fixed taps/space, update documentation
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Markus Rosenstihl
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@ -2,55 +2,58 @@ import numpy
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import sys
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import autophase
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class DamarisFFT:
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def clip(self, start=None, stop=None):
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"""
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:param float start: beginning of clipping
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:param float stop: end of clipping
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Method for clipping data, returns only the timesignal
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between start and stop
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is returned.
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class DamarisFFT:
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"""
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Class for Fourier transforming data.
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Provides several helper and apodization functions
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"""
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def clip( self, start=None, stop=None ):
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"""
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Method for clipping data, returns only the data between start and stop
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start and stop can be either time or frequency.
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The unit is automatically determined
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The unit is automatically determined (Hz or s).
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:param float start: beginning of clipping in s
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:param float stop: end of clipping in s
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"""
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# check if start/stop order is properly
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if start > stop:
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# I could swap start/stop actually
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# TODO swap values?
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raise
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# if one uses clip as a "placeholder"
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start, stop = stop, start
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# do nothing if one uses clip as a "placeholder"
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if start == None and stop == None:
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return self
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if start == None:
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start = 0
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start = self.x[ 0 ]
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if stop == None:
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stop = -1
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stop = self.x[ -1 ]
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# check if data is fft which changes the start/stop units
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# TODO should get nicer(failsafe), i.e. flags in the object?
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if self.xlabel == "Frequency / Hz":
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isfft = True
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start = self.x.size*(0.5 + start/self.sampling_rate)
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stop = self.x.size*(0.5 + stop/self.sampling_rate)
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start = self.x.size * (0.5 + start / self.sampling_rate)
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stop = self.x.size * (0.5 + stop / self.sampling_rate)
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else:
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isfft = False
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# get the corresponding indices
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start *= self.sampling_rate
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stop *= self.sampling_rate
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stop *= self.sampling_rate
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# check if boundaries make sense, raise exception otherwise
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if numpy.abs(int(start)-int(stop))<=0:
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raise ValueError("start stop too close: There are no values in the given boundaries!")
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for ch in xrange(len(self.y)):
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if numpy.abs( int( start ) - int( stop ) ) <= 0:
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raise ValueError( "start stop too close: There are no samples in the given boundaries!" )
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# clip the data for each channel
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# TODO multi records
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self.y[ch] = self.y[ch][int(start):int(stop)]
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# TODO what to do with x? Should it start from 0 or from start?
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# self.x = self.x[:int(stop)-int(start)]
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self.x = self.x[int(start):int(stop)]
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for ch in xrange( len( self.y ) ):
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self.y[ ch ] = self.y[ ch ][ int( start ):int( stop ) ]
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self.x = self.x[ int( start ):int( stop ) ]
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return self
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def baseline(self, last_part=0.1):
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def baseline( self, last_part=0.1 ):
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"""
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Correct the baseline of your data by subtracting the mean of the
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last_part fraction of your data.
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@ -59,152 +62,166 @@ class DamarisFFT:
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last_part defaults to 0.1, i.e. last 10% of your data
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"""
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# TODO baselinecorrection for spectra after:
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# TODO baseline correction for spectra after:
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# Heuer, A; Haeberlen, U.: J. Mag. Res.(1989) 85, Is 1, 79-94
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# Should I create an empty object?
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# I deided to do NOT a copy, but
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# rather modify the object
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n = int(self.x.size*last_part)
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for ch in xrange(len(self.y)):
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self.y[ch] -= self.y[ch][-n:].mean()
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# Skip the following due to design reasons
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# new_object.was_copied = True
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n = int( self.x.size * last_part )
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for ch in xrange( len( self.y ) ):
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self.y[ ch ] -= self.y[ ch ][ -n: ].mean( )
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return self
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"""
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Apodization functions:
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* exp_window and gauss_window are S/N enhancing,
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* dexp_window and traf_window are resolution enhancing
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* standard windows [hamming, hanning, bartlett, blackman, kaiser-bessel]
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are also available
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self.x = time points
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elf.aquisition_time = aquisition time (no. samples / sampling_rate)
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line_broadening = line broadening factor (standard = 10 Hz)
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gaussian_multiplicator = Gaussian Multiplication Factor for
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the double exponential apodization
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function (standard = 0.3)
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"""
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def exp_window(self, line_broadening=10):
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def exp_window( self, line_broadening=10 ):
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"""
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Exponential window function
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:param float line_broadening: Applies apodization to time signal
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:param float line_broadening: default 10, line broadening factor in Hz
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.. math::
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\\exp\\left(-\\pi\\cdot \\textsf{line_broadening} \\cdot t\\right)
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"""
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apod = numpy.exp(-self.x*numpy.pi*line_broadening)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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apod = numpy.exp( -self.x * numpy.pi * line_broadening )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def gauss_window(self, line_broadening=10):
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apod = numpy.exp(-(self.x*line_broadening)**2)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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def gauss_window( self, line_broadening=10 ):
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"""
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Gaussian window function
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:param float line_broadening: default 10, line broadening factor in Hz
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.. math:: \\exp\\left(- (\\textsf{line_broadening} \\cdot t)^2\\right)
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"""
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apod = numpy.exp( -(self.x * line_broadening) ** 2 )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def dexp_window(self, line_broadening=-10, gaussian_multiplicator=0.3):
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apod = numpy.exp(-(self.x*line_broadening - gaussian_multiplicator*self.x.max())**2)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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def dexp_window( self, line_broadening=-10, gaussian_multiplicator=0.3 ):
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apod = numpy.exp( -(self.x * line_broadening - gaussian_multiplicator * self.x.max( )) ** 2 )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def traf_window(self, line_broadening=10):
