biosppy.signals

This sub-package provides methods to process common physiological signals (biosignals).

Modules

biosppy.signals.abp 

This module provides methods to process Arterial Blood Pressure (ABP) signals.

copyright:

2015-2018 by Instituto de Telecomunicacoes

license:

BSD 3-clause, see LICENSE for more details.

biosppy.signals.abp.abp(signal=None, sampling_rate=1000.0, show=True)[source]

Process a raw ABP signal and extract relevant signal features using default parameters.

Parameters:

signal (array) – Raw ABP signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
show (bool, optional) – If True, show a summary plot.

Returns:

ts (array) – Signal time axis reference (seconds).
filtered (array) – Filtered ABP signal.
onsets (array) – Indices of ABP pulse onsets.
heart_rate_ts (array) – Heart rate time axis reference (seconds).
heart_rate (array) – Instantaneous heart rate (bpm).

biosppy.signals.abp.find_onsets_zong2003(signal=None, sampling_rate=1000.0, sm_size=None, size=None, alpha=2.0, wrange=None, d1_th=0, d2_th=None)[source]

Determine onsets of ABP pulses. Skips corrupted signal parts. Based on the approach by Zong et al. [Zong03].

Parameters:

signal (array) – Input filtered ABP signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
sm_size (int, optional) – Size of smoother kernel (seconds). Defaults to 0.25
size (int, optional) – Window to search for maxima (seconds). Defaults to 5
alpha (float, optional) – Normalization parameter. Defaults to 2.0
wrange (int, optional) – The window in which to search for a peak (seconds). Defaults to 0.1
d1_th (int, optional) – Smallest allowed difference between maxima and minima. Defaults to 0
d2_th (int, optional) – Smallest allowed time between maxima and minima (seconds), Defaults to 0.15

Returns:

onsets (array) – Indices of ABP pulse onsets.

References

[Zong03]

W Zong, T Heldt, GB Moody and RG Mark, “An Open-source Algorithm to Detect Onset of Arterial Blood Pressure Pulses”, IEEE Comp. in Cardiology, vol. 30, pp. 259-262, 2003

biosppy.signals.acc 

This module provides methods to process Acceleration (ACC) signals. Implemented code assumes ACC acquisition from a 3 orthogonal axis reference system.

copyright:

2015-2023 by Instituto de Telecomunicacoes

license:

BSD 3-clause, see LICENSE for more details.

Authors: Afonso Ferreira Diogo Vieira

biosppy.signals.acc.acc(signal=None, sampling_rate=100.0, units=None, path=None, show=True, interactive=False)[source]

Process a raw ACC signal and extract relevant signal features using default parameters.

Parameters:

signal (array) – Raw ACC signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
units (str, optional) – The units of the input signal. If specified, the plot will have the y-axis labeled with the corresponding units.
path (str, optional) – If provided, the plot will be saved to the specified file.
show (bool, optional) – If True, show a summary plot.
interactive (bool, optional) – If True, shows an interactive plot.

Returns:

ts (array) – Signal time axis reference (seconds).
signal (array) – Raw (unfiltered) ACC signal.
vm (array) – Vector Magnitude feature of the signal.
sm (array) – Signal Magnitude feature of the signal.
freq_features (dict) – Positive Frequency domains (Hz) of the signal.
amp_features (dict) – Normalized Absolute Amplitudes of the signal.

biosppy.signals.acc.activity_index(signal=None, sampling_rate=100.0, window_1=5, window_2=60)[source]

Compute the activity index of an ACC signal. Follows the method described in [Lin18], the activity index is computed as follows: 1) Calculate the ACC magnitude if the signal is triaxial 2) Calculate the standard deviation of the ACC magnitude for each ‘window_1’ seconds 3) The activity index will be the mean standard deviation for each ‘window_2’ seconds

Parameters:

signal (array) – Raw ACC signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
window_1 (int, float, optional) – Window length (seconds) for the first moving average filter. Default: 5
window_2 (int, float, optional) – Window length (seconds) for the second moving average filter. Default: 60

Returns:

ts (array) – Time axis reference (seconds).
activity_index (array) – Activity index of the signal.

References

[Lin18]

W.-Y. Lin, V. Verma, M.-Y. Lee, C.-S. Lai, Activity

Monitoring with a Wrist-Worn, Accelerometer-Based Device, Micromachines 9 (2018) 450

biosppy.signals.acc.frequency_domain_feature_extractor(signal=None, sampling_rate=100.0)[source]

Extracts the FFT from each ACC sub-signal (x, y, z), given the signal itself.

