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Musings about the peakdetect functions by Sixten Bergman | |
Note that this code should work with both python 2.7 and python3.x. | |
All the peak detection functions in __all__ of peakdetect.py will work on | |
consistent waveforms, but only peakdetect.peakdetect can properly handle | |
offsets. | |
The most accurate method for pure sine seems to be peakdetect_parabola, | |
which for a 50Hz sine wave lasting 0.1s with 10k samples has an error in | |
the order of 1e-10, whilst a naive most extreme sample will have an error | |
in the order of 7e-5 for the position and 4e-7 for the amplitude | |
Do note that this accuracy most likely doesn't stay true for any real world | |
data where you'll have noise and harmonics in the signal which may produce | |
errors in the functions, which may be smaller or larger then the error of | |
naively using the highest/lowest point in a local maxima/minima. | |
The sine fit function seem to perform even worse than a just retrieving the | |
highest or lowest data point and is as such not recommended. The reason for | |
this as far as I can tell is that the scipy.optimize.curve_fit can't optimize | |
the variables. | |
For parabola fit to function well, it must be fitted to a small section of the | |
peak as the curvature will start to mismatch with the function, but this also | |
means that the parabola should be quite sensitive to noise | |
FFT interpolation has between 0 to 2 orders of magnitude improvement over a | |
raw peak fit. To obtain this improvement the wave needs to be heavily padded | |
in length | |
Spline seems to have similar performance to a FFT interpolation of the time | |
domain. Spline does however seem to be better at estimating amplitude than the | |
FFT method, but is unknown if this will hold true for wave-shapes that are | |
noisy. | |
It should also be noted that the errors as given in "Missmatch data.txt" | |
generated by the test routine are for pure functions with no noise, so the only | |
error being reduced by the "non-raw" peakdetect functions are errors stemming | |
low time resolution and are in no way an indication of how the functions can | |
handle any kind of noise that real signals will have. | |
Automatic tests for sine fitted peak detection is disabled due to it's problems | |
Avoid using the following functions as they're questionable in performance: | |
peakdetect_sine | |
peakdetect_sine_locked |
#!/usr/bin/python2 | |
# Copyright (C) 2016 Sixten Bergman | |
# License WTFPL | |
# | |
# This program is free software. It comes without any warranty, to the extent | |
# permitted by applicable law. | |
# You can redistribute it and/or modify it under the terms of the Do What The | |
# Fuck You Want To Public License, Version 2, as published by Sam Hocevar. See | |
# http://www.wtfpl.net/ for more details. | |
# | |
import numpy as np | |
from math import pi, sqrt | |
__all__ = [ | |
'ACV_A1', | |
'ACV_A2', | |
'ACV_A3', | |
'ACV_A4', | |
'ACV_A5', | |
'ACV_A6', | |
'ACV_A7', | |
'ACV_A8' | |
] | |
#Heavyside step function | |
H_num = lambda t: 1 if t > 0 else 0 | |
H = lambda T: np.asarray([1 if t > 0 else 0 for t in T]) | |
# pure sine | |
def ACV_A1(T, Hz=50): | |
""" | |
Generate a pure sine wave at a specified frequency | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
T = np.asarray(T, dtype=np.float64) | |
return ampl * sqrt(2) * np.sin(2*pi*Hz * T) | |
def ACV_A2(T, Hz=50): | |
""" | |
Generate a pure sine wave with a DC offset at a specified frequency | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
offset = 500 | |
T = np.asarray(T, dtype=np.float64) | |
return ampl * sqrt(2) * np.sin(2*pi*Hz * T) + offset | |
def ACV_A3(T, Hz=50): | |
""" | |
Generate a fundamental with a 3rd overtone | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
T = np.asarray(T, dtype=np.float64) | |
main_wave = np.sin(2*pi*Hz * T) | |
harmonic_wave = 0.05 * np.sin(2*pi*Hz * T * 4 + pi * 2 / 3) | |
return ampl * sqrt(2) * (main_wave + harmonic_wave) | |
def ACV_A4(T, Hz=50): | |
""" | |
Generate a fundamental with a 4th overtone | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
T = np.asarray(T, dtype=np.float64) | |
main_wave = np.sin(2*pi*Hz * T) | |
harmonic_wave = 0.07 * np.sin(2*pi*Hz * T * 5 + pi * 22 / 18) | |
return ampl * sqrt(2) * (main_wave + harmonic_wave) | |
def ACV_A5(T, Hz=50): | |
""" | |
Generate a realistic triangle wave | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
T = np.asarray(T, dtype=np.float64) | |
wave_1 = np.sin(2*pi*Hz * T) | |
wave_2 = 0.05 * np.sin(2*pi*Hz * T * 3 - pi) | |
wave_3 = 0.05 * np.sin(2*pi*Hz * T * 5) | |
wave_4 = 0.02 * np.sin(2*pi*Hz * T * 7 - pi) | |
wave_5 = 0.01 * np.sin(2*pi*Hz * T * 9) | |
return ampl * sqrt(2) * (wave_1 + wave_2 + wave_3 + wave_4 + wave_5) | |
def ACV_A6(T, Hz=50): | |
""" | |
Generate a realistic triangle wave | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
T = np.asarray(T, dtype=np.float64) | |
wave_1 = np.sin(2*pi*Hz * T) | |
wave_2 = 0.02 * np.sin(2*pi*Hz * T * 3 - pi) | |
wave_3 = 0.02 * np.sin(2*pi*Hz * T * 5) | |
wave_4 = 0.0015 * np.sin(2*pi*Hz * T * 7 - pi) | |
wave_5 = 0.009 * np.sin(2*pi*Hz * T * 9) | |
return ampl * sqrt(2) * (wave_1 + wave_2 + wave_3 + wave_4 + wave_5) | |
def ACV_A7(T, Hz=50): | |
""" | |
Generate a growing sine wave, where the wave starts at 0 and reaches 0.9 of | |
full amplitude at 250 cycles. Thereafter it will linearly increase to full | |
amplitude at 500 cycles and terminate to 0 | |
Frequency locked to 50Hz and = 0 at t>10 | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
Hz = 50 | |
T = np.asarray(T, dtype=np.float64) | |
wave_main = np.sin(2*pi*Hz * T) | |
step_func = (0.9 * T / 5 * H(5-T) + H(T-5) * H(10-T) * (0.9 + 0.1 * (T-5) / 5)) | |
return ampl * sqrt(2) * wave_main * step_func | |
def ACV_A8(T, Hz=50): | |
""" | |
Generate a growing sine wave, which reaches 100 times the amplitude at | |
500 cycles | |
frequency not implemented and signal = 0 at t>1000*pi | |
signal frequency = 0.15915494309189535 Hz? | |
keyword arguments: | |
T -- time points to generate the waveform given in seconds | |
Hz -- The desired frequency of the signal (default:50) | |
""" | |
ampl = 1000 | |
Hz = 50 | |
T = np.asarray(T, dtype=np.float64) | |
wave_main = np.sin(T) | |
step_func = T / (10 * pi) * H(10 - T / (2*pi*Hz)) | |
return ampl * sqrt(2) * wave_main * step_func | |
_ACV_A1_L = lambda T, Hz = 50: 1000 * sqrt(2) * np.sin(2*pi*Hz * T) | |
# | |
_ACV_A2_L = lambda T, Hz = 50: 1000 * sqrt(2) * np.sin(2*pi*Hz * T) + 500 | |
# | |
_ACV_A3_L = lambda T, Hz = 50: 1000 * sqrt(2) * (np.sin(2*pi*Hz * T) + | |
0.05 * np.sin(2*pi*Hz * T * 4 + pi * 2 / 3)) | |
# | |
_ACV_A4_L = lambda T, Hz = 50:( 1000 * sqrt(2) * (np.sin(2*pi*Hz * T) + | |
0.07 * np.sin(2*pi*Hz * T * 5 + pi * 22 / 18))) | |
# Realistic triangle | |
_ACV_A5_L = lambda T, Hz = 50:( 1000 * sqrt(2) * (np.sin(2*pi*Hz * T) + | |
0.05 * np.sin(2*pi*Hz * T * 3 - pi) + | |
0.05 * np.sin(2*pi*Hz * T * 5) + | |
0.02 * np.sin(2*pi*Hz * T * 7 - pi) + | |
0.01 * np.sin(2*pi*Hz * T * 9))) | |
# | |
_ACV_A6_L = lambda T, Hz = 50:( 1000 * sqrt(2) * (np.sin(2*pi*Hz * T) + | |
0.02 * np.sin(2*pi*Hz * T * 3 - pi) + | |
0.02 * np.sin(2*pi*Hz * T * 5) + | |
0.0015 * np.sin(2*pi*Hz * T * 7 - pi) + | |
0.009 * np.sin(2*pi*Hz * T * 9))) | |
#A7 & A8 convert so that a input of 16*pi corresponds to a input 0.25 in the current version | |
_ACV_A7_OLD = lambda T: [1000 * sqrt(2) * np.sin(100 * pi * t) * | |
(0.9 * t / 5 * H_num(5-t) + H_num(t-5) * H_num(10-t) * (0.9 + 0.1 * (t-5) / 5)) for t in T] | |