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apod = (numpy.exp(-self.x*line_broadening))**2 / ( (numpy.exp(-self.x*line_broadening))**3
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+ (numpy.exp(-self.x.max()*line_broadening))**3 )
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for i in range(2):
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self.y[i] = self.y[i]*apod
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def traf_window( self, line_broadening=10 ):
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apod = (numpy.exp( -self.x * line_broadening )) ** 2 / ( (numpy.exp( -self.x * line_broadening )) ** 3
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+ (
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numpy.exp( -self.x.max( ) * line_broadening )) ** 3 )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def hanning_window(self):
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apod = numpy.hanning(self.x.size)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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def hanning_window( self ):
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"""
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Symmetric centered window (hanning)
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"""
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apod = numpy.hanning( self.x.size )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def hamming_window(self):
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apod = numpy.hamming(self.x.size)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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def hamming_window( self ):
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"""
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Symmetric centered window (hamming)
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"""
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apod = numpy.hamming( self.x.size )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def blackman_window(self):
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apod = numpy.blackman(self.x.size)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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def blackman_window( self ):
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"""
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Symmetric centered window (blackmann)
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"""
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apod = numpy.blackman( self.x.size )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def bartlett_window(self):
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apod = numpy.bartlett(self.x.size)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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def bartlett_window( self ):
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"""
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Symmetric centered window (bartlett)
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"""
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apod = numpy.bartlett( self.x.size )
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def kaiser_window(self, beta=4, use_scipy=None):
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def kaiser_window( self, beta=4, use_scipy=None ):
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"""
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Symmetric centered window (kaiser)
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"""
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if use_scipy == None:
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# modified Bessel function of zero kind order from somewhere
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def I_0(x):
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i0=0
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fac = lambda n:reduce(lambda a,b:a*(b+1),range(n),1)
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for n in xrange(20):
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i0 += ((x/2.0)**n/(fac(n)))**2
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def I_0( x ):
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i0 = 0
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fac = lambda n: reduce( lambda a, b: a * (b + 1), range( n ), 1 )
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for n in xrange( 20 ):
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i0 += ((x / 2.0) ** n / (fac( n ))) ** 2
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return i0
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t = numpy.arange(self.x.size, type=numpy.Float) - self.x.size/2.0
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t = numpy.arange( self.x.size, type=numpy.Float ) - self.x.size / 2.0
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T = self.x.size
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# this is the window function array
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apod = I_0(beta*numpy.sqrt(1-(2*t/T)**2))/I_0(beta)
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apod = I_0( beta * numpy.sqrt( 1 - (2 * t / T) ** 2 ) ) / I_0( beta )
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else:
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# alternative method using scipy
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import scipy
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apod=scipy.kaiser(self.x.size, beta)
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for i in range(2):
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self.y[i] = self.y[i]*apod
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return self
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apod = scipy.kaiser( self.x.size, beta )
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def autophase(self):
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"""
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works nice with a SNR above 20 dB
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10 V signal height to 1V noise width
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"""
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autophase.get_phase(self)
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for i in range( 2 ):
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self.y[ i ] = self.y[ i ] * apod
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return self
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def fft(self, samples=None):
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def autophase( self ):
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"""
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Fouriertransform the timesignal inplace.
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For "zerofilling" set "samples" to a value higher than your data length.
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Shorten "samples" to truncate your data.
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samples takes only integer values
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Automatically phases the data to maximize real part.
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Works nice with a SNR above 20 dB, i.e.
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10 V signal to 0.1 V noise amplitude.
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"""
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autophase.get_phase( self )
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return self
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def fft( self, samples=None ):
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"""
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Calculate the Fourier transform of the data inplace.
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For zero filling set **samples** to a value higher than your data length,
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smaller values will truncate your data.
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:param int samples: default=None, if given, number of samples returned
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"""
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# Is this smart performance wise? Should I create an empty object?
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# Tests showed that this try except block performed 3.78ms
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# timesignal.baseline().fft()
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# with out this it needed 4.41 ms, thus this is justified :-)
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#try:
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# if self.was_copied:
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# new_object = self
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#except:
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# new_object = self+0
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fft_of_signal = numpy.fft.fft(self.y[0] + 1j*self.y[1], n=samples)
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fft_of_signal = numpy.fft.fftshift(fft_of_signal)
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dwell = 1.0/self.sampling_rate
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fft_of_signal = numpy.fft.fft( self.y[ 0 ] + 1j * self.y[ 1 ], n=samples )
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fft_of_signal = numpy.fft.fftshift( fft_of_signal )
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dwell = 1.0 / self.sampling_rate
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n = fft_of_signal.size
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fft_frequencies = numpy.fft.fftfreq(n, dwell)
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self.x = numpy.fft.fftshift(fft_frequencies)
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self.y[0] = fft_of_signal.real
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self.y[1] = fft_of_signal.imag
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self.set_xlabel("Frequency / Hz")
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fft_frequencies = numpy.fft.fftfreq( n, dwell )
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self.x = numpy.fft.fftshift( fft_frequencies )
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self.y[ 0 ] = fft_of_signal.real
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self.y[ 1 ] = fft_of_signal.imag
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self.set_xlabel( "Frequency / Hz" )
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return self
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def magnitude(self):
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def magnitude( self ):
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"""
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Return absolute signal, i.e.:
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.. math::
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y[0] &= \\sqrt{y[0]^2 + y[1]^2} \\\\
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y[1] &= 0
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"""
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# this should calculate the absolute value, and set the imag channel to zero
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self.y[0] = numpy.sqrt(self.y [0]**2+self.y [1]**2)
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self.y[1] *= 0 #self.y[0].copy()
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self.y[ 0 ] = numpy.sqrt( self.y[ 0 ] ** 2 + self.y[ 1 ] ** 2 )
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self.y[ 1 ] *= 0 # self.y[0].copy()
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return self
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