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@ -34,8 +34,11 @@ __all__ = ['SmoothingType', 'smoothSpectralData', 'SmoothingWidth']
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from enum import Enum, unique
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import bisect
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import codecs
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import copy
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import json
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import numpy as np
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import os
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@unique
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@ -78,6 +81,72 @@ class SmoothingType:
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# TO DO: add possibility to insert data that is not lin spaced in frequency
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def smoothCalcMatrix(freq, sw: SmoothingWidth):
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"""
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Args:
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freq: array of frequencies of data points [Hz] - equally spaced
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sw: SmoothingWidth
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Returns:
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freq: array frequencies of data points [Hz]
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Q: matrix to smooth power: {fsm} = [Q] * {fraw}
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Warning: this method does not work on levels (dB)
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"""
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# Settings
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tr = 2 # truncate window after 2x std; shorter is faster and less accurate
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Noct = sw.value[0]
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assert Noct > 0, "'Noct' must be absolute positive"
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if Noct < 1:
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raise Warning('Check if \'Noct\' is entered correctly')
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# Initialize
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L = len(freq)
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Q = np.zeros(shape=(L, L))
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x0 = 1 if freq[0] == 0 else 0 # Skip first data point if zero frequency
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# Loop over indices of raw frequency vector
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for x in range(x0, L):
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# Find indices of data points to calculate current (smoothed) magnitude
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#
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# Indices beyond [0, L] point to non-existing data. Beyond 0 does not
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# occur in this implementation. Beyond L occurs when the smoothing
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# window nears the end of the series.
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# If one end of the window is truncated, the other end
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# could be truncated as well, to prevent an error on magnitude data
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# with a slope. It however results in unsmoothed looking data at the
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# end.
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fc = freq[x] # center freq. of smoothing window
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fl = fc / np.sqrt(2**(tr/Noct)) # lower cutoff
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fu = fc * np.sqrt(2**(tr/Noct)) # upper cutoff
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# If the upper (frequency) side of the window is truncated because
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# there is no data beyond the Nyquist frequency, also truncate the
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# other side to keep it symmetric in a log(frequency) scale.
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# So: fu / fc = fc / fl
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fNq = freq[-1]
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if fu > fNq:
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fu = fNq # no data beyond fNq
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fl = fc**2 / fu # keep window symmetric
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# Find indices corresponding to frequencies
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xl = bisect.bisect_left(freq, fl) # index corresponding to fl
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xu = bisect.bisect_left(freq, fu)
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xl = xu-1 if xu-xl <= 0 else xl # Guarantee window length of at least 1
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# Calculate window
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gs = np.zeros(xu-xl)
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for n, xi in enumerate(range(xl, xu)):
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fi = freq[xi] # current frequency
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gs[n] = np.sqrt( 1/ ((1+((fi/fc - fc/fi)*(1.507*Noct))**6)) )
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gs /= np.sum(gs) # normalize: integral=1
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Q[x, xl:xu] = gs # add to matrix
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return Q
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def smoothSpectralData(freq, M, sw: SmoothingWidth,
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st: SmoothingType = SmoothingType.levels):
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"""
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@ -91,6 +160,10 @@ def smoothSpectralData(freq, M, sw: SmoothingWidth,
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side. The deviation is largest when Noct is small (e.g. coarse smoothing).
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Casper Jansen, 07-05-2021
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Update 16-01-2023: speed up algorithm
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- Smoothing is performed using matrix multiplication
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- The smoothing matrix is not calculated if it already exists
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Args:
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freq: array of frequencies of data points [Hz] - equally spaced
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M: array of either power, transfer functin or dB points. Depending on
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@ -103,9 +176,6 @@ def smoothSpectralData(freq, M, sw: SmoothingWidth,
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"""
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# TODO: Make this function multi-dimensional array aware.
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# Settings
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tr = 2 # truncate window after 2x std; shorter is faster and less accurate
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# Safety
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MM = copy.deepcopy(M)
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Noct = sw.value[0]
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@ -134,169 +204,40 @@ def smoothSpectralData(freq, M, sw: SmoothingWidth,
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# P is power while smoothing. x are indices of P.
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Psm = np.zeros_like(P) # Smoothed power - to be calculated
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x0 = 1 if freq[0] == 0 else 0 # Skip first data point if zero frequency
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Psm[0] = P[0] # Reuse old value in case first data..
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if freq[0] == 0:
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Psm[0] = P[0] # Reuse old value in case first data..
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# ..point is skipped. Not plotted any way.