_ACV_A8_OLD = lambda T: [1000 * sqrt(2) * np.sin(t) * | |
t / (10 * pi) * H_num(10 - t / (100 * pi)) for t in T] | |
if __name__ == "__main__": | |
#create 1 period triangle | |
x = np.linspace(0, 0.02, 4000) | |
y = ACV_A5(x) | |
#!/usr/bin/python2 | |
# Copyright (C) 2016 Sixten Bergman | |
# License WTFPL | |
# | |
# This program is free software. It comes without any warranty, to the extent | |
# permitted by applicable law. | |
# You can redistribute it and/or modify it under the terms of the Do What The | |
# Fuck You Want To Public License, Version 2, as published by Sam Hocevar. See | |
# http://www.wtfpl.net/ for more details. | |
# | |
# note that the function peakdetect is derived from code which was released to | |
# public domain see: http://billauer.co.il/peakdet.html | |
# | |
import logging | |
from math import pi, log | |
import numpy as np | |
import pylab | |
from scipy import fft, ifft | |
from scipy.optimize import curve_fit | |
from scipy.signal import cspline1d_eval, cspline1d | |
__all__ = [ | |
"peakdetect", | |
"peakdetect_fft", | |
"peakdetect_parabola", | |
"peakdetect_sine", | |
"peakdetect_sine_locked", | |
"peakdetect_spline", | |
"peakdetect_zero_crossing", | |
"zero_crossings", | |
"zero_crossings_sine_fit" | |
] | |
def _datacheck_peakdetect(x_axis, y_axis): | |
if x_axis is None: | |
x_axis = range(len(y_axis)) | |
if len(y_axis) != len(x_axis): | |
raise ValueError( | |
"Input vectors y_axis and x_axis must have same length") | |
#needs to be a numpy array | |
y_axis = np.array(y_axis) | |
x_axis = np.array(x_axis) | |
return x_axis, y_axis | |
def _pad(fft_data, pad_len): | |
""" | |
Pads fft data to interpolate in time domain | |
keyword arguments: | |
fft_data -- the fft | |
pad_len -- By how many times the time resolution should be increased by | |
return: padded list | |
""" | |
l = len(fft_data) | |
n = _n(l * pad_len) | |
fft_data = list(fft_data) | |
return fft_data[:l // 2] + [0] * (2**n-l) + fft_data[l // 2:] | |
def _n(x): | |
""" | |
Find the smallest value for n, which fulfils 2**n >= x | |
keyword arguments: | |
x -- the value, which 2**n must surpass | |
return: the integer n | |
""" | |
return int(log(x)/log(2)) + 1 | |
def _peakdetect_parabola_fitter(raw_peaks, x_axis, y_axis, points): | |
""" | |
Performs the actual parabola fitting for the peakdetect_parabola function. | |
keyword arguments: | |
raw_peaks -- A list of either the maxima or the minima peaks, as given | |
by the peakdetect functions, with index used as x-axis | |
x_axis -- A numpy array of all the x values | |
y_axis -- A numpy array of all the y values | |
points -- How many points around the peak should be used during curve | |
fitting, must be odd. | |
return: A list giving all the peaks and the fitted waveform, format: | |
[[x, y, [fitted_x, fitted_y]]] | |
""" | |
func = lambda x, a, tau, c: a * ((x - tau) ** 2) + c | |
fitted_peaks = [] | |
distance = abs(x_axis[raw_peaks[1][0]] - x_axis[raw_peaks[0][0]]) / 4 | |
for peak in raw_peaks: | |
index = peak[0] | |
x_data = x_axis[index - points // 2: index + points // 2 + 1] | |
y_data = y_axis[index - points // 2: index + points // 2 + 1] | |
# get a first approximation of tau (peak position in time) | |
tau = x_axis[index] | |
# get a first approximation of peak amplitude | |
c = peak[1] | |
a = np.sign(c) * (-1) * (np.sqrt(abs(c))/distance)**2 | |
"""Derived from ABC formula to result in a solution where A=(rot(c)/t)**2""" | |
# build list of approximations | |
p0 = (a, tau, c) | |
popt, pcov = curve_fit(func, x_data, y_data, p0) | |
# retrieve tau and c i.e x and y value of peak | |
x, y = popt[1:3] | |
# create a high resolution data set for the fitted waveform | |
x2 = np.linspace(x_data[0], x_data[-1], points * 10) | |
y2 = func(x2, *popt) | |
fitted_peaks.append([x, y, [x2, y2]]) | |
return fitted_peaks | |
def peakdetect_parabole(*args, **kwargs): | |
""" | |
Misspelling of peakdetect_parabola | |
function is deprecated please use peakdetect_parabola | |
""" | |
logging.warn("peakdetect_parabole is deprecated due to misspelling use: peakdetect_parabola") | |
return peakdetect_parabola(*args, **kwargs) | |
def peakdetect(y_axis, x_axis = None, lookahead = 200, delta=0): | |
""" | |
Converted from/based on a MATLAB script at: | |
http://billauer.co.il/peakdet.html | |
function for detecting local maxima and minima in a signal. | |
Discovers peaks by searching for values which are surrounded by lower | |
or larger values for maxima and minima respectively | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list and is used | |
in the return to specify the position of the peaks. If omitted an | |
index of the y_axis is used. | |
(default: None) | |
lookahead -- distance to look ahead from a peak candidate to determine if | |
it is the actual peak | |
(default: 200) | |
'(samples / period) / f' where '4 >= f >= 1.25' might be a good value | |
delta -- this specifies a minimum difference between a peak and | |
the following points, before a peak may be considered a peak. Useful | |
to hinder the function from picking up false peaks towards to end of | |
the signal. To work well delta should be set to delta >= RMSnoise * 5. | |
(default: 0) | |
When omitted delta function causes a 20% decrease in speed. | |
When used Correctly it can double the speed of the function | |
return: two lists [max_peaks, min_peaks] containing the positive and | |
negative peaks respectively. Each cell of the lists contains a tuple | |
of: (position, peak_value) | |
to get the average peak value do: np.mean(max_peaks, 0)[1] on the | |
results to unpack one of the lists into x, y coordinates do: | |
x, y = zip(*max_peaks) | |
""" | |
max_peaks = [] | |
min_peaks = [] | |
dump = [] #Used to pop the first hit which almost always is false | |
# check input data | |
x_axis, y_axis = _datacheck_peakdetect(x_axis, y_axis) | |
# store data length for later use | |
length = len(y_axis) | |
#perform some checks | |
if lookahead < 1: | |
raise ValueError("Lookahead must be '1' or above in value") | |
if not (np.isscalar(delta) and delta >= 0): | |
raise ValueError("delta must be a positive number") | |
#maxima and minima candidates are temporarily stored in | |
#mx and mn respectively | |
mn, mx = np.Inf, -np.Inf | |
#Only detect peak if there is 'lookahead' amount of points after it | |
for index, (x, y) in enumerate(zip(x_axis[:-lookahead], | |
y_axis[:-lookahead])): | |
if y > mx: | |
mx = y | |
mxpos = x | |
if y < mn: | |
mn = y | |
mnpos = x | |
####look for max#### | |
if y < mx-delta and mx != np.Inf: | |
#Maxima peak candidate found | |
#look ahead in signal to ensure that this is a peak and not jitter | |
if y_axis[index:index+lookahead].max() < mx: | |
max_peaks.append([mxpos, mx]) | |
dump.append(True) | |
#set algorithm to only find minima now | |
mx = np.Inf | |
mn = np.Inf | |
if index+lookahead >= length: | |
#end is within lookahead no more peaks can be found | |
break | |
continue | |
#else: #slows shit down this does | |
# mx = ahead | |
# mxpos = x_axis[np.where(y_axis[index:index+lookahead]==mx)] | |
####look for min#### | |
if y > mn+delta and mn != -np.Inf: | |
#Minima peak candidate found | |
#look ahead in signal to ensure that this is a peak and not jitter | |
if y_axis[index:index+lookahead].min() > mn: | |
min_peaks.append([mnpos, mn]) | |
dump.append(False) | |
#set algorithm to only find maxima now | |
mn = -np.Inf | |
mx = -np.Inf | |
if index+lookahead >= length: | |
#end is within lookahead no more peaks can be found | |
break | |
#else: #slows shit down this does | |
