def test_scipy_resample():
""" Tests scipy signal's resample function
"""
# create a freq list with max freq < 16 Hz
freq_list = np.random.randint(0, high=15, size=5)
# make a test signal with sampling freq = 64 Hz
a = [
np.sin(2 * np.pi * f * np.linspace(0, 1, 64, endpoint=False))
for f in freq_list
]
tst = np.array(a).sum(axis=0)
# interpolate to 128 Hz sampling
t_up = signaltools.resample(tst, 128)
np.testing.assert_array_almost_equal(t_up[::2], tst)
# downsample to 32 Hz
t_dn = signaltools.resample(tst, 32)
np.testing.assert_array_almost_equal(t_dn, tst[::2])
# downsample to 48 Hz, and compute the sampling analytically for comparison
dn_samp_ana = np.array([
np.sin(2 * np.pi * f * np.linspace(0, 1, 48, endpoint=False))
for f in freq_list
]).sum(axis=0)
t_dn2 = signaltools.resample(tst, 48)
npt.assert_array_almost_equal(t_dn2, dn_samp_ana)
def test_coherence_linear_dependence():
"""
Tests that the coherence between two linearly dependent time-series
behaves as expected.
From William Wei's book, according to eq. 14.5.34, if two time-series are
linearly related through:
y(t) = alpha*x(t+time_shift)
then the coherence between them should be equal to:
.. :math:
C(\nu) = \frac{1}{1+\frac{fft_{noise}(\nu)}{fft_{x}(\nu) \cdot \alpha^2}}
"""
t = np.linspace(0,16*np.pi,2**14)
x = np.sin(t) + np.sin(2*t) + np.sin(3*t) + 0.1 *np.random.rand(t.shape[-1])
N = x.shape[-1]
alpha = 10
m = 3
noise = 0.1 * np.random.randn(t.shape[-1])
y = alpha*(np.roll(x,m)) + noise
f_noise = np.fft.fft(noise)[0:N/2]
f_x = np.fft.fft(x)[0:N/2]
c_t = ( 1/( 1 + ( f_noise/( f_x*(alpha**2)) ) ) )
f,c = tsa.coherence(np.vstack([x,y]))
c_t = np.abs(signaltools.resample(c_t,c.shape[-1]))
np.testing.assert_array_almost_equal(c[0,1],c_t,2)
def test_scipy_resample():
""" Tests scipy signal's resample function
"""
# create a freq list with max freq < 16 Hz
freq_list = np.random.randint(0,high=15,size=5)
# make a test signal with sampling freq = 64 Hz
a = [np.sin(2*np.pi*f*np.linspace(0,1,64,endpoint=False))
for f in freq_list]
tst = np.array(a).sum(axis=0)
# interpolate to 128 Hz sampling
t_up = signaltools.resample(tst, 128)
np.testing.assert_array_almost_equal(t_up[::2], tst)
# downsample to 32 Hz
t_dn = signaltools.resample(tst, 32)
np.testing.assert_array_almost_equal(t_dn, tst[::2])
# downsample to 48 Hz, and compute the sampling analytically for comparison
dn_samp_ana = np.array([np.sin(2*np.pi*f*np.linspace(0,1,48,endpoint=False))
for f in freq_list]).sum(axis=0)
t_dn2 = signaltools.resample(tst, 48)
npt.assert_array_almost_equal(t_dn2, dn_samp_ana)
def _is_VF(signal):
"""
This function checks if a signal array meets the criteria to be
considered a Ventricular Fibrillation following the method explained in:
'Amann: Detecting Ventricular Fibrillation by Time-Delay Methods. 2007'.
In our case, the measured variable is the Pearson's goodness of fit
statistic instead of the recurrence rate of the original paper.
"""
dfreq = 50
window = 8*dfreq
#The threshold is the 0.99 quantile of the chi square distribution.
thr = 6.64
tau = int(0.5*dfreq)
#The signal is filtered and resampled to 50 Hz
signal = fft_filt(signal, (0.5, 25), SAMPLING_FREQ)
signal = resample(signal, int(len(signal) * dfreq / SAMPLING_FREQ))
n = int(math.ceil(len(signal)/float(window)))
isvf = True
#The conditions are validated in fragments of *window* size
for i in range(n):
if i == n-1 and n > 1:
frag = signal[-window-tau:-tau]
dfrag = signal[-min(len(frag), window):]
else:
frag = signal[i*window:(i+1)*window]
dfrag = signal[i*window+tau:(i+1)*window+tau]
frag = frag[:len(dfrag)] if len(frag) > len(dfrag) else frag
#Constant arrays cannot be flutters.
if len(frag) > 1 and not np.allclose(frag, frag[0]):
#The size of the histogram scales with the size of the signal.
nbins = int(math.ceil(math.sqrt(len(frag)*40.0**2/window)))
H, _, _ = np.histogram2d(frag, dfrag, nbins)
H /= len(frag)
Ei = 1.0/(nbins*nbins)
#The measured variable for the dispersion is the statistic of the
#Pearson's goodnes of fit test (agains the uniform distribution).
det = np.sum((H-Ei)**2/Ei)
isvf = isvf and det < thr
else:
isvf = False
if not isvf:
break
return isvf
def test_coherence_linear_dependence():
"""
Tests that the coherence between two linearly dependent time-series
behaves as expected.