Parameters:

signal (array) – Input ACC signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).

Returns:

freq_features (dict) – Dictionary of positive frequencies (Hz) for all sub-signals.
amp_features (dict) – Dictionary of Normalized Absolute Amplitudes for all sub-signals.

biosppy.signals.acc.time_domain_feature_extractor(signal=None)[source]

Extracts the vector magnitude and signal magnitude features from an input ACC signal, given the signal itself.

Parameters:

signal (array) – Input ACC signal.

Returns:

vm_features (array) – Extracted Vector Magnitude (VM) feature.
sm_features (array) – Extracted Signal Magnitude (SM) feature.

biosppy.signals.bvp 

This module provides methods to process Blood Volume Pulse (BVP) signals.

——– DEPRECATED ——– PLEASE, USE THE PPG MODULE This module was left for compatibility —————————-

copyright:

2015-2018 by Instituto de Telecomunicacoes

license:

BSD 3-clause, see LICENSE for more details.

biosppy.signals.bvp.bvp(signal=None, sampling_rate=1000.0, path=None, show=True)[source]

Process a raw BVP signal and extract relevant signal features using default parameters. :param signal: Raw BVP signal. :type signal: array :param sampling_rate: Sampling frequency (Hz). :type sampling_rate: int, float, optional :param path: If provided, the plot will be saved to the specified file. :type path: str, optional :param show: If True, show a summary plot. :type show: bool, optional

Returns:

ts (array) – Signal time axis reference (seconds).
filtered (array) – Filtered BVP signal.
onsets (array) – Indices of BVP pulse onsets.
heart_rate_ts (array) – Heart rate time axis reference (seconds).
heart_rate (array) – Instantaneous heart rate (bpm).

biosppy.signals.ppg 

This module provides methods to process Photoplethysmogram (PPG) signals.

copyright:

2015-2018 by Instituto de Telecomunicacoes

license:

BSD 3-clause, see LICENSE for more details.

biosppy.signals.ppg.find_onsets_elgendi2013(signal=None, sampling_rate=1000.0, peakwindow=0.111, beatwindow=0.667, beatoffset=0.02, mindelay=0.3)[source]

Determines onsets of PPG pulses.

Parameters:

signal (array) – Input filtered PPG signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
peakwindow (float) – Parameter W1 on referenced article Optimized at 0.111
beatwindow (float) – Parameter W2 on referenced article Optimized at 0.667
beatoffset (float) – Parameter beta on referenced article Optimized at 0.2
mindelay (float) – Minimum delay between peaks. Avoids false positives

Returns:

onsets (array) – Indices of PPG pulse onsets.
params (dict) – Input parameters of the function

References

Elgendi M, Norton I, Brearley M, Abbott D, Schuurmans D (2013) Systolic Peak Detection in

Acceleration Photoplethysmograms Measured from Emergency Responders in Tropical Conditions. PLoS ONE 8(10): e76585. doi:10.1371/journal.pone.0076585.

Notes

Optimal ranges for signal filtering (from Elgendi et al. 2013): “Optimization of the beat detector’s spectral window for the lower frequency resulted in a value within 0.5– 1 Hz with the higher frequency within 7–15 Hz”

All the number references below between curly brackets {…} by the code refer to the line numbers of code in “Table 2 Algorithm IV: DETECTOR (PPG signal, F1, F2, W1, W2, b)” from Elgendi et al. 2013 for a better comparison of the algorithm

biosppy.signals.ppg.find_onsets_kavsaoglu2016(signal=None, sampling_rate=1000.0, alpha=0.2, k=4, init_bpm=90, min_delay=0.6, max_BPM=150)[source]

Determines onsets of PPG pulses.

Parameters:

signal (array) – Input filtered PPG signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
alpha (float, optional) – Low-pass filter factor. Avoids abrupt changes of BPM.
k (int, float, optional) – Number of segments by pulse. Width of each segment = Period of pulse according to current BPM / k
init_bpm (int, float, optional) – Initial BPM. Higher value results in a smaller segment width.
min_delay (float) – Minimum delay between peaks as percentage of current BPM pulse period. Avoids false positives
max_bpm (int, float, optional) – Maximum BPM. Maximum value accepted as valid BPM.