# mn = ahead | |
# mnpos = x_axis[np.where(y_axis[index:index+lookahead]==mn)] | |
#Remove the false hit on the first value of the y_axis | |
try: | |
if dump[0]: | |
max_peaks.pop(0) | |
else: | |
min_peaks.pop(0) | |
del dump | |
except IndexError: | |
#no peaks were found, should the function return empty lists? | |
pass | |
return [max_peaks, min_peaks] | |
def peakdetect_fft(y_axis, x_axis, pad_len = 20): | |
""" | |
Performs a FFT calculation on the data and zero-pads the results to | |
increase the time domain resolution after performing the inverse fft and | |
send the data to the 'peakdetect' function for peak | |
detection. | |
Omitting the x_axis is forbidden as it would make the resulting x_axis | |
value silly if it was returned as the index 50.234 or similar. | |
Will find at least 1 less peak then the 'peakdetect_zero_crossing' | |
function, but should result in a more precise value of the peak as | |
resolution has been increased. Some peaks are lost in an attempt to | |
minimize spectral leakage by calculating the fft between two zero | |
crossings for n amount of signal periods. | |
The biggest time eater in this function is the ifft and thereafter it's | |
the 'peakdetect' function which takes only half the time of the ifft. | |
Speed improvements could include to check if 2**n points could be used for | |
fft and ifft or change the 'peakdetect' to the 'peakdetect_zero_crossing', | |
which is maybe 10 times faster than 'peakdetct'. The pro of 'peakdetect' | |
is that it results in one less lost peak. It should also be noted that the | |
time used by the ifft function can change greatly depending on the input. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list and is used | |
in the return to specify the position of the peaks. | |
pad_len -- By how many times the time resolution should be | |
increased by, e.g. 1 doubles the resolution. The amount is rounded up | |
to the nearest 2**n amount | |
(default: 20) | |
return: two lists [max_peaks, min_peaks] containing the positive and | |
negative peaks respectively. Each cell of the lists contains a tuple | |
of: (position, peak_value) | |
to get the average peak value do: np.mean(max_peaks, 0)[1] on the | |
results to unpack one of the lists into x, y coordinates do: | |
x, y = zip(*max_peaks) | |
""" | |
# check input data | |
x_axis, y_axis = _datacheck_peakdetect(x_axis, y_axis) | |
zero_indices = zero_crossings(y_axis, window_len = 11) | |
#select a n amount of periods | |
last_indice = - 1 - (1 - len(zero_indices) & 1) | |
### | |
# Calculate the fft between the first and last zero crossing | |
# this method could be ignored if the beginning and the end of the signal | |
# are unnecessary as any errors induced from not using whole periods | |
# should mainly manifest in the beginning and the end of the signal, but | |
# not in the rest of the signal | |
# this is also unnecessary if the given data is an amount of whole periods | |
### | |
fft_data = fft(y_axis[zero_indices[0]:zero_indices[last_indice]]) | |
padd = lambda x, c: x[:len(x) // 2] + [0] * c + x[len(x) // 2:] | |
n = lambda x: int(log(x)/log(2)) + 1 | |
# pads to 2**n amount of samples | |
fft_padded = padd(list(fft_data), 2 ** | |
n(len(fft_data) * pad_len) - len(fft_data)) | |
# There is amplitude decrease directly proportional to the sample increase | |
sf = len(fft_padded) / float(len(fft_data)) | |
# There might be a leakage giving the result an imaginary component | |
# Return only the real component | |
y_axis_ifft = ifft(fft_padded).real * sf #(pad_len + 1) | |
x_axis_ifft = np.linspace( | |
x_axis[zero_indices[0]], x_axis[zero_indices[last_indice]], | |
len(y_axis_ifft)) | |
# get the peaks to the interpolated waveform | |
max_peaks, min_peaks = peakdetect(y_axis_ifft, x_axis_ifft, 500, | |
delta = abs(np.diff(y_axis).max() * 2)) | |
#max_peaks, min_peaks = peakdetect_zero_crossing(y_axis_ifft, x_axis_ifft) | |
# store one 20th of a period as waveform data | |
data_len = int(np.diff(zero_indices).mean()) / 10 | |
data_len += 1 - data_len & 1 | |
return [max_peaks, min_peaks] | |
def peakdetect_parabola(y_axis, x_axis, points = 31): | |
""" | |
Function for detecting local maxima and minima in a signal. | |
Discovers peaks by fitting the model function: y = k (x - tau) ** 2 + m | |
to the peaks. The amount of points used in the fitting is set by the | |
points argument. | |
Omitting the x_axis is forbidden as it would make the resulting x_axis | |
value silly, if it was returned as index 50.234 or similar. | |
will find the same amount of peaks as the 'peakdetect_zero_crossing' | |
function, but might result in a more precise value of the peak. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list and is used | |
in the return to specify the position of the peaks. | |
points -- How many points around the peak should be used during curve | |
fitting (default: 31) | |
return: two lists [max_peaks, min_peaks] containing the positive and | |
negative peaks respectively. Each cell of the lists contains a tuple | |
of: (position, peak_value) | |
to get the average peak value do: np.mean(max_peaks, 0)[1] on the | |
results to unpack one of the lists into x, y coordinates do: | |
x, y = zip(*max_peaks) | |
""" | |
# check input data | |
x_axis, y_axis = _datacheck_peakdetect(x_axis, y_axis) | |
# make the points argument odd | |
points += 1 - points % 2 | |
#points += 1 - int(points) & 1 slower when int conversion needed | |
# get raw peaks | |
max_raw, min_raw = peakdetect_zero_crossing(y_axis) | |
# define output variable | |
max_peaks = [] | |
min_peaks = [] | |
max_ = _peakdetect_parabola_fitter(max_raw, x_axis, y_axis, points) | |
min_ = _peakdetect_parabola_fitter(min_raw, x_axis, y_axis, points) | |
max_peaks = map(lambda x: [x[0], x[1]], max_) | |
max_fitted = map(lambda x: x[-1], max_) | |
min_peaks = map(lambda x: [x[0], x[1]], min_) | |
min_fitted = map(lambda x: x[-1], min_) | |
return [max_peaks, min_peaks] | |
def peakdetect_sine(y_axis, x_axis, points = 31, lock_frequency = False): | |
""" | |
Function for detecting local maxima and minima in a signal. | |
Discovers peaks by fitting the model function: | |
y = A * sin(2 * pi * f * (x - tau)) to the peaks. The amount of points used | |
in the fitting is set by the points argument. | |
Omitting the x_axis is forbidden as it would make the resulting x_axis | |
value silly if it was returned as index 50.234 or similar. | |
will find the same amount of peaks as the 'peakdetect_zero_crossing' | |
function, but might result in a more precise value of the peak. | |
The function might have some problems if the sine wave has a | |
non-negligible total angle i.e. a k*x component, as this messes with the | |
internal offset calculation of the peaks, might be fixed by fitting a | |
y = k * x + m function to the peaks for offset calculation. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list and is used | |
in the return to specify the position of the peaks. | |
points -- How many points around the peak should be used during curve | |
fitting (default: 31) | |
lock_frequency -- Specifies if the frequency argument of the model | |
function should be locked to the value calculated from the raw peaks | |
or if optimization process may tinker with it. | |
(default: False) | |
return: two lists [max_peaks, min_peaks] containing the positive and | |
negative peaks respectively. Each cell of the lists contains a tuple | |
of: (position, peak_value) | |
to get the average peak value do: np.mean(max_peaks, 0)[1] on the | |
results to unpack one of the lists into x, y coordinates do: | |
x, y = zip(*max_peaks) | |
""" | |