From William Wei's book, according to eq. 14.5.34, if two time-series are
linearly related through:
y(t) = alpha*x(t+time_shift)
then the coherence between them should be equal to:
.. :math:
C(\nu) = \frac{1}{1+\frac{fft_{noise}(\nu)}{fft_{x}(\nu) \cdot \alpha^2}}
"""
t = np.linspace(0, 16 * np.pi, 2**14)
x = (np.sin(t) + np.sin(2 * t) + np.sin(3 * t) +
0.1 * np.random.rand(t.shape[-1]))
N = x.shape[-1]
alpha = 10
m = 3
noise = 0.1 * np.random.randn(t.shape[-1])
y = alpha * np.roll(x, m) + noise
f_noise = fftpack.fft(noise)[0:N // 2]
f_x = fftpack.fft(x)[0:N // 2]
c_t = (1 / (1 + (f_noise / (f_x * (alpha**2)))))
method = {"this_method": 'welch', "NFFT": 2048, "Fs": 2 * np.pi}
f, c = tsa.coherence(np.vstack([x, y]), csd_method=method)
c_t = np.abs(signaltools.resample(c_t, c.shape[-1]))
npt.assert_array_almost_equal(c[0, 1], c_t, 2)
# define the sfa node
sfaNode = mdp.nodes.SFANode(output_dim=sfaNum)
# define the ica node
icaNode = mdp.nodes.FastICANode()
icaNode.set_output_dim(icaNum)
#define the flow
flow = mdp.Flow(resNode + sfaNode + icaNode)
#train the flow
flow.train(sensorData.T)
#
icaOutput = flow.execute(sensorData.T)
#resample the ica layer output back to 50 times the length
icaOutputLong = resample(icaOutput, location.shape[0])
# number of components to plot
plotsNum = 20
plt.subplot(plotsNum + 1, 1, 1)
# first subplot of the numbered location of the robot
plt.plot(location)
# plot the independent components
for i in range(plotsNum):
plt.subplot(plotsNum + 1, 1, i + 2)
plt.plot(icaOutputLong[:, i])
plt.show()
resNode.initialize()
# define the sfa node
sfaNode = mdp.nodes.SFANode(output_dim=sfaNum)
# define the ica node
icaNode = mdp.nodes.FastICANode()
icaNode.set_output_dim(icaNum)
#define the flow
flow = mdp.Flow(resNode + sfaNode + icaNode)
#train the flow
flow.train(sensorData.T)
#
icaOutput = flow.execute(sensorData.T)
#resample the ica layer output back to 50 times the length
icaOutputLong = resample(icaOutput, location.shape[0])
# number of components to plot
plotsNum = 20
plt.subplot(plotsNum + 1, 1, 1)
# first subplot of the numbered location of the robot
plt.plot(location)
# plot the independent components
for i in range(plotsNum):
plt.subplot(plotsNum + 1, 1, i + 2)
plt.plot(icaOutputLong[:, i])
plt.show()
def preprocess_signal(raw_sig: np.ndarray,
fs: Real,
config: Optional[ED] = None) -> Dict[str, np.ndarray]:
""" finished, checked,
Parameters
----------
raw_sig: ndarray,
the raw ecg signal
fs: real number,
sampling frequency of `raw_sig`
config: dict, optional,
extra process configuration,
`PreprocCfg` will be updated by this `config`
Returns
-------
retval: dict,
with items
- 'filtered_ecg': the array of the processed ecg signal
- 'rpeaks': the array of indices of rpeaks; empty if 'rpeaks' in `config` is not set
NOTE
----
output (`retval`) are resampled to have sampling frequency
equal to `config.fs` (if `config` has item `fs`) or `PreprocCfg.fs`
"""
filtered_ecg = raw_sig.copy()
cfg = deepcopy(PreprocCfg)
cfg.update(deepcopy(config) or {})
if fs != cfg.fs:
filtered_ecg = resample(filtered_ecg,
int(round(len(filtered_ecg) * cfg.fs / fs)))
# remove baseline
if 'baseline' in cfg.preproc:
window1 = 2 * (cfg.baseline_window1 //
2) + 1 # window size must be odd
window2 = 2 * (cfg.baseline_window2 // 2) + 1
baseline = median_filter(filtered_ecg, size=window1, mode='nearest')
baseline = median_filter(baseline, size=window2, mode='nearest')
filtered_ecg = filtered_ecg - baseline
# filter signal
if 'bandpass' in cfg.preproc:
filtered_ecg = filter_signal(
signal=filtered_ecg,
ftype='FIR',
band='bandpass',
order=int(0.3 * fs),
sampling_rate=fs,
frequency=cfg.filter_band,
)['signal']
if cfg.rpeaks and cfg.rpeaks.lower() not in DL_QRS_DETECTORS:
# dl detectors not for parallel computing using `mp`
detector = QRS_DETECTORS[cfg.rpeaks.lower()]
rpeaks = detector(sig=filtered_ecg, fs=fs).astype(int)
else:
rpeaks = np.array([], dtype=int)
retval = ED({
"filtered_ecg": filtered_ecg,
"rpeaks": rpeaks,
})
return retval