Returns:

onsets (array) – Indices of PPG pulse onsets.
window_marks (array) – Indices of segments window boundaries.
params (dict) – Input parameters of the function

References

Kavsaoğlu, Ahmet & Polat, Kemal & Bozkurt, Mehmet. (2016). An innovative peak detection algorithm for

photoplethysmography signals: An adaptive segmentation method. TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES. 24. 1782-1796. 10.3906/elk-1310-177.

Notes

This algorithm is an adaption of the one described on Kavsaoğlu et al. (2016). This version takes into account a minimum delay between peaks and builds upon the adaptive segmentation by using a low-pass filter for BPM changes. This way, even if the algorithm wrongly detects a peak, the BPM value will stay relatively constant so the next pulse can be correctly segmented.

biosppy.signals.ppg.ppg(signal=None, sampling_rate=1000.0, units=None, show=True)[source]

Process a raw PPG signal and extract relevant signal features using default parameters.

Parameters:

signal (array) – Raw PPG signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
units (str, optional) – The units of the input signal. If specified, the plot will have the y-axis labeled with the corresponding units.
show (bool, optional) – If True, show a summary plot.

Returns:

ts (array) – Signal time axis reference (seconds).
filtered (array) – Filtered PPG signal.
peaks (array) – Indices of PPG pulse peaks.
templates_ts (array) – Templates time axis reference (seconds).
templates (array) – Extracted heartbeat templates.
heart_rate_ts (array) – Heart rate time axis reference (seconds).
heart_rate (array) – Instantaneous heart rate (bpm).

biosppy.signals.ppg.ppg_segmentation(signal=None, sampling_rate=1000.0, peaks=None, selection=False, peak_threshold=None)[source]

Segments a filtered PPG signal. Segmentation filtering is achieved by taking into account segments selected by peak height and pulse morphology.

Parameters:

signal (array) – Filtered PPG signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
peaks (array) – List of PPG systolic peaks.
selection (bool, optional) – If True, performs selection with peak height and pulse morphology.
peak_threshold (int, float, optional) – If selection is True, selects peaks with height greater than defined threshold.

Returns:

onsets (array) – Indices of PPG pulse onsets (i.e., start of beats) of the selected segments.
peaks (array) – List of PPG systolic peaks of the selected segments.
segments_loc (array) – Start and end indices for each selected pulse segment.

biosppy.signals.tools 

This module provides various signal analysis methods in the time and frequency domains.

copyright:

2015-2023 by Instituto de Telecomunicacoes

license:

BSD 3-clause, see LICENSE for more details.

class biosppy.signals.tools.OnlineFilter(b=None, a=None)[source]

Bases: object

Online filtering.

Parameters:

b (array) – Numerator coefficients.
a (array) – Denominator coefficients.

filter(signal=None)[source]

Filter a signal segment.

Parameters:: signal (array) – Signal segment to filter.
Returns:: filtered (array) – Filtered signal segment.

reset()[source]: Reset the filter state.

biosppy.signals.tools.analytic_signal(signal=None, N=None)[source]

Compute analytic signal, using the Hilbert Transform.

Parameters:

signal (array) – Input signal.
N (int, optional) – Number of Fourier components; default is len(signal).

Returns:

amplitude (array) – Amplitude envelope of the analytic signal.
phase (array) – Instantaneous phase component of the analystic signal.

biosppy.signals.tools.band_power(freqs=None, power=None, frequency=None, decibel=True)[source]

Compute the avearge power in a frequency band.

Parameters:

freqs (array) – Array of frequencies (Hz) at which the power was computed.
power (array) – Input power spectrum.
frequency (list, array) – Pair of frequencies defining the band.
decibel (bool, optional) – If True, input power is in decibels.

Returns:

avg_power (float) – The average power in the band.

biosppy.signals.tools.detrend_smoothness_priors(signal, smoothing_factor=10)[source]

Detrending method based on smoothness priors applied to HRV signal analysis.

Follows the approach by Tarvainen et al. [Tarivainen2002].

Parameters:

signal (array) – Signal to be detrended.
smoothing_factor (int, float, optional) – Smoothing parameter lambda. Default: 10.

Returns:

detrended (array) – Detrended signal.
trend (array) – The trend component of the signal.

