processing

The processing subpackage contains signal-processing tools.

Basic Utility

Basic signal processing functions

wfdb.processing.resample_ann(resampled_t, ann_sample)

Compute the new annotation indices

resampled_t : numpy array

Array of signal locations as returned by scipy.signal.resample

ann_sample : numpy array

Array of annotation locations

resampled_ann_sample : numpy array

Array of resampled annotation locations

wfdb.processing.resample_sig(x, fs, fs_target)

Resample a signal to a different frequency.

x : numpy array

Array containing the signal

fs : int, or float

The original sampling frequency

fs_target : int, or float

The target frequency

resampled_x : numpy array

Array of the resampled signal values

resampled_t : numpy array

Array of the resampled signal locations

wfdb.processing.resample_singlechan(x, ann, fs, fs_target)

Resample a single-channel signal with its annotations

x: numpy array

The signal array

ann : wfdb Annotation

The wfdb annotation object

fs : int, or float

The original frequency

fs_target : int, or float

The target frequency

resampled_x : numpy array

Array of the resampled signal values

resampled_ann : wfdb Annotation

Annotation containing resampled annotation locations

wfdb.processing.resample_multichan(xs, ann, fs, fs_target, resamp_ann_chan=0)

Resample multiple channels with their annotations

xs: numpy array

The signal array

ann : wfdb Annotation

The wfdb annotation object

fs : int, or float

The original frequency

fs_target : int, or float

The target frequency

resample_ann_channel : int, optional

The signal channel used to compute new annotation indices

resampled_xs : numpy array

Array of the resampled signal values

resampled_ann : wfdb Annotation

Annotation containing resampled annotation locations

wfdb.processing.normalize_bound(sig, lb=0, ub=1)

Normalize a signal between the lower and upper bound

sig : numpy array

Original signal to be normalized

lb : int, or float

Lower bound

ub : int, or float

Upper bound

x_normalized : numpy array

Normalized signal

wfdb.processing.get_filter_gain(b, a, f_gain, fs)

Given filter coefficients, return the gain at a particular frequency.

b : list

List of linear filter b coefficients

a : list

List of linear filter a coefficients

f_gain : int or float, optional

The frequency at which to calculate the gain

fs : int or float, optional

The sampling frequency of the system

Heart Rate

wfdb.processing.compute_hr(sig_len, qrs_inds, fs)

Compute instantaneous heart rate from peak indices.

sig_len : int

The length of the corresponding signal

qrs_inds : numpy array

The qrs index locations

fs : int, or float

The corresponding signal’s sampling frequency.

heart_rate : numpy array

An array of the instantaneous heart rate, with the length of the corresponding signal. Contains numpy.nan where heart rate could not be computed.

Peaks

wfdb.processing.find_peaks(sig)

Find hard peaks and soft peaks in a signal, defined as follows:

• Hard peak: a peak that is either /or /
• Soft peak: a peak that is either /-or -/ In this case we define the middle as the peak

sig : np array

The 1d signal array

hard_peaks : numpy array

Array containing the indices of the hard peaks:

soft_peaks : numpy array

Array containing the indices of the soft peaks

wfdb.processing.find_local_peaks(sig, radius)

Find all local peaks in a signal. A sample is a local peak if it is the largest value within the <radius> samples on its left and right.

In cases where it shares the max value with nearby samples, the middle sample is classified as the local peak.

sig : numpy array

1d numpy array of the signal.

radius : int

The radius in which to search for defining local maxima.

wfdb.processing.correct_peaks(sig, peak_inds, search_radius, smooth_window_size, peak_dir='compare')

Adjust a set of detected peaks to coincide with local signal maxima, and

sig : numpy array

The 1d signal array

peak_inds : np array

Array of the original peak indices

max_gap : int

The radius within which the original peaks may be shifted.

smooth_window_size : int

The window size of the moving average filter applied on the signal. Peak distance is calculated on the difference between the original and smoothed signal.

peak_dir : str, optional

The expected peak direction: ‘up’ or ‘down’, ‘both’, or ‘compare’.