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# Loop through data points
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for x in range(x0, L):
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# Find indices of data points to calculate current (smoothed) magnitude
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#
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# Indices beyond [0, L] point to non-existing data. Beyond 0 does not
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# occur in this implementation. Beyond L occurs when the smoothing
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# window nears the end of the series.
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# If one end of the window is truncated, the other end
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# could be truncated as well, to prevent an error on magnitude data
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# with a slope. It however results in unsmoothed looking data at the
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# end.
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fc = freq[x] # center freq. of smoothing window
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fl = fc / np.sqrt(2**(tr/Noct)) # lower cutoff
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fu = fc * np.sqrt(2**(tr/Noct)) # upper cutoff
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# Find smoothing matrix. Look it up, otherwise calculate and store.
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fname = 'smoothing_tables.json' # storage file
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nfft = int(2*(len(freq)-1))
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key = f"nfft{nfft}_Noct{Noct}" # name
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if os.path.isfile(fname):
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with open(fname) as f:
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Qdict = json.load(f)
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else:
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Qdict = {'Help': 'This file contains smoothing tables'}
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json.dump(Qdict, codecs.open(fname, 'w', encoding='utf-8'),
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separators=(',', ':'), sort_keys=True, indent=4)
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# If the upper (frequency) side of the window is truncated because
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# there is no data beyond the Nyquist frequency, also truncate the
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# other side to keep it symmetric in a log(frequency) scale.
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# So: fu / fc = fc / fl
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fNq = freq[-1]
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if fu > fNq:
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fu = fNq # no data beyond fNq
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fl = fc**2 / fu # keep window symmetric
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if key in Qdict:
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# Load = fast
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Q = np.asarray(Qdict[key])
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else:
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# Calculate new matrix; store
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Q = smoothCalcMatrix(freq, sw)
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Qdict[key] = Q.tolist() # json cannot handle ndarray
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json.dump(Qdict, codecs.open(fname, 'w', encoding='utf-8'),
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separators=(',', ':'), sort_keys=True, indent=4)
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# Find indices corresponding to frequencies
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xl = bisect.bisect_left(freq, fl) # index corresponding to fl
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xu = bisect.bisect_left(freq, fu)
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# Guarantee window length of at least 1
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if xu - xl <= 0:
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xl = xu - 1
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# Calculate window
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g = np.zeros(xu-xl)
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for n, xi in enumerate(range(xl, xu)):
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fi = freq[xi] # current frequency
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g[n] = np.sqrt( 1/ ((1+((fi/fc - fc/fi)*(1.507*Noct))**6)) )
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g /= np.sum(g) # normalize: integral=1
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# Apply smoothing
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Psm[x] = np.dot(g, P[xl:xu])
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# Apply smoothing
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Psm = np.matmul(Q, P)
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if st == SmoothingType.levels:
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Psm = 10*np.log10(Psm)
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return Psm
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## OLD VERSION
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#from scipy.signal.windows import gaussian
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#def smoothSpectralData(freq, M, sw: SmoothingWidth,
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# st: SmoothingType = SmoothingType.levels):
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# """
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# Apply fractional octave smoothing to magnitude data in frequency domain.
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# Smoothing is performed to power, using a sliding Gaussian window with
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# variable length. The window is truncated after 2x std at either side.
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#
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# The implementation is not exact, because f is linearly spaced and
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# fractional octave smoothing is related to log spaced data. In this
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# implementation, the window extends with a fixed frequency step to either
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# side. The deviation is largest when Noct is small (e.g. coarse smoothing).
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# Casper Jansen, 07-05-2021
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#
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# Args:
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# freq: array of frequencies of data points [Hz] - equally spaced
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# M: array of either power, transfer functin or dB points. Depending on
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# the smoothing type `st`, the smoothing is applied.
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#
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# Returns:
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# freq : array frequencies of data points [Hz]
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# Msm : float smoothed magnitude of data points
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#
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# """
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# # TODO: Make this function multi-dimensional array aware.
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#
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# # Settings
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# tr = 2 # truncate window after 2x std; shorter is faster and less accurate
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#
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# # Safety
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# Noct = sw.value[0]
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# assert Noct > 0, "'Noct' must be absolute positive"
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# if Noct < 1: raise Warning('Check if \'Noct\' is entered correctly')
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# assert len(freq)==len(M), 'f and M should have equal length'
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#
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# if st == SmoothingType.ps:
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# assert np.min(M) >= 0, 'absolute magnitude M cannot be negative'
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# if st == SmoothingType.levels and isinstance(M.dtype, complex):
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# raise RuntimeError('Decibel input should be real-valued')
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#
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# # Initialize
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# L = M.shape[0] # number of data points
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#
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# P = M
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# if st == SmoothingType.levels:
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# P = 10**(P/10)
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# # TODO: This does not work due to complex numbers. Should be split up in
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# # magnitude and phase.