References

[Tarivainen2002]

M. P. Tarvainen, P. O. Ranta-aho and P. A. Karjalainen, “An advanced detrending method with application to HRV analysis,” in IEEE Transactions on Biomedical Engineering, vol. 49, no. 2, pp. 172-175, Feb. 2002, doi: 10.1109/10.979357.

biosppy.signals.tools.distance_profile(query=None, signal=None, metric='euclidean')[source]

Compute the distance profile of a query sequence against a signal.

Implements the algorithm described in [Mueen2014].

Parameters:

query (array) – Input query signal sequence.
signal (array) – Input target time series signal.
metric (str, optional) – The distance metric to use; one of ‘euclidean’ or ‘pearson’; default is ‘euclidean’.

Returns:

dist (array) – Distance of the query sequence to every sub-sequnce in the signal.

Notes

Computes distances on z-normalized data.

References

[Mueen2014]

Abdullah Mueen, Hossein Hamooni, “Trilce Estrada: Time Series Join on Subsequence Correlation”, ICDM 2014: 450-459

biosppy.signals.tools.filter_signal(signal=None, ftype='FIR', band='lowpass', order=None, frequency=None, sampling_rate=1000.0, **kwargs)[source]

Filter a signal according to the given parameters.

Parameters:

signal (array) – Signal to filter.
ftype (str) –
Filter type:
- Finite Impulse Response filter (‘FIR’);
- Butterworth filter (‘butter’);
- Chebyshev filters (‘cheby1’, ‘cheby2’);
- Elliptic filter (‘ellip’);
- Bessel filter (‘bessel’).
- Notch filter (‘notch’).
band (str) –
Band type:
- Low-pass filter (‘lowpass’);
- High-pass filter (‘highpass’);
- Band-pass filter (‘bandpass’);
- Band-stop filter (‘bandstop’).
order (int) – Order of the filter.
frequency (int, float, list, array) –
Cutoff frequencies; format depends on type of band:
- ’lowpass’ or ‘bandpass’: single frequency;
- ’bandpass’ or ‘bandstop’: pair of frequencies.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
**kwargs (dict, optional) –
Additional keyword arguments are passed to the underlying scipy.signal function. - Q : float

Quality factor (only for ‘notch’ filter). Default: 30.

Returns:

signal (array) – Filtered signal.
sampling_rate (float) – Sampling frequency (Hz).
params (dict) – Filter parameters.

Notes

Uses a forward-backward filter implementation. Therefore, the combined filter has linear phase.

biosppy.signals.tools.find_extrema(signal=None, mode='both')[source]

Locate local extrema points in a signal.

Based on Fermat’s Theorem [Ferm].

Parameters:

signal (array) – Input signal.
mode (str, optional) – Whether to find maxima (‘max’), minima (‘min’), or both (‘both’).

Returns:

extrema (array) – Indices of the extrema points.
values (array) – Signal values at the extrema points.

References

[Ferm]

Wikipedia, “Fermat’s theorem (stationary points)”, https://en.wikipedia.org/wiki/Fermat%27s_theorem_(stationary_points)

biosppy.signals.tools.find_intersection(x1=None, y1=None, x2=None, y2=None, alpha=1.5, xtol=1e-06, ytol=1e-06)[source]

Find the intersection points between two lines using piecewise polynomial interpolation.

Parameters:

x1 (array) – Array of x-coordinates of the first line.
y1 (array) – Array of y-coordinates of the first line.
x2 (array) – Array of x-coordinates of the second line.
y2 (array) – Array of y-coordinates of the second line.
alpha (float, optional) – Resolution factor for the x-axis; fraction of total number of x-coordinates.
xtol (float, optional) – Tolerance for the x-axis.
ytol (float, optional) – Tolerance for the y-axis.

Returns:

roots (array) – Array of x-coordinates of found intersection points.
values (array) – Array of y-coordinates of found intersection points.

Notes

If no intersection is found, returns the closest point.

biosppy.signals.tools.finite_difference(signal=None, weights=None)[source]

Apply the Finite Difference method to compute derivatives.

Parameters:

signal (array) – Signal to differentiate.
weights (list, array) – Finite difference weight coefficients.

Returns:

index (array) – Indices from signal for which the derivative was computed.
derivative (array) – Computed derivative.

Notes

The method assumes central differences weights.
The method accounts for the delay introduced by the algorithm.

Raises:: ValueError – If the number of weights is not odd.

biosppy.signals.tools.get_filter(ftype='FIR', band='lowpass', order=None, frequency=None, sampling_rate=1000.0, **kwargs)[source]

Compute digital (FIR or IIR) filter coefficients with the given parameters.

