Updated octave smoothing function; completely different approach
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@ -3,19 +3,46 @@
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"""
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Author: C. Jansen, J.A. de Jong - ASCEE V.O.F.
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Smooth data in the frequency domain. TODO: This function is rather slow as it
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Smooth data in the frequency domain.
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TODO: This function is rather slow as it
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used Python for loops. The implementations should be speed up in the near
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future.
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TODO: check if the smoothing is correct: depending on whether the data points
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are spaced lin of log in frequency, they should be given different weights.
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TODO: accept data that is not equally spaced in frequency
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TODO: output data that is log spaced in frequency
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Cutoff frequencies of window taken from
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http://www.huennebeck-online.de/software/download/src/index.html 15-10-2021
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math --> ReduceSpectrum.c --> ReduceSpectrum::smoothLogXScale()
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fl = fcenter / sqrt(2^(1/Noct)) # lower cutoff
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fu = fcenter * sqrt(2^(1/Noct)) # upper cutoff
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such that:
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sqrt(fl * fu) = fcenter
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fu = 2^(1/Noct) * fl
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Smoothing window taken from
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https://www.ap.com/technical-library/deriving-fractional-octave-spectra-from-
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the-fft-with-apx/ 15-10-2021
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g = sqrt( 1/ ([1+[(f/fm - fm/f)*(1.507*b)]^6]) )
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where b = 3 for 1/3rd octave, f = frequency, fm = mid-band frequency, g = gain.
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Gain is related to magnitude; power is related to gain^2
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"""
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from enum import Enum, unique
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__all__ = ['SmoothingType', 'smoothSpectralData', 'SmoothingWidth']
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from enum import Enum, unique
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import bisect
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import numpy as np
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@unique
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class SmoothingWidth(Enum):
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none = (0, 'No smoothing')
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# three = (3, '1/3th octave smoothing')
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one = (1, '1/1stoctave smoothing')
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two = (2, '1/2th octave smoothing')
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three = (3, '1/3rd octave smoothing')
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six = (6, '1/6th octave smoothing')
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twelve = (12, '1/12th octave smoothing')
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twfo = (24, '1/24th octave smoothing')
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@ -38,6 +65,7 @@ class SmoothingWidth(Enum):
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def getCurrent(cb):
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return list(SmoothingWidth)[cb.currentIndex()]
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class SmoothingType:
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levels = 'l', 'Levels'
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# tf = 'tf', 'Transfer function',
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@ -48,9 +76,6 @@ class SmoothingType:
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# TO DO: add possibility to insert data that is not lin spaced in frequency
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import numpy as np
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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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@ -77,13 +102,14 @@ def smoothSpectralData(freq, M, sw: SmoothingWidth,
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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
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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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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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if Noct < 1:
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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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if st == SmoothingType.ps:
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assert np.min(M) >= 0, 'absolute magnitude M cannot be negative'
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@ -93,108 +119,217 @@ def smoothSpectralData(freq, M, sw: SmoothingWidth,
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# Initialize
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L = M.shape[0] # number of data points
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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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P = 10**(M/10) # magnitude [dB] --> power
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else:
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P = M # data already given as power
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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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# 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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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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# 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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# 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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# 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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# Create window
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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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# 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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# Implicitly, the window is truncated in this implementation, because
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# of the bisect search
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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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xl = bisect.bisect_left(f, fl) # index corresponding to fl
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xu = bisect.bisect_left(f, fu)
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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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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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# 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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# 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 = f[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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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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Psm[x] = np.dot(g, P[xl:xu])
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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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""" Test function for evaluation and debugging
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Note: make a distinction between lin and log spaced (in frequency) data
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points. They should be treated and weighted differently.
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"""
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import matplotlib.pyplot as plt
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# Initialize
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Noct = 6 # 1/6 oct. smoothing
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Noct = 6 # Noct = 6 for 1/6 oct. smoothing
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# Create dummy data
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fmin = 3e3 # [Hz] min freq
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# Create dummy data set 1: noise
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fmin = 3e3 # [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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Ndata = 200 # number of data points
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f = np.linspace(fmin, fmax, Ndata) # frequency points
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M = abs(1+0.4*np.random.normal(size=(Ndata,)))+0.01 #
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dB = False
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M = 20*np.log10(M)
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dB = True
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# M = f+1 # magnitude
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# dB = False # True if M is given in dB
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# # Create dummy data set 2: dirac delta
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# fmin = 3e3 # [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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# f = np.linspace(fmin, fmax, Ndata) # frequency points
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# M = 0 * abs(1+0.4*np.random.normal(size=(Ndata,))) + 0.01 #
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# M[int(Ndata/5)] = 1
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# M = 20*np.log10(M)
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# Apply function
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Msm = oct_smooth(f, M, Noct, dB)
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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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Msm = smoothSpectralData(f, M, sw, st)
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fsm = f
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# Plot
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# Plot - lin frequency
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plt.figure()
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# plt.semilogx(f, M, '.b')
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# plt.semilogx(fsm, Msm, 'r')
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plt.plot(f, M, '.b')
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plt.plot(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('lin frequency')
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# Plot - log frequency
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plt.figure()
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plt.semilogx(f, M, '.b')
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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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