# check input data | |
x_axis, y_axis = _datacheck_peakdetect(x_axis, y_axis) | |
# make the points argument odd | |
points += 1 - points % 2 | |
#points += 1 - int(points) & 1 slower when int conversion needed | |
# get raw peaks | |
max_raw, min_raw = peakdetect_zero_crossing(y_axis) | |
# define output variable | |
max_peaks = [] | |
min_peaks = [] | |
# get global offset | |
offset = np.mean([np.mean(max_raw, 0)[1], np.mean(min_raw, 0)[1]]) | |
# fitting a k * x + m function to the peaks might be better | |
#offset_func = lambda x, k, m: k * x + m | |
# calculate an approximate frequency of the signal | |
Hz_h_peak = np.diff(zip(*max_raw)[0]).mean() | |
Hz_l_peak = np.diff(zip(*min_raw)[0]).mean() | |
Hz = 1 / np.mean([Hz_h_peak, Hz_l_peak]) | |
# model function | |
# if cosine is used then tau could equal the x position of the peak | |
# if sine were to be used then tau would be the first zero crossing | |
if lock_frequency: | |
func = lambda x_ax, A, tau: A * np.sin( | |
2 * pi * Hz * (x_ax - tau) + pi / 2) | |
else: | |
func = lambda x_ax, A, Hz, tau: A * np.sin( | |
2 * pi * Hz * (x_ax - tau) + pi / 2) | |
#func = lambda x_ax, A, Hz, tau: A * np.cos(2 * pi * Hz * (x_ax - tau)) | |
#get peaks | |
fitted_peaks = [] | |
for raw_peaks in [max_raw, min_raw]: | |
peak_data = [] | |
for peak in raw_peaks: | |
index = peak[0] | |
x_data = x_axis[index - points // 2: index + points // 2 + 1] | |
y_data = y_axis[index - points // 2: index + points // 2 + 1] | |
# get a first approximation of tau (peak position in time) | |
tau = x_axis[index] | |
# get a first approximation of peak amplitude | |
A = peak[1] | |
# build list of approximations | |
if lock_frequency: | |
p0 = (A, tau) | |
else: | |
p0 = (A, Hz, tau) | |
# subtract offset from wave-shape | |
y_data -= offset | |
popt, pcov = curve_fit(func, x_data, y_data, p0) | |
# retrieve tau and A i.e x and y value of peak | |
x = popt[-1] | |
y = popt[0] | |
# create a high resolution data set for the fitted waveform | |
x2 = np.linspace(x_data[0], x_data[-1], points * 10) | |
y2 = func(x2, *popt) | |
# add the offset to the results | |
y += offset | |
y2 += offset | |
y_data += offset | |
peak_data.append([x, y, [x2, y2]]) | |
fitted_peaks.append(peak_data) | |
# structure date for output | |
max_peaks = map(lambda x: [x[0], x[1]], fitted_peaks[0]) | |
max_fitted = map(lambda x: x[-1], fitted_peaks[0]) | |
min_peaks = map(lambda x: [x[0], x[1]], fitted_peaks[1]) | |
min_fitted = map(lambda x: x[-1], fitted_peaks[1]) | |
return [max_peaks, min_peaks] | |
def peakdetect_sine_locked(y_axis, x_axis, points = 31): | |
""" | |
Convenience function for calling the 'peakdetect_sine' function with | |
the lock_frequency argument as True. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list and is used | |
in the return to specify the position of the peaks. | |
points -- How many points around the peak should be used during curve | |
fitting (default: 31) | |
return: see the function 'peakdetect_sine' | |
""" | |
return peakdetect_sine(y_axis, x_axis, points, True) | |
def peakdetect_spline(y_axis, x_axis, pad_len=20): | |
""" | |
Performs a b-spline interpolation on the data to increase resolution and | |
send the data to the 'peakdetect_zero_crossing' function for peak | |
detection. | |
Omitting the x_axis is forbidden as it would make the resulting x_axis | |
value silly if it was returned as the index 50.234 or similar. | |
will find the same amount of peaks as the 'peakdetect_zero_crossing' | |
function, but might result in a more precise value of the peak. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list and is used | |
in the return to specify the position of the peaks. | |
x-axis must be equally spaced. | |
pad_len -- By how many times the time resolution should be increased by, | |
e.g. 1 doubles the resolution. | |
(default: 20) | |
return: two lists [max_peaks, min_peaks] containing the positive and | |
negative peaks respectively. Each cell of the lists contains a tuple | |
of: (position, peak_value) | |
to get the average peak value do: np.mean(max_peaks, 0)[1] on the | |
results to unpack one of the lists into x, y coordinates do: | |
x, y = zip(*max_peaks) | |
""" | |
# check input data | |
x_axis, y_axis = _datacheck_peakdetect(x_axis, y_axis) | |
# could perform a check if x_axis is equally spaced | |
#if np.std(np.diff(x_axis)) > 1e-15: raise ValueError | |
# perform spline interpolations | |
dx = x_axis[1] - x_axis[0] | |
x_interpolated = np.linspace(x_axis.min(), x_axis.max(), len(x_axis) * (pad_len + 1)) | |
cj = cspline1d(y_axis) | |
y_interpolated = cspline1d_eval(cj, x_interpolated, dx=dx,x0=x_axis[0]) | |
# get peaks | |
max_peaks, min_peaks = peakdetect_zero_crossing(y_interpolated, x_interpolated) | |
return [max_peaks, min_peaks] | |
def peakdetect_zero_crossing(y_axis, x_axis = None, window = 11): | |
""" | |
Function for detecting local maxima and minima in a signal. | |
Discovers peaks by dividing the signal into bins and retrieving the | |
maximum and minimum value of each the even and odd bins respectively. | |
Division into bins is performed by smoothing the curve and finding the | |
zero crossings. | |
Suitable for repeatable signals, where some noise is tolerated. Executes | |
faster than 'peakdetect', although this function will break if the offset | |
of the signal is too large. It should also be noted that the first and | |
last peak will probably not be found, as this function only can find peaks | |
between the first and last zero crossing. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list | |
and is used in the return to specify the position of the peaks. If | |
omitted an index of the y_axis is used. | |
(default: None) | |
window -- the dimension of the smoothing window; should be an odd integer | |
(default: 11) | |
return: two lists [max_peaks, min_peaks] containing the positive and | |
negative peaks respectively. Each cell of the lists contains a tuple | |
of: (position, peak_value) | |
to get the average peak value do: np.mean(max_peaks, 0)[1] on the | |
results to unpack one of the lists into x, y coordinates do: | |
x, y = zip(*max_peaks) | |
""" | |
# check input data | |
x_axis, y_axis = _datacheck_peakdetect(x_axis, y_axis) | |
zero_indices = zero_crossings(y_axis, window_len = window) | |
period_lengths = np.diff(zero_indices) | |
bins_y = [y_axis[index:index + diff] for index, diff in | |
zip(zero_indices, period_lengths)] | |
bins_x = [x_axis[index:index + diff] for index, diff in | |
zip(zero_indices, period_lengths)] | |
even_bins_y = bins_y[::2] | |
odd_bins_y = bins_y[1::2] | |
even_bins_x = bins_x[::2] | |
odd_bins_x = bins_x[1::2] | |
hi_peaks_x = [] | |
lo_peaks_x = [] | |
#check if even bin contains maxima | |
if abs(even_bins_y[0].max()) > abs(even_bins_y[0].min()): | |
hi_peaks = [bin.max() for bin in even_bins_y] | |
lo_peaks = [bin.min() for bin in odd_bins_y] | |
# get x values for peak | |
for bin_x, bin_y, peak in zip(even_bins_x, even_bins_y, hi_peaks): | |
hi_peaks_x.append(bin_x[np.where(bin_y==peak)[0][0]]) | |
for bin_x, bin_y, peak in zip(odd_bins_x, odd_bins_y, lo_peaks): | |
lo_peaks_x.append(bin_x[np.where(bin_y==peak)[0][0]]) | |
else: | |
hi_peaks = [bin.max() for bin in odd_bins_y] | |
lo_peaks = [bin.min() for bin in even_bins_y] | |
# get x values for peak | |
for bin_x, bin_y, peak in zip(odd_bins_x, odd_bins_y, hi_peaks): | |
hi_peaks_x.append(bin_x[np.where(bin_y==peak)[0][0]]) | |
for bin_x, bin_y, peak in zip(even_bins_x, even_bins_y, lo_peaks): | |
lo_peaks_x.append(bin_x[np.where(bin_y==peak)[0][0]]) | |
max_peaks = [[x, y] for x,y in zip(hi_peaks_x, hi_peaks)] | |