Parameters:

ftype (str) –
Filter type:
- Finite Impulse Response filter (‘FIR’);
- Butterworth filter (‘butter’);
- Chebyshev filters (‘cheby1’, ‘cheby2’);
- Elliptic filter (‘ellip’);
- Bessel filter (‘bessel’).
- Notch filter (‘notch’).
band (str) –
Band type:
- Low-pass filter (‘lowpass’);
- High-pass filter (‘highpass’);
- Band-pass filter (‘bandpass’);
- Band-stop filter (‘bandstop’).
order (int) – Order of the filter.
frequency (int, float, list, array) –
Cutoff frequencies; format depends on type of band:
- ’lowpass’ or ‘highpass’: single frequency;
- ’bandpass’ or ‘bandstop’: pair of frequencies.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
**kwargs (dict, optional) –
Additional keyword arguments are passed to the underlying scipy.signal function. - Q : float

Quality factor (only for ‘notch’ filter). Default: 30.

Returns:

b (array) – Numerator coefficients.
a (array) – Denominator coefficients.
See Also – scipy.signal

biosppy.signals.tools.get_heart_rate(beats=None, sampling_rate=1000.0, smooth=False, size=3)[source]

Compute instantaneous heart rate from an array of beat indices.

Parameters:

beats (array) – Beat location indices.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
smooth (bool, optional) – If True, perform smoothing on the resulting heart rate.
size (int, optional) – Size of smoothing window; ignored if smooth is False.

Returns:

index (array) – Heart rate location indices.
heart_rate (array) – Instantaneous heart rate (bpm).

Notes

Assumes normal human heart rate to be between 40 and 200 bpm.

biosppy.signals.tools.mean_waves(data=None, size=None, step=None)[source]

Extract mean samples from a data set.

Parameters:

data (array) – An m by n array of m data samples in an n-dimensional space.
size (int) – Number of samples to use for each mean sample.
step (int, optional) – Number of samples to jump, controlling overlap; default is equal to size (no overlap).

Returns:

waves (array) – An k by n array of mean samples.

Notes

Discards trailing samples if they are not enough to satify the size parameter.

Raises:

ValueError – If step is an invalid value.
ValueError – If there are not enough samples for the given size.

biosppy.signals.tools.median_waves(data=None, size=None, step=None)[source]

Extract median samples from a data set.

Parameters:

data (array) – An m by n array of m data samples in an n-dimensional space.
size (int) – Number of samples to use for each median sample.
step (int, optional) – Number of samples to jump, controlling overlap; default is equal to size (no overlap).

Returns:

waves (array) – An k by n array of median samples.

Notes

Discards trailing samples if they are not enough to satify the size parameter.

Raises:

ValueError – If step is an invalid value.
ValueError – If there are not enough samples for the given size.

biosppy.signals.tools.normalize(signal=None, ddof=1)[source]

Normalize a signal to zero mean and unitary standard deviation.

Parameters:

signal (array) – Input signal.
ddof (int, optional) – Delta degrees of freedom for standard deviation computation; the divisor is N - ddof, where N is the number of elements; default is one.

Returns:

signal (array) – Normalized signal.

biosppy.signals.tools.pearson_correlation(x=None, y=None)[source]

Compute the Pearson Correlation Coefficient bertween two signals.

The coefficient is given by:

$r_{xy} = \frac{E[(X - \mu_X) (Y - \mu_Y)]}{\sigma_X \sigma_Y}$

Parameters:

x (array) – First input signal.
y (array) – Second input signal.

Returns:

rxy (float) – Pearson correlation coefficient, ranging between -1 and +1.

Raises:

ValueError – If the input signals do not have the same length.

biosppy.signals.tools.phase_locking(signal1=None, signal2=None, N=None)[source]

Compute the Phase-Locking Factor (PLF) between two signals.

Parameters:

signal1 (array) – First input signal.
signal2 (array) – Second input signal.
N (int, optional) – Number of Fourier components.

Returns:

plf (float) – The PLF between the two signals.

biosppy.signals.tools.power_spectrum(signal=None, sampling_rate=1000.0, pad=None, pow2=False, decibel=True)[source]

Compute the power spectrum of a signal (one-sided).

Parameters:

signal (array) – Input signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
pad (int, optional) – Padding for the Fourier Transform (number of zeros added); defaults to no padding..
pow2 (bool, optional) – If True, rounds the number of points N = len(signal) + pad to the nearest power of 2 greater than N.
decibel (bool, optional) – If True, returns the power in decibels.

