|
""" Functions which are common and require SciPy Base and Level 1 SciPy (special, linalg) """
'electrocardiogram']
""" Return weights for an Np-point central derivative.
Assumes equally-spaced function points.
If weights are in the vector w, then derivative is w[0] * f(x-ho*dx) + ... + w[-1] * f(x+h0*dx)
Parameters ---------- Np : int Number of points for the central derivative. ndiv : int, optional Number of divisions. Default is 1.
Notes ----- Can be inaccurate for large number of points.
""" if Np < ndiv + 1: raise ValueError("Number of points must be at least the derivative order + 1.") if Np % 2 == 0: raise ValueError("The number of points must be odd.") from scipy import linalg ho = Np >> 1 x = arange(-ho,ho+1.0) x = x[:,newaxis] X = x**0.0 for k in range(1,Np): X = hstack([X,x**k]) w = product(arange(1,ndiv+1),axis=0)*linalg.inv(X)[ndiv] return w
""" Find the n-th derivative of a function at a point.
Given a function, use a central difference formula with spacing `dx` to compute the `n`-th derivative at `x0`.
Parameters ---------- func : function Input function. x0 : float The point at which `n`-th derivative is found. dx : float, optional Spacing. n : int, optional Order of the derivative. Default is 1. args : tuple, optional Arguments order : int, optional Number of points to use, must be odd.
Notes ----- Decreasing the step size too small can result in round-off error.
Examples -------- >>> from scipy.misc import derivative >>> def f(x): ... return x**3 + x**2 >>> derivative(f, 1.0, dx=1e-6) 4.9999999999217337
""" if order < n + 1: raise ValueError("'order' (the number of points used to compute the derivative), " "must be at least the derivative order 'n' + 1.") if order % 2 == 0: raise ValueError("'order' (the number of points used to compute the derivative) " "must be odd.") # pre-computed for n=1 and 2 and low-order for speed. if n == 1: if order == 3: weights = array([-1,0,1])/2.0 elif order == 5: weights = array([1,-8,0,8,-1])/12.0 elif order == 7: weights = array([-1,9,-45,0,45,-9,1])/60.0 elif order == 9: weights = array([3,-32,168,-672,0,672,-168,32,-3])/840.0 else: weights = central_diff_weights(order,1) elif n == 2: if order == 3: weights = array([1,-2.0,1]) elif order == 5: weights = array([-1,16,-30,16,-1])/12.0 elif order == 7: weights = array([2,-27,270,-490,270,-27,2])/180.0 elif order == 9: weights = array([-9,128,-1008,8064,-14350,8064,-1008,128,-9])/5040.0 else: weights = central_diff_weights(order,2) else: weights = central_diff_weights(order, n) val = 0.0 ho = order >> 1 for k in range(order): val += weights[k]*func(x0+(k-ho)*dx,*args) return val / product((dx,)*n,axis=0)
""" Get an 8-bit grayscale bit-depth, 512 x 512 derived image for easy use in demos
The image is derived from accent-to-the-top.jpg at http://www.public-domain-image.com/people-public-domain-images-pictures/
Parameters ---------- None
Returns ------- ascent : ndarray convenient image to use for testing and demonstration
Examples -------- >>> import scipy.misc >>> ascent = scipy.misc.ascent() >>> ascent.shape (512, 512) >>> ascent.max() 255
>>> import matplotlib.pyplot as plt >>> plt.gray() >>> plt.imshow(ascent) >>> plt.show()
""" import pickle import os fname = os.path.join(os.path.dirname(__file__),'ascent.dat') with open(fname, 'rb') as f: ascent = array(pickle.load(f)) return ascent
""" Get a 1024 x 768, color image of a raccoon face.