• If ‘up’, the peaks will be shifted to local maxima
• If ‘down’, the peaks will be shifted to local minima
• If ‘both’, the peaks will be shifted to local maxima of the rectified signal
• If ‘compare’, the function will try both ‘up’ and ‘down’ options, and choose the direction that gives the largest mean distance from the smoothed signal.

corrected_peak_inds : numpy array

Array of the corrected peak indices

QRS Detectors

class wfdb.processing.XQRS(sig, fs, conf=None)

The qrs detector class for the xqrs algorithm.

The XQRS.Conf class is the configuration class that stores initial parameters for the detection.

The XQRS.detect method runs the detection algorithm.

The process works as follows:

• Load the signal and configuration parameters.
• Bandpass filter the signal between 5 and 20 Hz, to get the filtered signal.
• Apply moving wave integration (mwi) with a ricker (Mexican hat) wavelet onto the filtered signal, and save the square of the integrated signal.
• Conduct learning if specified, to initialize running parameters of noise and qrs amplitudes, the qrs detection threshold, and recent rr intervals. If learning is unspecified or fails, use default parameters. See the docstring for the _learn_init_params method of this class for details.
• Run the main detection. Iterate through the local maxima of the mwi signal. For each local maxima:
  • Check if it is a qrs complex. To be classified as a qrs, it must come after the refractory period, cross the qrs detection threshold, and not be classified as a t-wave if it comes close enough to the previous qrs. If successfully classified, update running detection threshold and heart rate parameters.
  • If not a qrs, classify it as a noise peak and update running parameters.
  • Before continuing to the next local maxima, if no qrs was detected within 1.66 times the recent rr interval, perform backsearch qrs detection. This checks previous peaks using a lower qrs detection threshold.

>>> import wfdb
>>> from wfdb import processing

>>> sig, fields = wfdb.rdsamp('sample-data/100', channels=[0])
>>> xqrs = processing.XQRS(sig=sig[:,0], fs=fields['fs'])
>>> xqrs.detect()

>>> wfdb.plot_items(signal=sig, ann_samp=[xqrs.qrs_inds])

class Conf(hr_init=75, hr_max=200, hr_min=25, qrs_width=0.1, qrs_thr_init=0.13, qrs_thr_min=0, ref_period=0.2, t_inspect_period=0.36)

Initial signal configuration object for this qrs detector

detect(sampfrom=0, sampto='end', learn=True, verbose=True)

Detect qrs locations between two samples.

sampfrom : int, optional

The starting sample number to run the detection on.

sampto : int, optional

The final sample number to run the detection on. Set as ‘end’ to run on the entire signal.

learn : bool, optional

Whether to apply learning on the signal before running the main detection. If learning fails or is not conducted, the default configuration parameters will be used to initialize these variables. See the XQRS._learn_init_params docstring for details.

verbose : bool, optional

Whether to display the stages and outcomes of the detection process.

wfdb.processing.xqrs_detect(sig, fs, sampfrom=0, sampto='end', conf=None, learn=True, verbose=True)

Run the ‘xqrs’ qrs detection algorithm on a signal. See the docstring of the XQRS class for algorithm details.

sig : numpy array

The input ecg signal to apply the qrs detection on.

fs : int or float

The sampling frequency of the input signal.

sampfrom : int, optional

The starting sample number to run the detection on.

sampto :

The final sample number to run the detection on. Set as ‘end’ to run on the entire signal.

conf : XQRS.Conf object, optional

The configuration object specifying signal configuration parameters. See the docstring of the XQRS.Conf class.

learn : bool, optional

Whether to apply learning on the signal before running the main detection. If learning fails or is not conducted, the default configuration parameters will be used to initialize these variables.

verbose : bool, optional

Whether to display the stages and outcomes of the detection process.

qrs_inds : numpy array

The indices of the detected qrs complexes

>>> import wfdb
>>> from wfdb import processing

>>> sig, fields = wfdb.rdsamp('sample-data/100', channels=[0])
>>> qrs_inds = processing.xqrs_detect(sig=sig[:,0], fs=fields['fs'])

wfdb.processing.gqrs_detect(sig=None, fs=None, d_sig=None, adc_gain=None, adc_zero=None, threshold=1.0, hr=75, RRdelta=0.2, RRmin=0.28, RRmax=2.4, QS=0.07, QT=0.35, RTmin=0.25, RTmax=0.33, QRSa=750, QRSamin=130)

Detect qrs locations in a single channel ecg. Functionally, a direct port of the gqrs algorithm from the original wfdb package. Accepts either a physical signal, or a digital signal with known adc_gain and adc_zero.