Returns:

freqs (array) – Array of frequencies (Hz) at which the power was computed.
power (array) – Power spectrum.

biosppy.signals.tools.rms_error(x=None, y=None)[source]

Compute the Root-Mean-Square Error between two signals.

The error is given by:

$rmse = \sqrt{E[(X - Y)^2]}$

Parameters:

x (array) – First input signal.
y (array) – Second input signal.

Returns:

rmse (float) – Root-mean-square error.

Raises:

ValueError – If the input signals do not have the same length.

biosppy.signals.tools.signal_cross_join(signal1=None, signal2=None, size=None, index=None, limit=None)[source]

Compute the matrix profile for a similarity join of two time series.

Computes the nearest sub-sequence in signal2 for each sub-sequence in signal1. Implements the algorithm described in [Yeh2016_c].

Parameters:

signal1 (array) – Fisrt input time series signal.
signal2 (array) – Second input time series signal.
size (int) – Size of the query sub-sequences.
index (list, array, optional) – Starting indices for query sub-sequences; the default is to search all sub-sequences.
limit (int, optional) – Upper limit for the number of query sub-sequences; the default is to search all sub-sequences.

Returns:

matrix_index (array) – Matric profile index.
matrix_profile (array) – Computed matrix profile (distances).

Notes

Computes euclidean distances on z-normalized data.

References

[Yeh2016_c]

Chin-Chia Michael Yeh, Yan Zhu, Liudmila Ulanova, Nurjahan Begum, Yifei Ding, Hoang Anh Dau, Diego Furtado Silva, Abdullah Mueen, Eamonn Keogh, “Matrix Profile I: All Pairs Similarity Joins for Time Series: A Unifying View that Includes Motifs, Discords and Shapelets”, IEEE ICDM 2016

biosppy.signals.tools.signal_self_join(signal=None, size=None, index=None, limit=None)[source]

Compute the matrix profile for a self-similarity join of a time series.

Implements the algorithm described in [Yeh2016_b].

Parameters:

signal (array) – Input target time series signal.
size (int) – Size of the query sub-sequences.
index (list, array, optional) – Starting indices for query sub-sequences; the default is to search all sub-sequences.
limit (int, optional) – Upper limit for the number of query sub-sequences; the default is to search all sub-sequences.

Returns:

matrix_index (array) – Matric profile index.
matrix_profile (array) – Computed matrix profile (distances).

Notes

Computes euclidean distances on z-normalized data.

References

[Yeh2016_b]

Chin-Chia Michael Yeh, Yan Zhu, Liudmila Ulanova, Nurjahan Begum, Yifei Ding, Hoang Anh Dau, Diego Furtado Silva, Abdullah Mueen, Eamonn Keogh, “Matrix Profile I: All Pairs Similarity Joins for Time Series: A Unifying View that Includes Motifs, Discords and Shapelets”, IEEE ICDM 2016

biosppy.signals.tools.signal_stats(signal=None)[source]

Compute various metrics describing the signal.

Parameters:

signal (array) – Input signal.

Returns:

mean (float) – Mean of the signal.
median (float) – Median of the signal.
min (float) – Minimum signal value.
max (float) – Maximum signal value.
max_amp (float) – Maximum absolute signal amplitude, in relation to the mean.
range (float) – Signal range (max - min).
q1 (float) – First quartile of the signal.
q3 (float) – Third quartile of the signal.
var (float) – Signal variance (unbiased).
std_dev (float) – Standard signal deviation (unbiased).
abs_dev (float) – Mean absolute signal deviation around the median.
rms (float) – Root-mean-square of the signal.
kurtosis (float) – Signal kurtosis (unbiased).
skew (float) – Signal skewness (unbiased).

biosppy.signals.tools.smoother(signal=None, kernel='boxzen', size=10, mirror=True, **kwargs)[source]

Smooth a signal using an N-point moving average [MAvg] filter.

This implementation uses the convolution of a filter kernel with the input signal to compute the smoothed signal [Smit97].

Availabel kernels: median, boxzen, boxcar, triang, blackman, hamming, hann, bartlett, flattop, parzen, bohman, blackmanharris, nuttall, barthann, kaiser (needs beta), gaussian (needs std), general_gaussian (needs power, width), slepian (needs width), chebwin (needs attenuation).