min_peaks = [[x, y] for x,y in zip(lo_peaks_x, lo_peaks)] | |
return [max_peaks, min_peaks] | |
def _smooth(x, window_len=11, window="hanning"): | |
""" | |
smooth the data using a window of the requested size. | |
This method is based on the convolution of a scaled window on the signal. | |
The signal is prepared by introducing reflected copies of the signal | |
(with the window size) in both ends so that transient parts are minimized | |
in the beginning and end part of the output signal. | |
keyword arguments: | |
x -- the input signal | |
window_len -- the dimension of the smoothing window; should be an odd | |
integer (default: 11) | |
window -- the type of window from 'flat', 'hanning', 'hamming', | |
'bartlett', 'blackman', where flat is a moving average | |
(default: 'hanning') | |
return: the smoothed signal | |
example: | |
t = linspace(-2,2,0.1) | |
x = sin(t)+randn(len(t))*0.1 | |
y = _smooth(x) | |
see also: | |
numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, | |
numpy.convolve, scipy.signal.lfilter | |
""" | |
if x.ndim != 1: | |
raise ValueError("smooth only accepts 1 dimension arrays.") | |
if x.size < window_len: | |
raise ValueError("Input vector needs to be bigger than window size.") | |
if window_len<3: | |
return x | |
#declare valid windows in a dictionary | |
window_funcs = { | |
"flat": lambda _len: np.ones(_len, "d"), | |
"hanning": np.hanning, | |
"hamming": np.hamming, | |
"bartlett": np.bartlett, | |
"blackman": np.blackman | |
} | |
s = np.r_[x[window_len-1:0:-1], x, x[-1:-window_len:-1]] | |
try: | |
w = window_funcs[window](window_len) | |
except KeyError: | |
raise ValueError( | |
"Window is not one of '{0}', '{1}', '{2}', '{3}', '{4}'".format( | |
*window_funcs.keys())) | |
y = np.convolve(w / w.sum(), s, mode = "valid") | |
return y | |
def zero_crossings(y_axis, window_len = 11, | |
window_f="hanning", offset_corrected=False): | |
""" | |
Algorithm to find zero crossings. Smooths the curve and finds the | |
zero-crossings by looking for a sign change. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find zero-crossings | |
window_len -- the dimension of the smoothing window; should be an odd | |
integer (default: 11) | |
window_f -- the type of window from 'flat', 'hanning', 'hamming', | |
'bartlett', 'blackman' (default: 'hanning') | |
offset_corrected -- Used for recursive calling to remove offset when needed | |
return: the index for each zero-crossing | |
""" | |
# smooth the curve | |
length = len(y_axis) | |
# discard tail of smoothed signal | |
y_axis = _smooth(y_axis, window_len, window_f)[:length] | |
indices = np.where(np.diff(np.sign(y_axis)))[0] | |
# check if zero-crossings are valid | |
diff = np.diff(indices) | |
if diff.std() / diff.mean() > 0.1: | |
#Possibly bad zero crossing, see if it's offsets | |
if ((diff[::2].std() / diff[::2].mean()) < 0.1 and | |
(diff[1::2].std() / diff[1::2].mean()) < 0.1 and | |
not offset_corrected): | |
#offset present attempt to correct by subtracting the average | |
offset = np.mean([y_axis.max(), y_axis.min()]) | |
return zero_crossings(y_axis-offset, window_len, window_f, True) | |
#Invalid zero crossings and the offset has been removed | |
print(diff.std() / diff.mean()) | |
print(np.diff(indices)) | |
raise ValueError( | |
"False zero-crossings found, indicates problem {0!s} or {1!s}".format( | |
"with smoothing window", "unhandled problem with offset")) | |
# check if any zero crossings were found | |
if len(indices) < 1: | |
raise ValueError("No zero crossings found") | |
#remove offset from indices due to filter function when returning | |
return indices - (window_len // 2 - 1) | |
# used this to test the fft function's sensitivity to spectral leakage | |
#return indices + np.asarray(30 * np.random.randn(len(indices)), int) | |
############################Frequency calculation############################# | |
# diff = np.diff(indices) | |
# time_p_period = diff.mean() | |
# | |
# if diff.std() / time_p_period > 0.1: | |
# raise ValueError( | |
# "smoothing window too small, false zero-crossing found") | |
# | |
# #return frequency | |
# return 1.0 / time_p_period | |
############################################################################## | |
def zero_crossings_sine_fit(y_axis, x_axis, fit_window = None, smooth_window = 11): | |
""" | |
Detects the zero crossings of a signal by fitting a sine model function | |
around the zero crossings: | |
y = A * sin(2 * pi * Hz * (x - tau)) + k * x + m | |
Only tau (the zero crossing) is varied during fitting. | |
Offset and a linear drift of offset is accounted for by fitting a linear | |
function the negative respective positive raw peaks of the wave-shape and | |
the amplitude is calculated using data from the offset calculation i.e. | |
the 'm' constant from the negative peaks is subtracted from the positive | |
one to obtain amplitude. | |
Frequency is calculated using the mean time between raw peaks. | |
Algorithm seems to be sensitive to first guess e.g. a large smooth_window | |
will give an error in the results. | |
keyword arguments: | |
y_axis -- A list containing the signal over which to find peaks | |
x_axis -- A x-axis whose values correspond to the y_axis list | |
and is used in the return to specify the position of the peaks. If | |
omitted an index of the y_axis is used. (default: None) | |
fit_window -- Number of points around the approximate zero crossing that | |
should be used when fitting the sine wave. Must be small enough that | |
no other zero crossing will be seen. If set to none then the mean | |
distance between zero crossings will be used (default: None) | |
smooth_window -- the dimension of the smoothing window; should be an odd | |
integer (default: 11) | |
return: A list containing the positions of all the zero crossings. | |
""" | |
# check input data | |
x_axis, y_axis = _datacheck_peakdetect(x_axis, y_axis) | |
#get first guess | |
zero_indices = zero_crossings(y_axis, window_len = smooth_window) | |
#modify fit_window to show distance per direction | |
if fit_window == None: | |
fit_window = np.diff(zero_indices).mean() // 3 | |
else: | |
fit_window = fit_window // 2 | |
#x_axis is a np array, use the indices to get a subset with zero crossings | |
approx_crossings = x_axis[zero_indices] | |
#get raw peaks for calculation of offsets and frequency | |
raw_peaks = peakdetect_zero_crossing(y_axis, x_axis) | |
#Use mean time between peaks for frequency | |
ext = lambda x: list(zip(*x)[0]) | |
_diff = map(np.diff, map(ext, raw_peaks)) | |
Hz = 1 / np.mean(map(np.mean, _diff)) | |
#Hz = 1 / np.diff(approx_crossings).mean() #probably bad precision | |
#offset model function | |
offset_func = lambda x, k, m: k * x + m | |
k = [] | |
m = [] | |
amplitude = [] | |
for peaks in raw_peaks: | |
#get peak data as nparray | |
x_data, y_data = map(np.asarray, zip(*peaks)) | |
#x_data = np.asarray(x_data) | |
#y_data = np.asarray(y_data) | |
#calc first guess | |
A = np.mean(y_data) | |
p0 = (0, A) | |
popt, pcov = curve_fit(offset_func, x_data, y_data, p0) | |
#append results | |
k.append(popt[0]) | |
m.append(popt[1]) | |
amplitude.append(abs(A)) | |
#store offset constants | |
p_offset = (np.mean(k), np.mean(m)) | |
A = m[0] - m[1] | |
#define model function to fit to zero crossing | |
#y = A * sin(2*pi * Hz * (x - tau)) + k * x + m | |
func = lambda x, tau: A * np.sin(2 * pi * Hz * (x - tau)) + offset_func(x, *p_offset) | |
#get true crossings | |
true_crossings = [] | |
for indice, crossing in zip(zero_indices, approx_crossings): | |
p0 = (crossing, ) | |
subset_start = max(indice - fit_window, 0.0) | |