raccoon-procyon-lotor.jpg at http://www.public-domain-image.com
Parameters ---------- gray : bool, optional If True return 8-bit grey-scale image, otherwise return a color image
Returns ------- face : ndarray image of a racoon face
Examples -------- >>> import scipy.misc >>> face = scipy.misc.face() >>> face.shape (768, 1024, 3) >>> face.max() 255 >>> face.dtype dtype('uint8')
>>> import matplotlib.pyplot as plt >>> plt.gray() >>> plt.imshow(face) >>> plt.show()
""" import bz2 import os with open(os.path.join(os.path.dirname(__file__), 'face.dat'), 'rb') as f: rawdata = f.read() data = bz2.decompress(rawdata) face = frombuffer(data, dtype='uint8') face.shape = (768, 1024, 3) if gray is True: face = (0.21 * face[:,:,0] + 0.71 * face[:,:,1] + 0.07 * face[:,:,2]).astype('uint8') return face
""" Load an electrocardiogram as an example for a one-dimensional signal.
The returned signal is a 5 minute long electrocardiogram (ECG), a medical recording of the heart's electrical activity, sampled at 360 Hz.
Returns ------- ecg : ndarray The electrocardiogram in millivolt (mV) sampled at 360 Hz.
Notes ----- The provided signal is an excerpt (19:35 to 24:35) from the `record 208`_ (lead MLII) provided by the MIT-BIH Arrhythmia Database [1]_ on PhysioNet [2]_. The excerpt includes noise induced artifacts, typical heartbeats as well as pathological changes.
.. _record 208: https://physionet.org/physiobank/database/html/mitdbdir/records.htm#208
.. versionadded:: 1.1.0
References ---------- .. [1] Moody GB, Mark RG. The impact of the MIT-BIH Arrhythmia Database. IEEE Eng in Med and Biol 20(3):45-50 (May-June 2001). (PMID: 11446209); https://doi.org/10.13026/C2F305 .. [2] Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101(23):e215-e220; https://doi.org/10.1161/01.CIR.101.23.e215
Examples -------- >>> from scipy.misc import electrocardiogram >>> ecg = electrocardiogram() >>> ecg array([-0.245, -0.215, -0.185, ..., -0.405, -0.395, -0.385]) >>> ecg.shape, ecg.mean(), ecg.std() ((108000,), -0.16510875, 0.5992473991177294)
As stated the signal features several areas with a different morphology. E.g. the first few seconds show the electrical activity of a heart in normal sinus rhythm as seen below.
>>> import matplotlib.pyplot as plt >>> fs = 360 >>> time = np.arange(ecg.size) / fs >>> plt.plot(time, ecg) >>> plt.xlabel("time in s") >>> plt.ylabel("ECG in mV") >>> plt.xlim(9, 10.2) >>> plt.ylim(-1, 1.5) >>> plt.show()
After second 16 however, the first premature ventricular contractions, also called extrasystoles, appear. These have a different morphology compared to typical heartbeats. The difference can easily be observed in the following plot.
>>> plt.plot(time, ecg) >>> plt.xlabel("time in s") >>> plt.ylabel("ECG in mV") >>> plt.xlim(46.5, 50) >>> plt.ylim(-2, 1.5) >>> plt.show()
At several points large artifacts disturb the recording, e.g.:
>>> plt.plot(time, ecg) >>> plt.xlabel("time in s") >>> plt.ylabel("ECG in mV") >>> plt.xlim(207, 215) >>> plt.ylim(-2, 3.5) >>> plt.show()
Finally, examining the power spectrum reveals that most of the biosignal is made up of lower frequencies. At 60 Hz the noise induced by the mains electricity can be clearly observed.
>>> from scipy.signal import welch >>> f, Pxx = welch(ecg, fs=fs, nperseg=2048, scaling="spectrum") >>> plt.semilogy(f, Pxx) >>> plt.xlabel("Frequency in Hz") >>> plt.ylabel("Power spectrum of the ECG in mV**2") >>> plt.xlim(f[[0, -1]]) >>> plt.show() """ import os file_path = os.path.join(os.path.dirname(__file__), "ecg.dat") with load(file_path) as file: ecg = file["ecg"].astype(int) # np.uint16 -> int # Convert raw output of ADC to mV: (ecg - adc_zero) / adc_gain ecg = (ecg - 1024) / 200.0 return ecg |