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Merge remote-tracking branch 'origin/develop' into develop
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Anne de Jong 2023-03-10 15:44:48 +01:00
commit 2b22af5d2c
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77
src/lasp/filter/biquad.py
View File

@ -23,11 +23,11 @@ y[n] = 1/ba[3] * ( ba[0] * x[n] + ba[1] * x[n-1] + ba[2] * x[n-2] +
"""
__all__ = ['peaking', 'biquadTF', 'notch', 'lowpass', 'highpass',
'highshelf', 'lowshelf']
'highshelf', 'lowshelf', 'LPcompensator', 'HPcompensator']
from numpy import array, cos, pi, sin, sqrt
from scipy.interpolate import interp1d
from scipy.signal import sosfreqz
from scipy.signal import sosfreqz, bilinear_zpk, zpk2sos
def peaking(fs, f0, Q, gain):
@ -157,6 +157,79 @@ def lowshelf(fs, f0, Q, gain):
a2 = (A+1) + (A-1)*cos(w0) - 2*sqrt(A)*alpha
return array([b0/a0, b1/a0, b2/a0, a0/a0, a1/a0, a2/a0])
def LPcompensator(fs, f0o, Qo, f0n, Qn):
"""
Shelving type filter that, when multiplied with a second-order low-pass
filter, alters the response of that filter to a different second-order
low-pass filter.
Args:
fs: Sampling frequency [Hz]
f0o: Cut-off frequency of the original filter [Hz]
Qo: Quality factor of the original filter (~inverse of bandwidth)
f0n: Desired cut-off frequency [Hz]
Qn: Desired quality factor(~inverse of bandwidth)
"""
omg0o = 2*pi*f0o
omg0n = 2*pi*f0n
zRe = omg0o/(2*Qo)
zIm = omg0o*sqrt(1-1/(4*Qo**2))
z1 = -zRe + zIm*1j
z2 = -zRe - zIm*1j
pRe = omg0n/(2*Qn)
pIm = omg0n*sqrt(1-1/(4*Qn**2))
p1 = -pRe + pIm*1j
p2 = -pRe - pIm*1j
z= [z1, z2]
p = [p1, p2]
k = (pRe**2 + pIm**2)/(zRe**2 + zIm**2)
zd, pd, kd = bilinear_zpk(z, p, k, fs)
sos = zpk2sos(zd,pd,kd)
return sos[0]
def HPcompensator(fs, f0o, Qo, f0n, Qn):
"""
Shelving type filter that, when multiplied with a second-order high-pass
filter, alters the response of that filter to a different second-order
high-pass filter.
Args:
fs: Sampling frequency [Hz]
f0o: Cut-on frequency of the original filter [Hz]
Qo: Quality factor of the original filter (~inverse of bandwidth)
f0n: Desired cut-on frequency [Hz]
Qn: Desired quality factor(~inverse of bandwidth)
"""
omg0o = 2*pi*f0o
omg0n = 2*pi*f0n
zRe = omg0o/(2*Qo)
zIm = omg0o*sqrt(1-1/(4*Qo**2))
z1 = -zRe + zIm*1j
z2 = -zRe - zIm*1j
pRe = omg0n/(2*Qn)
pIm = omg0n*sqrt(1-1/(4*Qn**2))
p1 = -pRe + pIm*1j
p2 = -pRe - pIm*1j
z= [z1, z2]
p = [p1, p2]
k = 1
zd, pd, kd = bilinear_zpk(z, p, k, fs)
sos = zpk2sos(zd,pd,kd)
return sos[0]
def biquadTF(fs, freq, sos):
"""

179
src/lasp/tools/tools.py
View File

@ -1,41 +1,25 @@
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Author: C. Jansen, J.A. de Jong - ASCEE V.O.F.
Author: T. Hekman, C. Jansen, J.A. de Jong - ASCEE V.O.F.
Smooth data in the frequency domain.
TODO: This function is rather slow as it
used Python for loops. The implementations should be speed up in the near
future.
TODO: check if the smoothing is correct: depending on whether the data points
are spaced lin of log in frequency, they should be given different weights.
TODO: accept data that is not equally spaced in frequency
TODO: output data that is log spaced in frequency
Cutoff frequencies of window taken from
http://www.huennebeck-online.de/software/download/src/index.html 15-10-2021
math --> ReduceSpectrum.c --> ReduceSpectrum::smoothLogXScale()
fl = fcenter / sqrt(2^(1/Noct)) # lower cutoff
fu = fcenter * sqrt(2^(1/Noct)) # upper cutoff
such that:
sqrt(fl * fu) = fcenter
fu = 2^(1/Noct) * fl
Smoothing window taken from
https://www.ap.com/technical-library/deriving-fractional-octave-spectra-from-
the-fft-with-apx/ 15-10-2021
g = sqrt( 1/ ([1+[(f/fm - fm/f)*(1.507*b)]^6]) )
where b = 3 for 1/3rd octave, f = frequency, fm = mid-band frequency, g = gain.
Gain is related to magnitude; power is related to gain^2
TODO: This function is rather slow as it uses [for loops] in Python. Speed up.