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# # elif st == SmoothingType.tf:
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# # P = P**2
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#
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# # P is power while smoothing. x are indices of P.
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# Psm = np.zeros_like(P) # Smoothed power - to be calculated
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# x0 = 1 if freq[0]==0 else 0 # Skip first data point if zero frequency
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# Psm[0] = P[0] # Reuse old value in case first data..
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# # ..point is skipped. Not plotted any way.
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# df = freq[1] - freq[0] # Frequency step
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#
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# # Loop through data points
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# for x in range(x0, L):
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# # Find indices of data points to calculate current (smoothed) magnitude
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# fc = freq[x] # center freq. of smoothing window
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# Df = tr * fc / Noct # freq. range of smoothing window
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#
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# # desired lower index of frequency array to be used during smoothing
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# xl = int(np.ceil(x - 0.5*Df/df))
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#
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# # upper index + 1 (because half-open interval)
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# xu = int(np.floor(x + 0.5*Df/df)) + 1
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#
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# # Create window, suitable for frequency lin-spaced data points
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# Np = xu - xl # number of points
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# std = Np / (2 * tr)
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# wind = gaussian(Np, std) # Gaussian window
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#
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# # Clip indices to valid range
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# #
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# # Indices beyond [0, L] point to non-existing data. This occurs when
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# # the smoothing windows nears the beginning or end of the series.
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# # Optional: if one end of the window is clipped, the other end
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# # could be clipped as well, to prevent an error on magnitude data with
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# # a slope. It however results in unsmoothed looking data at the ends.
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# if xl < 0:
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# rl = 0 - xl # remove this number of points at the lower end
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# xl = xl + rl # .. from f
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# wind = wind[rl:] # .. and from window
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#
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# # rl = 0 - xl # remove this number of points at the lower end
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# # xl = xl + rl # .. from f
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# # xu = xu - rl
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# # wind = wind[rl:-rl] # .. and from window
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#
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# if xu > L:
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# ru = xu - L # remove this number of points at the upper end
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# xu = xu - ru
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# wind = wind[:-ru]
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#
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# # ru = xu - L # remove this number of points at the upper end
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# # xl = xl + ru
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# # xu = xu - ru
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# # wind = wind[ru:-ru]
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#
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# # Apply smoothing
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# wind_int = np.sum(wind) # integral
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# Psm[x] = np.dot(wind, P[xl:xu]) / wind_int # apply window
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#
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# if st == SmoothingType.levels:
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# Psm = 10*np.log10(Psm)
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#
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# return Psm
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# %% Test
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if __name__ == "__main__":
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@ -310,7 +251,7 @@ if __name__ == "__main__":
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Noct = 2 # Noct = 6 for 1/6 oct. smoothing
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# Create dummy data set 1: noise
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fmin = 3e3 # [Hz] min freq
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fmin = 1e3 # [Hz] min freq
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fmax = 24e3 # [Hz] max freq
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Ndata = 200 # number of data points
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freq = np.linspace(fmin, fmax, Ndata) # frequency points
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@ -330,10 +271,13 @@ if __name__ == "__main__":
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class sw:
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value = [Noct]
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st = SmoothingType.levels # so data is given in dB
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# st = SmoothingType.ps # so data is given in power
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# Smooth
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Msm = smoothSpectralData(freq, M, sw, st)
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fsm = freq
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# Plot - lin frequency
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plt.figure()
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plt.plot(freq, M, '.b')
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@ -342,12 +286,14 @@ if __name__ == "__main__":
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plt.ylabel('magnitude')
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plt.xlim([100, fmax])
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plt.title('lin frequency')
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plt.legend(['Raw', 'Smooth'])
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# Plot - log frequency
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plt.figure()
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plt.semilogx(freq, M, '.b')
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plt.semilogx(fsm, Msm, 'r')
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plt.semilogx(fsm, Msm, 'r')
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plt.xlabel('f (Hz)')
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plt.ylabel('magnitude')
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plt.xlim([100, fmax])
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plt.title('log frequency')
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plt.legend(['Raw', 'Smooth 1'])
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