subset_end = min(indice + fit_window + 1, len(x_axis) - 1.0) | |
x_subset = np.asarray(x_axis[subset_start:subset_end]) | |
y_subset = np.asarray(y_axis[subset_start:subset_end]) | |
#fit | |
popt, pcov = curve_fit(func, x_subset, y_subset, p0) | |
true_crossings.append(popt[0]) | |
return true_crossings | |
def _test_zero(): | |
_max, _min = peakdetect_zero_crossing(y,x) | |
def _test(): | |
_max, _min = peakdetect(y,x, delta=0.30) | |
def _test_graph(): | |
i = 10000 | |
x = np.linspace(0,3.7*pi,i) | |
y = (0.3*np.sin(x) + np.sin(1.3 * x) + 0.9 * np.sin(4.2 * x) + 0.06 * | |
np.random.randn(i)) | |
y *= -1 | |
x = range(i) | |
_max, _min = peakdetect(y,x,750, 0.30) | |
xm = [p[0] for p in _max] | |
ym = [p[1] for p in _max] | |
xn = [p[0] for p in _min] | |
yn = [p[1] for p in _min] | |
plot = pylab.plot(x,y) | |
pylab.hold(True) | |
pylab.plot(xm, ym, "r+") | |
pylab.plot(xn, yn, "g+") | |
_max, _min = peak_det_bad.peakdetect(y, 0.7, x) | |
xm = [p[0] for p in _max] | |
ym = [p[1] for p in _max] | |
xn = [p[0] for p in _min] | |
yn = [p[1] for p in _min] | |
pylab.plot(xm, ym, "y*") | |
pylab.plot(xn, yn, "k*") | |
pylab.show() | |
def _test_graph_cross(window = 11): | |
i = 10000 | |
x = np.linspace(0,8.7*pi,i) | |
y = (2*np.sin(x) + 0.006 * | |
np.random.randn(i)) | |
y *= -1 | |
pylab.plot(x,y) | |
#pylab.show() | |
crossings = zero_crossings_sine_fit(y,x, smooth_window = window) | |
y_cross = [0] * len(crossings) | |
plot = pylab.plot(x,y) | |
pylab.hold(True) | |
pylab.plot(crossings, y_cross, "b+") | |
pylab.show() | |
if __name__ == "__main__": | |
from math import pi | |
import pylab | |
i = 10000 | |
x = np.linspace(0,3.7*pi,i) | |
y = (0.3*np.sin(x) + np.sin(1.3 * x) + 0.9 * np.sin(4.2 * x) + 0.06 * | |
np.random.randn(i)) | |
y *= -1 | |
_max, _min = peakdetect(y, x, 750, 0.30) | |
xm = [p[0] for p in _max] | |
ym = [p[1] for p in _max] | |
xn = [p[0] for p in _min] | |
yn = [p[1] for p in _min] | |
plot = pylab.plot(x, y) | |
pylab.hold(True) | |
pylab.plot(xm, ym, "r+") | |
pylab.plot(xn, yn, "g+") | |
pylab.show() |
#!/usr/bin/python2 | |
# Copyright (C) 2016 Sixten Bergman | |
# License WTFPL | |
# | |
# This program is free software. It comes without any warranty, to the extent | |
# permitted by applicable law. | |
# You can redistribute it and/or modify it under the terms of the Do What The | |
# Fuck You Want To Public License, Version 2, as published by Sam Hocevar. See | |
# http://www.wtfpl.net/ for more details. | |
# | |
import analytic_wfm | |
import numpy as np | |
import peakdetect | |
import unittest | |
import pdb | |
#generate time axis for 5 cycles @ 50 Hz | |
linspace_standard = np.linspace(0, 0.10, 1000) | |
linspace_peakdetect = np.linspace(0, 0.10, 10000) | |
def prng(): | |
""" | |
A numpy random number generator with a known starting state | |
return: a random number generator | |
""" | |
return np.random.RandomState(773889874) | |
def _write_log(file, header, message): | |
with open(file, "ab") as f: | |
f.write(header) | |
f.write("\n") | |
f.writelines(message) | |
f.write("\n") | |
f.write("\n") | |
def _calculate_missmatch(received, expected): | |
""" | |
Calculates the mean mismatch between received and expected data | |
keyword arguments: | |
received -- [[time of peak], [ampl of peak]] | |
expected -- [[time of peak], [ampl of peak]] | |
return (time mismatch, ampl mismatch) | |
""" | |
#t_diff = np.abs(np.asarray(received[0]) - expected[0]) | |
t_diff = np.asarray(received[0]) - expected[0] | |
a_diff = np.abs(np.asarray(received[1]) - expected[1]) | |
#t_diff /= np.abs(expected[0]) time error in absolute terms | |
a_diff /= np.abs(expected[1]) | |
return (t_diff, a_diff) | |
def _log_diff(t_max, y_max, | |
t_min, y_min, | |
t_max_expected, y_max_expected, | |
t_min_expected, y_min_expected, | |
file, name | |
): | |
""" | |
keyword arguments: | |
t_max -- time of maxima | |
y_max -- amplitude of maxima | |
t_min -- time of minima | |
y_min -- amplitude of maxima | |
t_max_expected -- expected time of maxima | |
y_max_expected -- expected amplitude of maxima | |
t_min_expected -- expected time of minima | |
y_min_expected -- expected amplitude of maxima | |
file -- log file to write to | |
name -- name of the test performed | |
""" | |
t_diff_h, a_diff_h = _calculate_missmatch([t_max, y_max], | |
[t_max_expected, y_max_expected]) | |
t_diff_l, a_diff_l = _calculate_missmatch([t_min, y_min], | |
[t_min_expected, y_min_expected]) | |
#data = ["\t{0:.2e}\t{1:.2e}\t{2:.2e}\t{3:.2e}".format(*d) for d in | |
# [t_diff_h, t_diff_l, a_diff_h, a_diff_l] | |
# ] | |
frt = "val:{0} error:{1:.2e}" | |
data = ["\t{0}".format("\t".join(map(frt.format, val, err))) for val, err in | |
[(t_max, t_diff_h), | |
(t_min, t_diff_l), | |
(y_max, a_diff_h), | |
(y_min, a_diff_l)] | |
] | |
_write_log(file, name, "\n".join(data)) | |
def _is_close(max_p, min_p, | |
expected_max, expected_min, | |
atol_time, tol_ampl, | |
file, name): | |
""" | |
Determines if the peaks are within the given tolerance | |
keyword arguments: | |
max_p -- location and value of maxima | |
min_p -- location and value of minima | |
expected_max -- expected location and value of maxima | |
expected_min -- expected location and value of minima | |
atol_time -- absolute tolerance of location of vertex | |
tol_ampl -- relative tolerance of value of vertex | |
file -- log file to write to | |
name -- name of the test performed | |
""" | |
if len(max_p) == 5: | |
t_max_expected, y_max_expected = zip(*expected_max) | |
else: | |
if abs(max_p[0][0] - expected_max[0][0]) > 0.001: | |
t_max_expected, y_max_expected = zip(*expected_max[1:]) | |
else: | |
t_max_expected, y_max_expected = zip(*expected_max[:-1]) | |
if len(min_p) == 5: | |
t_min_expected, y_min_expected = zip(*expected_min) | |
else: | |
t_min_expected, y_min_expected = zip(*expected_min[:-1]) | |
t_max, y_max = zip(*max_p) | |
t_min, y_min = zip(*min_p) | |
t_max_close = np.isclose(t_max, t_max_expected, atol=atol_time, rtol=1e-12) | |
y_max_close = np.isclose(y_max, y_max_expected, tol_ampl) | |
t_min_close = np.isclose(t_min, t_min_expected, atol=atol_time, rtol=1e-12) | |
y_min_close = np.isclose(y_min, y_min_expected, tol_ampl) | |
_log_diff(t_max, y_max, t_min, y_min, | |
t_max_expected, y_max_expected, | |
t_min_expected, y_min_expected, | |
file, name) | |
return(t_max_close, y_max_close, t_min_close, y_min_close) | |
class Test_analytic_wfm(unittest.TestCase): | |
def test_ACV1(self): | |
#compare with previous lambda implementation | |
old = analytic_wfm._ACV_A1_L(linspace_standard) | |
acv = analytic_wfm.ACV_A1(linspace_standard) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
def test_ACV2(self): | |
#compare with previous lambda implementation | |
old = analytic_wfm._ACV_A2_L(linspace_standard) | |
acv = analytic_wfm.ACV_A2(linspace_standard) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
def test_ACV3(self): | |
#compare with previous lambda implementation | |
old = analytic_wfm._ACV_A3_L(linspace_standard) | |
acv = analytic_wfm.ACV_A3(linspace_standard) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
def test_ACV4(self): | |
#compare with previous lambda implementation | |
old = analytic_wfm._ACV_A4_L(linspace_standard) | |
acv = analytic_wfm.ACV_A4(linspace_standard) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
def test_ACV5(self): | |
#compare with previous lambda implementation | |
old = analytic_wfm._ACV_A5_L(linspace_standard) | |
acv = analytic_wfm.ACV_A5(linspace_standard) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
def test_ACV6(self): | |
#compare with previous lambda implementation | |