Parameters:

signal (array) – Signal to smooth.
kernel (str, array, optional) – Type of kernel to use; if array, use directly as the kernel.
size (int, optional) – Size of the kernel; ignored if kernel is an array.
mirror (bool, optional) – If True, signal edges are extended to avoid boundary effects.
**kwargs (dict, optional) – Additional keyword arguments are passed to the underlying scipy.signal.windows function.

Returns:

signal (array) – Smoothed signal.
params (dict) – Smoother parameters.

Notes

When the kernel is ‘median’, mirror is ignored.

References

[MAvg]

Wikipedia, “Moving Average”, http://en.wikipedia.org/wiki/Moving_average

[Smit97]

S. W. Smith, “Moving Average Filters - Implementation by Convolution”, http://www.dspguide.com/ch15/1.htm, 1997

biosppy.signals.tools.synchronize(x=None, y=None, detrend=True)[source]

Align two signals based on cross-correlation.

Parameters:

x (array) – First input signal.
y (array) – Second input signal.
detrend (bool, optional) – If True, remove signal means before computation.

Returns:

delay (int) – Delay (number of samples) of ‘x’ in relation to ‘y’; if ‘delay’ < 0 , ‘x’ is ahead in relation to ‘y’; if ‘delay’ > 0 , ‘x’ is delayed in relation to ‘y’.
corr (float) – Value of maximum correlation.
synch_x (array) – Biggest possible portion of ‘x’ in synchronization.
synch_y (array) – Biggest possible portion of ‘y’ in synchronization.

biosppy.signals.tools.welch_spectrum(signal=None, sampling_rate=1000.0, size=None, overlap=None, window='hanning', window_kwargs=None, pad=None, decibel=True)[source]

Compute the power spectrum of a signal using Welch’s method (one-sided).

Parameters:

signal (array) – Input signal.
sampling_rate (int, float, optional) – Sampling frequency (Hz).
size (int, optional) – Number of points in each Welch segment; defaults to the equivalent of 1 second; ignored when ‘window’ is an array.
overlap (int, optional) – Number of points to overlap between segments; defaults to size / 2.
window (str, array, optional) – Type of window to use.
window_kwargs (dict, optional) – Additional keyword arguments to pass on window creation; ignored if ‘window’ is an array.
pad (int, optional) – Padding for the Fourier Transform (number of zeros added); defaults to no padding.
decibel (bool, optional) – If True, returns the power in decibels.

Returns:

freqs (array) – Array of frequencies (Hz) at which the power was computed.
power (array) – Power spectrum.

Notes

Detrends each Welch segment by removing the mean.

biosppy.signals.tools.windower(signal=None, size=None, step=None, fcn=None, fcn_kwargs=None, kernel='boxcar', kernel_kwargs=None)[source]

Apply a function to a signal in sequential windows, with optional overlap.

Availabel window kernels: boxcar, triang, blackman, hamming, hann, bartlett, flattop, parzen, bohman, blackmanharris, nuttall, barthann, kaiser (needs beta), gaussian (needs std), general_gaussian (needs power, width), slepian (needs width), chebwin (needs attenuation).

Parameters:

signal (array) – Input signal.
size (int) – Size of the signal window.
step (int, optional) – Size of window shift; if None, there is no overlap.
fcn (callable) – Function to apply to each window.
fcn_kwargs (dict, optional) – Additional keyword arguments to pass to ‘fcn’.
kernel (str, array, optional) – Type of kernel to use; if array, use directly as the kernel.
kernel_kwargs (dict, optional) – Additional keyword arguments to pass on window creation; ignored if ‘kernel’ is an array.

Returns:

index (array) – Indices characterizing window locations (start of the window).
values (array) – Concatenated output of calling ‘fcn’ on each window.

biosppy.signals.tools.zero_cross(signal=None, detrend=False)[source]

Locate the indices where the signal crosses zero.

Parameters:

signal (array) – Input signal.
detrend (bool, optional) – If True, remove signal mean before computation.

Returns:

zeros (array) – Indices of zero crossings.

Notes

When the signal crosses zero between samples, the first index is returned.

biosppy.signals

Modules

biosppy.signals.abp

biosppy.signals.acc

biosppy.signals.bvp

biosppy.signals.ppg

biosppy.signals.tools

biosppy.signals.abp 

biosppy.signals.acc 

biosppy.signals.bvp 

biosppy.signals.ppg 

biosppy.signals.tools 