See the notes below for a summary of the program. This algorithm is not being developed/supported.

sig : 1d numpy array, optional

The input physical signal. The detection algorithm which replicates the original, works using digital samples, and this physical option is provided as a convenient interface. If this is the specified input signal, automatic adc is performed using 24 bit precision, to obtain the d_sig, adc_gain, and adc_zero parameters. There may be minor differences in detection results (ie. an occasional 1 sample difference) between using sig and d_sig. To replicate the exact output of the original gqrs algorithm, use the d_sig argument instead.

fs : int, or float

The sampling frequency of the signal.

d_sig : 1d numpy array, optional

The input digital signal. If this is the specified input signal rather than sig, the adc_gain and adc_zero parameters must be specified.

adc_gain : int, or float, optional

The analogue to digital gain of the signal (the number of adus per physical unit).

adc_zero: int, optional

The value produced by the ADC given a 0 volt input.

threshold : int, or float, optional

The relative amplitude detection threshold. Used to initialize the peak and qrs detection threshold.

hr : int, or float, optional

Typical heart rate, in beats per minute.

RRdelta : int or float, optional

Typical difference between successive RR intervals in seconds.

RRmin : int or float, optional

Minimum RR interval (“refractory period”), in seconds.

RRmax : int or float, optional

Maximum RR interval, in seconds. Thresholds will be adjusted if no peaks are detected within this interval.

QS : int or float, optional

Typical QRS duration, in seconds.

QT : int or float, optional

Typical QT interval, in seconds.

RTmin : int or float, optional

Minimum interval between R and T peaks, in seconds.

RTmax : int or float, optional

Maximum interval between R and T peaks, in seconds.

QRSa : int or float, optional

Typical QRS peak-to-peak amplitude, in microvolts.

QRSamin : int or float, optional

Minimum QRS peak-to-peak amplitude, in microvolts.

qrs_locs : numpy array

Detected qrs locations

This function should not be used for signals with fs <= 50Hz

The algorithm theoretically works as follows:

• Load in configuration parameters. They are used to set/initialize the:

  • allowed rr interval limits (fixed)
  • initial recent rr interval (running)
  • qrs width, used for detection filter widths (fixed)
  • allowed rt interval limits (fixed)
  • initial recent rt interval (running)
  • initial peak amplitude detection threshold (running)
  • initial qrs amplitude detection threshold (running)
  • Note: this algorithm does not normalize signal amplitudes, and hence is highly dependent on configuration amplitude parameters.

• Apply trapezoid low-pass filtering to the signal

• Convolve a QRS matched filter with the filtered signal

• Run the learning phase using a calculated signal length: detect qrs and non-qrs peaks as in the main detection phase, without saving the qrs locations. During this phase, running parameters of recent intervals and peak/qrs thresholds are adjusted.

• Run the detection::

  if a sample is bigger than its immediate neighbors and larger than the peak detection threshold, it is a peak.

  if it is further than RRmin from the previous qrs, and is a *primary peak.

  if it is further than 2 standard deviations from the previous qrs, do a backsearch for a missed low amplitude beat

  return the primary peak between the current sample and the previous qrs if any.

  if it surpasses the qrs threshold, it is a qrs complex

  save the qrs location. update running rr and qrs amplitude parameters. look for the qrs complex’s t-wave and mark it if found.

  else if it is not a peak

  lower the peak detection threshold if the last peak found was more than RRmax ago, and not already at its minimum.

*A peak is secondary if there is a larger peak within its neighborhood (time +- rrmin), or if it has been identified as a T-wave associated with a previous primary peak. A peak is primary if it is largest in its neighborhood, or if the only larger peaks are secondary.