NOTE: function requires lin frequency spaced input data
TODO: accept input data that is not lin spaced in frequency
TODO: it makes more sense to output data that is log spaced in frequency
TODO: Make SmoothSpectralData() multi-dimensional array aware.
TODO: Smoothing does not work due to complex numbers. Is it reasonable to
smooth complex data? If so, the data could be split in magnitude and phase.
"""
__all__ = ['SmoothingType', 'smoothSpectralData', 'SmoothingWidth']
from enum import Enum, unique
import bisect
import copy
import numpy as np
from numpy import log2, pi, sin
@unique
@ -76,6 +60,22 @@ class SmoothingType:
# TO DO: check if everything is correct
# TO DO: add possibility to insert data that is not lin spaced in frequency
# Integrated Hann window
def intHann(x1, x2):
"""
Calculate integral of (part of) Hann window.
If the args are vectors, the return value will match those.
Args:
x1: lower bound [-0.5, 0.5]
x2: upper bound [-0.5, 0.5]
Return:
Integral of Hann window between x1 and x2
"""
x1 = np.clip(x1, -0.5, 0.5)
x2 = np.clip(x2, -0.5, 0.5)
return (sin(2*pi*x2) - sin(2*pi*x1))/(2*pi) + (x2-x1)
def smoothCalcMatrix(freq, sw: SmoothingWidth):
@ -86,58 +86,68 @@ def smoothCalcMatrix(freq, sw: SmoothingWidth):
Returns:
freq: array frequencies of data points [Hz]
Q: matrix to smooth power: {fsm} = [Q] * {fraw}
Q: matrix to smooth, power: {fsm} = [Q] * {fraw}
Warning: this method does not work on levels (dB)
According to Tylka_JAES_SmoothingWeights.pdf
"A Generalized Method for Fractional-Octave Smoothing of Transfer Functions
that Preserves Log-Frequency Symmetry"
https://doi.org/10.17743/jaes.2016.0053
par 1.3
eq. 16
"""
# Settings
tr = 2 # truncate window after 2x std; shorter is faster and less accurate
Noct = sw.value[0]
assert Noct > 0, "'Noct' must be absolute positive"
assert np.isclose(freq[-1]-freq[-2], freq[1]-freq[0]), "Input data must "\
"have a linear frequency spacing"
if Noct < 1:
raise Warning('Check if \'Noct\' is entered correctly')
# Initialize
L = len(freq)
Q = np.zeros(shape=(L, L), dtype=np.float16) # float16: keep size small
Q[0, 0] = 1 # in case first point is skipped
x0 = 1 if freq[0] == 0 else 0 # skip first data point if zero frequency
x0 = 1 if freq[0] == 0 else 0 # Skip first data point if zero frequency
# Loop over indices of raw frequency vector
for x in range(x0, L):
# Find indices of data points to calculate current (smoothed) magnitude
#
# Indices beyond [0, L] point to non-existing data. Beyond 0 does not
# occur in this implementation. Beyond L occurs when the smoothing
# window nears the end of the series.
# If one end of the window is truncated, the other end
# could be truncated as well, to prevent an error on magnitude data
# with a slope. It however results in unsmoothed looking data at the
# end.
fc = freq[x] # center freq. of smoothing window
fl = fc / np.sqrt(2**(tr/Noct)) # lower cutoff
fu = fc * np.sqrt(2**(tr/Noct)) # upper cutoff
Noct /= 2 # corr. factor: window @ -3dB at Noct bounds (Noct/1.5 for -6dB)
ifreq = freq/(freq[1]-freq[0]) # frequency, normalized to step=1
ifreq = np.array(ifreq.astype(int))
