTaps - number of filter coefficients
OUTPUTS
matchedFilt - matched filter that should be convolved with the data
to get the pulse heights
'''
#check normalized to 1
template /= np.max(np.abs(template))
#mimic antialiasing filter
fft = np.fft.rfft(template)
spectrum = 1 / (1 +
(np.fft.rfftfreq(len(template), d=1e-6) / 250000.0)**8.0)
fft = fft * spectrum
template1 = np.fft.irfft(fft)
template1 /= np.max(np.abs(template1))
noiseCov = mNS.covFromPsd(noiseSpectrum, nTaps)['covMatrix']
template1 = template1[:nTaps] #shorten template to length nTaps
template = template[:nTaps]
filterNorm = np.dot(template, np.linalg.solve(noiseCov, template1))
matchedFilt = np.linalg.solve(noiseCov, template1) / filterNorm
return -matchedFilt
def makeMatchedFilter(noiseSpectDict, template):
"""
Calculate Matched Filter coefficients
Does not work yet 08/18/2016
INPUTS:
noiseSpectDict - Dictionary containing noise spectrum and list of corresponding frequencies
template - template of pulse shape
OUTPUTS:
matchedFilter - list of Matched Filter coefficients
"""
noiseSpectrum = noiseSpectDict["noiseSpectrum"]
noiseCovInv = mNS.covFromPsd(noiseSpectrum)["covMatrixInv"]
filterNorm = np.sqrt(np.dot(template, np.dot(noiseCovInv, template))) # filterNorm not working correctly
matchedFilt = np.dot(noiseCovInv, template) / filterNorm
return matchedFilt
def superMatchedFilter(template, noiseSpectrum, nTaps=50):
'''
Make a matched filter that is robust against pulse pileup using prescription from
Alpert 2013 Rev. of Sci. Inst. 84. (Untested)
INPUTS:
template - array containing pulse template
noiseSpectrum - noise PSD
nTaps - number of filter coefficients
OUTPUTS
superMatchedFilt - super matched filter that should be convolved with
the data to get the pulse heights
'''
#get the fall time for the end of the pulse
#(only a good idea to use this formula if using a fitted template)
fallTime = (template[-1] - template[-2]) / np.log(
template[-2] / template[-1])
#determine pulse direction
if np.min(template) > np.max(template):
pos_neg = -1.
else:
pos_neg = 1
#check normalized to 1
template /= np.abs(template[np.argmax(np.abs(template))])
#create covariance inverse matrix
noiseCovInv = mNS.covFromPsd(noiseSpectrum, nTaps)['covMatrixInv']
#shorten template to length nTaps
template = template[:nTaps]
#create exponential to be orthogonal to
exponential = pos_neg * np.exp(-np.arange(0, len(template)) / fallTime)
#create filter
orthMat = np.array([template, exponential])
orthMat = orthMat.T
e1 = np.array([1, 0])
norm = np.linalg.inv(np.dot(orthMat.T, np.dot(noiseCovInv, orthMat)))
superMatchedFilter = np.dot(noiseCovInv, np.dot(orthMat, np.dot(norm, e1)))
#flip so that filter works with correlation and not convolution
superMatchedFilter = superMatchedFilter[::-1]
return superMatchedFilter
def makeSuperMatchedFilter(template, noiseSpectrum, fallTime, nTaps=50, tempOffs=90,sampleRate=1e6):
'''
Make a matched filter that is robust against pulse pileup using prescription from
Alpert 2013 Rev. of Sci. Inst. 84
INPUTS:
template - array containing pulse template
noiseSpectrum - noise PSD
fallTime - pulse fall time to make fits robust to
nTaps - number of filter coefficients
tempOffs - offset of template subset to use for filter
sampleRate - sample rate of template in Hz
OUTPUTS
superMatchedFilt - super matched filter that should be convolved with
the data to get the pulse heights
'''
#determine pulse direction
if np.min(template)>np.max(template):
pos_neg=-1.
else:
pos_neg=1
#check normalized to 1
template/=np.abs(template[np.argmax(np.abs(template))])
#create covariance inverse matrix
noiseCovInv = noise.covFromPsd(noiseSpectrum, nTaps)['covMatrixInv']
#shorten template to length nTaps
template = template[tempOffs:tempOffs+nTaps]
#create exponential to be orthogonal to
exponential=pos_neg*np.exp(-np.arange(0,len(template))/fallTime/sampleRate)
#create filter
orthMat=np.array([template,exponential])
orthMat=orthMat.T
e1=np.array([1,0])
norm=np.linalg.inv(np.dot(orthMat.T,np.dot(noiseCovInv,orthMat)))
superMatchedFilter=np.dot(noiseCovInv,np.dot(orthMat,np.dot(norm,e1)))
superMatchedFilter=superMatchedFilter[::-1]
return superMatchedFilter
def makeMatchedFilter(template, noiseSpectrum, nTaps=50, tempOffs=90):
'''
Make a matched filter using a template and noise PSD
INPUTS:
template - array containing pulse template
noiseSpectrum - noise PSD
nTaps - number of filter coefficients
tempOffs - offset of template subset to use for filter
OUTPUTS
matchedFilt - matched filter that should be convolved with the data
to get the pulse heights
'''
#check normalized to 1
template/=np.abs(template[np.argmax(np.abs(template))])
noiseCovInv = noise.covFromPsd(noiseSpectrum, nTaps)['covMatrixInv']
#print np.dot(noise.covFromPsd(noiseSpectrum, nTaps)['covMatrixInv'] ,noise.covFromPsd(noiseSpectrum, nTaps)['covMatrix'] )
template = template[tempOffs:tempOffs+nTaps] #shorten template to length nTaps
filterNorm = np.dot(template, np.dot(noiseCovInv, template))
matchedFilt = np.dot(noiseCovInv, template)/filterNorm
matchedFilt=matchedFilt[::-1]
return matchedFilt