old = analytic_wfm._ACV_A6_L(linspace_standard) | |
acv = analytic_wfm.ACV_A6(linspace_standard) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
def test_ACV7(self): | |
num = np.linspace(0, 20, 1000) | |
old = analytic_wfm._ACV_A7_OLD(num) | |
acv = analytic_wfm.ACV_A7(num) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
def test_ACV8(self): | |
num = np.linspace(0, 3150, 10000) | |
old = analytic_wfm._ACV_A8_OLD(num) | |
acv = analytic_wfm.ACV_A8(num) | |
self.assertTrue(np.allclose(acv, old, rtol=1e-9)) | |
class _Test_peakdetect_template(unittest.TestCase): | |
func = None | |
file = "Mismatch data.txt" | |
name = "template" | |
args = [] | |
kwargs = {} | |
msg_t = "Time of {0!s} not within tolerance:\n\t{1}" | |
msg_y = "Amplitude of {0!s} not within tolerance:\n\t{1}" | |
def _test_peak_template(self, waveform, | |
expected_max, expected_min, | |
wav_name, | |
atol_time = 1e-5, tol_ampl = 1e-5): | |
""" | |
keyword arguments: | |
waveform -- a function that given x can generate a test waveform | |
expected_max -- position and amplitude where maxima are expected | |
expected_min -- position and amplitude where minima are expected | |
wav_name -- Name of the test waveform | |
atol_time -- absolute tolerance for position of vertex (default: 1e-5) | |
tol_ampl -- relative tolerance for position of vertex (default: 1e-5) | |
""" | |
y = waveform(linspace_peakdetect) | |
max_p, min_p = self.func(y, linspace_peakdetect, | |
*self.args, **self.kwargs | |
) | |
#check if the correct amount of peaks were discovered | |
self.assertIn(len(max_p), [4,5]) | |
self.assertIn(len(min_p), [4,5]) | |
# | |
# check if position and amplitude is within 0.001% which is approx the | |
# numeric uncertainty from the amount of samples used | |
# | |
t_max_close, y_max_close, t_min_close, y_min_close = _is_close(max_p, | |
min_p, | |
expected_max, | |
expected_min, | |
atol_time, tol_ampl, | |
self.file, "{0}: {1}".format(wav_name, self.name)) | |
#assert if values are outside of tolerance | |
self.assertTrue(np.all(t_max_close), | |
msg=self.msg_t.format("maxima", t_max_close)) | |
self.assertTrue(np.all(y_max_close), | |
msg=self.msg_y.format("maxima", y_max_close)) | |
self.assertTrue(np.all(t_min_close), | |
msg=self.msg_t.format("minima", t_min_close)) | |
self.assertTrue(np.all(y_min_close), | |
msg=self.msg_y.format("minima", y_min_close)) | |
def test_peak_ACV1(self): | |
peak_pos = 1000*np.sqrt(2) #1414.2135623730951 | |
peak_neg = -peak_pos | |
expected_max = [ | |
(0.005, peak_pos), | |
(0.025, peak_pos), | |
(0.045, peak_pos), | |
(0.065, peak_pos), | |
(0.085, peak_pos) | |
] | |
expected_min = [ | |
(0.015, peak_neg), | |
(0.035, peak_neg), | |
(0.055, peak_neg), | |
(0.075, peak_neg), | |
(0.095, peak_neg) | |
] | |
atol_time = 1e-5 | |
tol_ampl = 1e-6 | |
self._test_peak_template(analytic_wfm.ACV_A1, | |
expected_max, expected_min, | |
"ACV1", | |
atol_time, tol_ampl | |
) | |
def test_peak_ACV2(self): | |
peak_pos = 1000*np.sqrt(2) + 500 #1414.2135623730951 + 500 | |
peak_neg = (-1000*np.sqrt(2)) + 500 #-914.2135623730951 | |
expected_max = [ | |
(0.005, peak_pos), | |
(0.025, peak_pos), | |
(0.045, peak_pos), | |
(0.065, peak_pos), | |
(0.085, peak_pos) | |
] | |
expected_min = [ | |
(0.015, peak_neg), | |
(0.035, peak_neg), | |
(0.055, peak_neg), | |
(0.075, peak_neg), | |
(0.095, peak_neg) | |
] | |
atol_time = 1e-5 | |
tol_ampl = 2e-6 | |
self._test_peak_template(analytic_wfm.ACV_A2, | |
expected_max, expected_min, | |
"ACV2", | |
atol_time, tol_ampl | |
) | |
def test_peak_ACV3(self): | |
""" | |
Sine wave with a 3rd overtone | |
WolframAlpha solution | |
max{y = sin(100 pi x)+0.05 sin(400 pi x+(2 pi)/3)}~~ | |
sin(6.28319 n+1.51306)-0.05 sin(25.1327 n+5.00505) | |
at x~~0.00481623+0.02 n for integer n | |
min{y = sin(100 pi x)+0.05 sin(400 pi x+(2 pi)/3)}~~ | |
0.05 sin(6.55488-25.1327 n)-sin(1.37692-6.28319 n) | |
at x~~-0.00438287+0.02 n for integer n | |
Derivative for 50 Hz in 2 alternative forms | |
y = 100pi*cos(100pi*x) - 25pi*cos(400pi*x)-0.3464*50*pi*sin(400pi*x) | |
y = 100pi*cos(100pi*x) + 20pi*cos(400pi*x + 2*pi/3) | |
root 0 = 1/(50 * pi) * (pi*0 - 0.68846026579266880983) | |
The exact solution according to WolframAlpha - I haven't the foggiest | |
(tan^(-1)(root of | |
{#1^2-3&, 11 #2^8-8 #1 #2^7-8 #2^6+56 #1 #2^5+70 #2^4-56 #1 #2^3-48 #2^2+8 #1 #2-9&}(x) | |
near x = -0.822751)+pi n) / (50 * pi) | |
root 1 = 1/(50 * pi) * (pi*0 + 0.75653155241276430710) | |
period = 0.02 | |
""" | |
base = 1000*np.sqrt(2) | |
#def peak_pos(n): | |
# return base * (np.sin(6.28319 * n + 1.51306) | |
# -0.05*np.sin(25.1327 * n + 5.00505)) | |
#def peak_neg(n): | |
# return base * (0.05 * np.sin(6.55488 - 25.1327 * n) | |
# - np.sin(1.37692 - 6.28319 * n)) | |
def peak_pos(n): | |
return base * (np.sin(2*np.pi * n + 1.51306) | |
-0.05*np.sin(8*np.pi * n + 5.00505)) | |
def peak_neg(n): | |
return base * (0.05 * np.sin(6.55488 - 8*np.pi * n) | |
- np.sin(1.37692 - 2*np.pi * n)) | |
t_max = [ | |
0.75653155241276430710/(50*np.pi)+0.00,#0.004816229446859069 | |
0.75653155241276430710/(50*np.pi)+0.02,#0.024816229446859069 | |
0.75653155241276430710/(50*np.pi)+0.04,#0.044816229446859069 | |
0.75653155241276430710/(50*np.pi)+0.06,#0.064816229446859069 | |
0.75653155241276430710/(50*np.pi)+0.08 #0.084816229446859069 | |
] | |
t_min = [ | |
-0.68846026579266880983/(50*np.pi)+0.02,#0.015617125823069466 | |
-0.68846026579266880983/(50*np.pi)+0.04,#0.035617125823069466 | |
-0.68846026579266880983/(50*np.pi)+0.06,#0.055617125823069466 | |
-0.68846026579266880983/(50*np.pi)+0.08,#0.075617125823069466 | |
-0.68846026579266880983/(50*np.pi)+0.10 #0.095617125823069466 | |
] | |
expected_max = [ | |
(t_max[0], analytic_wfm.ACV_A3(t_max[0])), | |
(t_max[1], analytic_wfm.ACV_A3(t_max[1])), | |
(t_max[2], analytic_wfm.ACV_A3(t_max[2])), | |
(t_max[3], analytic_wfm.ACV_A3(t_max[3])), | |
(t_max[4], analytic_wfm.ACV_A3(t_max[4])), | |
] | |
expected_min = [ | |
(t_min[0], analytic_wfm.ACV_A3(t_min[0])), | |
(t_min[1], analytic_wfm.ACV_A3(t_min[1])), | |
(t_min[2], analytic_wfm.ACV_A3(t_min[2])), | |
(t_min[3], analytic_wfm.ACV_A3(t_min[3])), | |
(t_min[4], analytic_wfm.ACV_A3(t_min[4])), | |
] | |
atol_time = 1e-5 | |
tol_ampl = 2e-6 | |
#reduced tolerance since the expected values are only approximated | |
self._test_peak_template(analytic_wfm.ACV_A3, | |
expected_max, expected_min, | |
"ACV3", | |
atol_time, tol_ampl | |
) | |
def test_peak_ACV4(self): | |
""" | |
Sine wave with a 4th overtone | |
Expected data is from a numerical solution using 1e8 samples | |
The numerical solution used about 2 GB memory and required 64-bit | |
python | |
Test is currently disabled as it pushes time index forward enough to | |
change what peaks are discovers by peakdetect_fft, such that the last | |
maxima is lost instead of the first one, which is expected from all the | |
other functions | |
""" | |
expected_max = [ | |
(0.0059351920593519207, 1409.2119572886963), | |
(0.025935191259351911, 1409.2119572887088), | |
(0.045935191459351918, 1409.2119572887223), | |
(0.065935191659351911, 1409.2119572887243), | |
(0.085935191859351917, 1409.2119572887166) | |
] | |
expected_min = [ | |
(0.015935191159351911, -1409.2119572886984), | |
(0.035935191359351915, -1409.2119572887166), | |
(0.055935191559351914, -1409.2119572887245), | |
(0.075935191759351914, -1409.2119572887223), | |
(0.09593519195935192, -1409.2119572887068) | |
] | |
atol_time = 1e-5 | |
tol_ampl = 2.5e-6 | |
#reduced tolerance since the expected values are only approximated | |
self._test_peak_template(analytic_wfm.ACV_A4, | |
expected_max, expected_min, | |