ifreqMin = ifreq[x0] # min. freq, normalized to step=1
ifreqMax = ifreq[L-1] # max. freq, normalized to step=1
sfact = 2**((1/Noct)/2) # bounds are this factor from the center freq
# If the upper (frequency) side of the window is truncated because
# there is no data beyond the Nyquist frequency, also truncate the
# other side to keep it symmetric in a log(frequency) scale.
# So: fu / fc = fc / fl
fNq = freq[-1]
if fu > fNq:
fu = fNq # no data beyond fNq
fl = fc**2 / fu # keep window symmetric
kpmin = np.floor(ifreq/sfact).astype(int) # min freq of window
kpmax = np.ceil(ifreq*sfact).astype(int) # max freq of window
# Find indices corresponding to frequencies
xl = bisect.bisect_left(freq, fl) # index corresponding to fl
xu = bisect.bisect_left(freq, fu)
for ff in range(x0, L): # loop over input freq
# Find window bounds and actual smoothing width
# Keep window symmetrical if one side is truncated
if kpmin[ff] < ifreqMin:
kpmin[ff] = ifreqMin
kpmax[ff] = np.ceil(ifreq[ff]**2/ifreqMin) # decrease smooth width
if np.isclose(kpmin[ff], kpmax[ff]):
kpmax[ff] += 1
NoctAct = 1/log2(kpmax[ff]/kpmin[ff])
elif kpmax[ff] > ifreqMax:
kpmin[ff] = np.floor(ifreq[ff]**2/ifreqMax) # decrease smoothwidth
kpmax[ff] = ifreqMax
if np.isclose(kpmin[ff], kpmax[ff]):
kpmin[ff] -= 1
NoctAct = 1/log2(kpmax[ff]/kpmin[ff])
else:
NoctAct = Noct
xl = xu-1 if xu-xl <= 0 else xl # Guarantee window length of at least 1
kp = np.arange(kpmin[ff], kpmax[ff]+1) # freqs of window
Phi1 = log2((kp - 0.5)/ifreq[ff]) * NoctAct # integr. bounds Hann wind
Phi2 = log2((kp + 0.5)/ifreq[ff]) * NoctAct
W = intHann(Phi1, Phi2) # smoothing window
Q[ff, kpmin[ff]-ifreq[0]:kpmax[ff]-ifreq[0]+1] = W
# Calculate window
xg = np.arange(xl, xu) # indices
fg = freq[xg] # [Hz] corresponding freq
gs = np.sqrt( 1/ ((1+((fg/fc - fc/fg)*(1.507*Noct))**6)) ) # raw windw
gs /= np.sum(gs) # normalize: integral=1
Q[x, xl:xu] = gs # add to matrix
# Normalize to conserve input power
Qpower = np.sum(Q, axis=0)
Q = Q / Qpower[np.newaxis, :]
return Q
@ -145,57 +155,40 @@ def smoothCalcMatrix(freq, sw: SmoothingWidth):
def smoothSpectralData(freq, M, sw: SmoothingWidth,
st: SmoothingType = SmoothingType.levels):
"""
Apply fractional octave smoothing to magnitude data in frequency domain.
Smoothing is performed to power, using a sliding Gaussian window with
variable length. The window is truncated after 2x std at either side.
The implementation is not exact, because f is linearly spaced and
fractional octave smoothing is related to log spaced data. In this
implementation, the window extends with a fixed frequency step to either
side. The deviation is largest when Noct is small (e.g. coarse smoothing).
Casper Jansen, 07-05-2021
Update 16-01-2023: speed up algorithm
- Smoothing is performed using matrix multiplication
- The smoothing matrix is not calculated if it already exists
Apply fractional octave smoothing to data in the frequency domain.
Args:
freq: array of frequencies of data points [Hz] - equally spaced
M: array of either power, transfer functin or dB points. Depending on
M: array of data, either power or dB
the smoothing type `st`, the smoothing is applied.
sw: smoothing width
st: smoothing type = data type of input data
Returns:
freq : array frequencies of data points [Hz]
Msm : float smoothed magnitude of data points
"""
# TODO: Make this function multi-dimensional array aware.
# Safety
MM = copy.deepcopy(M)
Noct = sw.value[0]
assert len(M) > 0, "Smoothing function: input array is empty" # not sure if this works
assert len(MM) > 0, "Smoothing function: input array is empty" # not sure if this works
assert Noct > 0, "'Noct' must be absolute positive"
if Noct < 1:
raise Warning('Check if \'Noct\' is entered correctly')
assert len(freq) == len(M), 'f and M should have equal length'
assert len(freq) == len(MM), "f and M should have equal length"
# if st == SmoothingType.ps:
# assert np.min(M) >= 0, 'absolute magnitude M cannot be negative'
if st == SmoothingType.levels and isinstance(M.dtype, complex):
if st == SmoothingType.ps:
assert np.min(MM) >= 0, 'Power spectrum values cannot be negative'
if st == SmoothingType.levels and isinstance(MM.dtype, complex):
raise RuntimeError('Decibel input should be real-valued')
# Initialize
L = M.shape[0] # number of data points
# Convert to power
if st == SmoothingType.levels:
P = 10**(MM/10) # magnitude [dB] --> power
P = 10**(MM/10)
elif st == SmoothingType.ps:
P = MM
else:
P = MM # data already given as power
# TODO: This does not work due to complex numbers. Should be split up in
# magnitude and phase.
# elif st == SmoothingType.tf:
# P = P**2
raise RuntimeError(f"Incorrect SmoothingType: {st}")
# P is power while smoothing. x are indices of P.
Psm = np.zeros_like(P) # Smoothed power - to be calculated
@ -221,6 +214,7 @@ def smoothSpectralData(freq, M, sw: SmoothingWidth,
# Apply smoothing
Psm = np.matmul(Q, P)
# Convert to original format
if st == SmoothingType.levels:
Psm = 10*np.log10(Psm)
@ -243,7 +237,8 @@ if __name__ == "__main__":
fmax = 24e3 # [Hz] max freq
Ndata = 200 # number of data points
freq = np.linspace(fmin, fmax, Ndata) # frequency points
M = abs(0.4*np.random.normal(size=(Ndata,)))+0.01 #
# freq = np.hstack((0, freq))
M = abs(0.4*np.random.normal(size=(len(freq),)))+0.01 #
M = 20*np.log10(M)
# # Create dummy data set 2: dirac delta