The above describes how the algorithm should theoretically work, but there are bugs which make the program contradict certain parts of its supposed logic. A list of issues from the original c, code and hence this python implementation can be found here:

https://github.com/bemoody/wfdb/issues/17

gqrs will not be supported/developed in this library.

>>> import numpy as np
>>> import wfdb
>>> from wfdb import processing

>>> # Detect using a physical input signal
>>> record = wfdb.rdrecord('sample-data/100', channels=[0])
>>> qrs_locs = processing.gqrs_detect(record.p_signal[:,0], fs=record.fs)

>>> # Detect using a digital input signal
>>> record_2 = wfdb.rdrecord('sample-data/100', channels=[0], physical=False)
>>> qrs_locs_2 = processing.gqrs_detect(d_sig=record_2.d_signal[:,0],
                                        fs=record_2.fs,
                                        adc_gain=record_2.adc_gain[0],
                                        adc_zero=record_2.adc_zero[0])

Annotation Evaluators

class wfdb.processing.Comparitor(ref_sample, test_sample, window_width, signal=None)

The class to implement and hold comparisons between two sets of annotations.

See methods compare, print_summary and plot.

>>> import wfdb
>>> from wfdb import processing

>>> sig, fields = wfdb.rdsamp('sample-data/100', channels=[0])
>>> ann_ref = wfdb.rdann('sample-data/100','atr')
>>> xqrs = processing.XQRS(sig=sig[:,0], fs=fields['fs'])
>>> xqrs.detect()

>>> comparitor = processing.Comparitor(ann_ref.sample[1:],
                                       xqrs.qrs_inds,
                                       int(0.1 * fields['fs']),
                                       sig[:,0])
>>> comparitor.compare()
>>> comparitor.print_summary()
>>> comparitor.plot()

compare()

Main comparison function

plot(sig_style='', title=None, figsize=None, return_fig=False)

Plot the comparison of two sets of annotations, possibly overlaid on their original signal.

sig_style : str, optional

The matplotlib style of the signal

title : str, optional

The title of the plot

figsize: tuple, optional

Tuple pair specifying the width, and height of the figure. It is the’figsize’ argument passed into matplotlib.pyplot’s figure function.

return_fig : bool, optional

Whether the figure is to be returned as an output argument.

print_summary()

Print summary metrics of the annotation comparisons.

wfdb.processing.compare_annotations(ref_sample, test_sample, window_width, signal=None)

Compare a set of reference annotation locations against a set of test annotation locations.

See the Comparitor class docstring for more information.

ref_sample : 1d numpy array

Array of reference sample locations

test_sample : 1d numpy array

Array of test sample locations to compare

window_width : int

The maximum absolute difference in sample numbers that is permitted for matching annotations.

signal : 1d numpy array, optional

The original signal of the two annotations. Only used for plotting.

comparitor : Comparitor object

Object containing parameters about the two sets of annotations

>>> import wfdb
>>> from wfdb import processing

>>> sig, fields = wfdb.rdsamp('sample-data/100', channels=[0])
>>> ann_ref = wfdb.rdann('sample-data/100','atr')
>>> xqrs = processing.XQRS(sig=sig[:,0], fs=fields['fs'])
>>> xqrs.detect()

>>> comparitor = processing.compare_annotations(ann_ref.sample[1:],
                                                xqrs.qrs_inds,
                                                int(0.1 * fields['fs']),
                                                sig[:,0])
>>> comparitor.print_summary()
>>> comparitor.plot()

wfdb.processing.benchmark_mitdb(detector, verbose=False, print_results=False)

Benchmark a qrs detector against mitdb’s records.

detector : function

The detector function.

verbose : bool, optional

The verbose option of the detector function.

print_results : bool, optional

Whether to print the overall performance, and the results for each record.

comparitors : dictionary

Dictionary of Comparitor objects run on the records, keyed on the record names.

sensitivity : float

Aggregate sensitivity.

positive_predictivity : float

Aggregate positive_predictivity.

TODO: - remove non-qrs detections from reference annotations - allow kwargs

>>> import wfdb
>> from wfdb.processing import benchmark_mitdb, xqrs_detect

>>> comparitors, spec, pp = benchmark_mitdb(xqrs_detect)