"ACV4", | |
atol_time, tol_ampl | |
) | |
def test_peak_ACV5(self): | |
""" | |
Realistic triangle wave | |
Easy enough to solve, but here is the numerical solution from 1e8 | |
samples. Numerical solution used about 2 GB memory and required | |
64-bit python | |
expected_max = [ | |
[0.0050000000500000008, 1598.0613254815967] | |
[0.025000000250000001, 1598.0613254815778], | |
[0.045000000450000008, 1598.0613254815346], | |
[0.064999999650000001, 1598.0613254815594], | |
[0.084999999849999994, 1598.0613254815908] | |
] | |
expected_min = [ | |
[0.015000000150000001, -1598.0613254815908], | |
[0.035000000350000005, -1598.0613254815594], | |
[0.054999999549999998, -1598.0613254815346], | |
[0.074999999750000004, -1598.0613254815778], | |
[0.094999999949999997, -1598.0613254815967] | |
] | |
""" | |
peak_pos = 1130*np.sqrt(2) #1598.0613254815976 | |
peak_neg = -1130*np.sqrt(2) #-1598.0613254815967 | |
expected_max = [ | |
(0.005, peak_pos), | |
(0.025, peak_pos), | |
(0.045, peak_pos), | |
(0.065, peak_pos), | |
(0.085, peak_pos) | |
] | |
expected_min = [ | |
(0.015, peak_neg), | |
(0.035, peak_neg), | |
(0.055, peak_neg), | |
(0.075, peak_neg), | |
(0.095, peak_neg) | |
] | |
atol_time = 1e-5 | |
tol_ampl = 4e-6 | |
self._test_peak_template(analytic_wfm.ACV_A5, | |
expected_max, expected_min, | |
"ACV5", | |
atol_time, tol_ampl | |
) | |
def test_peak_ACV6(self): | |
""" | |
Realistic triangle wave | |
Easy enough to solve, but here is the numerical solution from 1e8 | |
samples. Numerical solution used about 2 GB memory and required | |
64-bit python | |
expected_max = [ | |
[0.0050000000500000008, 1485.6313472729362], | |
[0.025000000250000001, 1485.6313472729255], | |
[0.045000000450000008, 1485.6313472729012], | |
[0.064999999650000001, 1485.6313472729153], | |
[0.084999999849999994, 1485.6313472729323] | |
] | |
expected_min = [ | |
[0.015000000150000001, -1485.6313472729323], | |
[0.035000000350000005, -1485.6313472729153], | |
[0.054999999549999998, -1485.6313472729012], | |
[0.074999999750000004, -1485.6313472729255], | |
[0.094999999949999997, -1485.6313472729362] | |
] | |
""" | |
peak_pos = 1050.5*np.sqrt(2) #1485.6313472729364 | |
peak_neg = -1050.5*np.sqrt(2) #1485.6313472729255 | |
expected_max = [ | |
(0.005, peak_pos), | |
(0.025, peak_pos), | |
(0.045, peak_pos), | |
(0.065, peak_pos), | |
(0.085, peak_pos) | |
] | |
expected_min = [ | |
(0.015, peak_neg), | |
(0.035, peak_neg), | |
(0.055, peak_neg), | |
(0.075, peak_neg), | |
(0.095, peak_neg) | |
] | |
atol_time = 1e-5 | |
tol_ampl = 2.5e-6 | |
self._test_peak_template(analytic_wfm.ACV_A6, | |
expected_max, expected_min, | |
"ACV6", | |
atol_time, tol_ampl | |
) | |
class Test_peakdetect(_Test_peakdetect_template): | |
name = "peakdetect" | |
def __init__(self, *args, **kwargs): | |
super(Test_peakdetect, self).__init__(*args, **kwargs) | |
self.func = peakdetect.peakdetect | |
class Test_peakdetect_fft(_Test_peakdetect_template): | |
name = "peakdetect_fft" | |
def __init__(self, *args, **kwargs): | |
super(Test_peakdetect_fft, self).__init__(*args, **kwargs) | |
self.func = peakdetect.peakdetect_fft | |
class Test_peakdetect_parabola(_Test_peakdetect_template): | |
name = "peakdetect_parabola" | |
def __init__(self, *args, **kwargs): | |
super(Test_peakdetect_parabola, self).__init__(*args, **kwargs) | |
self.func = peakdetect.peakdetect_parabola | |
class Test_peakdetect_sine(_Test_peakdetect_template): | |
name = "peakdetect_sine" | |
def __init__(self, *args, **kwargs): | |
super(Test_peakdetect_sine, self).__init__(*args, **kwargs) | |
self.func = peakdetect.peakdetect_sine | |
class Test_peakdetect_sine_locked(_Test_peakdetect_template): | |
name = "peakdetect_sine_locked" | |
def __init__(self, *args, **kwargs): | |
super(Test_peakdetect_sine_locked, self).__init__(*args, **kwargs) | |
self.func = peakdetect.peakdetect_sine_locked | |
class Test_peakdetect_spline(_Test_peakdetect_template): | |
name = "peakdetect_spline" | |
def __init__(self, *args, **kwargs): | |
super(Test_peakdetect_spline, self).__init__(*args, **kwargs) | |
self.func = peakdetect.peakdetect_spline | |
class Test_peakdetect_zero_crossing(_Test_peakdetect_template): | |
name = "peakdetect_zero_crossing" | |
def __init__(self, *args, **kwargs): | |
super(Test_peakdetect_zero_crossing, self).__init__(*args, **kwargs) | |
self.func = peakdetect.peakdetect_zero_crossing | |
class Test_peakdetect_misc(unittest.TestCase): | |
def test__pad(self): | |
data = [1,2,3,4,5,6,5,4,3,2,1] | |
pad_len = 2 | |
pad = lambda x, c: x[:len(x) // 2] + [0] * c + x[len(x) // 2:] | |
expected = pad(list(data), 2 ** | |
peakdetect._n(len(data) * pad_len) - len(data)) | |
received = peakdetect._pad(data, pad_len) | |
self.assertListEqual(received, expected) | |
def test__n(self): | |
self.assertEqual(2**peakdetect._n(1000), 1024) | |
def test_zero_crossings(self): | |
y = analytic_wfm.ACV_A1(linspace_peakdetect) | |
expected_indice = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000] | |
indice = peakdetect.zero_crossings(y, 50) | |
msg = "index:{0:d} should be within 1 of expected:{1:d}" | |
for rec, exp in zip(indice, expected_indice): | |
self.assertAlmostEqual(rec, exp, delta=1, msg=msg.format(rec, exp)) | |
#class zero_crossings(unittest.TestCase): | |
if __name__ == "__main__": | |
tests_to_run = [ | |
#Test_analytic_wfm, | |
Test_peakdetect, | |
Test_peakdetect_parabola, | |
Test_peakdetect_fft, | |
#Test_peakdetect_sine, #sine tests disabled pending rework | |
#Test_peakdetect_sine_locked, | |
Test_peakdetect_spline, | |
Test_peakdetect_zero_crossing, | |
Test_peakdetect_misc | |
] | |
suites_list = [unittest.TestLoader().loadTestsFromTestCase(test_class) for test_class in tests_to_run] | |
big_suite = unittest.TestSuite(suites_list) | |
unittest.TextTestRunner(verbosity=2).run(big_suite) |
Thanks. The code saved me a lot of time. @cancan101 Is the pypi version being updated regularly? Not that I'm going to use it, but I might have to suggest the pypi version to my friends.
@Sakthi-G33k it not like this gist is seeing much in terms of updates, so I don't see any pypi getting regular updates either. There isn't much to update, unless adding additional logic like processing the indata for frequency domain padding for time domain interpolation to reduce edge effects, but personally I would prefer to just sample 2**n samples over x amount of whole periods of the signal.
Revised and published on PyPI and GitHub: https://pypi.org/project/peakdetect/
Hi,
The code is not working under python 3.8.6.
Below I put the diff for changes I made to make it work.
diff --git a/peakdetect.py b/peakdetect.py
index e388408..5d070fa 100644
--- a/peakdetect.py
+++ b/peakdetect.py
@@ -333,7 +333,7 @@ def peakdetect_fft(y_axis, x_axis, pad_len = 20):
#max_peaks, min_peaks = peakdetect_zero_crossing(y_axis_ifft, x_axis_ifft)
# store one 20th of a period as waveform data
- data_len = int(np.diff(zero_indices).mean()) / 10
+ data_len = int(np.diff(zero_indices).mean()) // 10
data_len += 1 - data_len & 1
diff --git a/test.py b/test.py
index 680c2a8..c7c6dfa 10644
--- a/test.py
+++ b/test.py
@@ -31,7 +31,7 @@ def prng():
def _write_log(file, header, message):
- with open(file, "ab") as f:
+ with open(file, "a") as f:
f.write(header)
f.write("\n")
f.writelines(message)
@@ -241,6 +241,8 @@ class _Test_peakdetect_template(unittest.TestCase):
*self.args, **self.kwargs
)
#check if the correct amount of peaks were discovered
+ max_p = list(max_p)
+ min_p = list(min_p)
self.assertIn(len(max_p), [4,5])
self.assertIn(len(min_p), [4,5])
published: https://pypi.python.org/pypi/analytic-wfm