def test_welch_psd_multidim_input(self):
# generate multidimensional data
num_channel = 4
data_length = 5000
sampling_period = 0.001
noise = np.random.normal(size=(num_channel, data_length))
data_np = np.array(noise)
# Since row-column order in AnalogSignalArray is different from the
# conventional one, `data_np` needs to be transposed when its used to
# define an AnalogSignalArray
data_neo = n.AnalogSignalArray(data_np.T,
sampling_period=sampling_period * pq.s,
units='mV')
data_neo_1dim = n.AnalogSignalArray(data_np[0],
sampling_period=sampling_period *
pq.s,
units='mV')
# check if the results from different input types are identical
freqs_np, psd_np = elephant.spectral.welch_psd(data_np,
fs=1 / sampling_period)
freqs_neo, psd_neo = elephant.spectral.welch_psd(data_neo)
freqs_neo_1dim, psd_neo_1dim = elephant.spectral.welch_psd(
data_neo_1dim)
self.assertTrue(np.all(freqs_np == freqs_neo))
self.assertTrue(np.all(psd_np == psd_neo))
self.assertTrue(np.all(psd_neo_1dim == psd_neo[0]))
def test_welch_cohere_errors(self):
# generate a dummy data
x = n.AnalogSignalArray(np.zeros(5000),
sampling_period=0.001 * pq.s,
units='mV')
y = n.AnalogSignalArray(np.zeros(5000),
sampling_period=0.001 * pq.s,
units='mV')
# check for invalid parameter values
# - length of segments
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
len_seg=0)
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
len_seg=x.shape[-1] * 2)
# - number of segments
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
num_seg=0)
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
num_seg=x.shape[-1] * 2)
# - frequency resolution
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
freq_res=-1)
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
freq_res=x.sampling_rate / (x.shape[-1] + 1))
# - overlap
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
overlap=-1.0)
self.assertRaises(ValueError,
elephant.spectral.welch_cohere,
x,
y,
overlap=1.1)
def test_welch_psd_behavior(self):
# generate data by adding white noise and a sinusoid
data_length = 5000
sampling_period = 0.001
signal_freq = 100.0
noise = np.random.normal(size=data_length)
signal = [
np.sin(2 * np.pi * signal_freq * t)
for t in np.arange(0, data_length *
sampling_period, sampling_period)
]
data = n.AnalogSignalArray(np.array(signal + noise),
sampling_period=sampling_period * pq.s,
units='mV')
# consistency between different ways of specifying segment length
freqs1, psd1 = elephant.spectral.welch_psd(data,
len_seg=data_length // 5,
overlap=0)
freqs2, psd2 = elephant.spectral.welch_psd(data, num_seg=5, overlap=0)
self.assertTrue(np.all((psd1 == psd2, freqs1 == freqs2)))
# frequency resolution and consistency with data
freq_res = 1.0 * pq.Hz
freqs, psd = elephant.spectral.welch_psd(data, freq_res=freq_res)
self.assertAlmostEqual(freq_res, freqs[1] - freqs[0])
self.assertEqual(freqs[psd.argmax()], signal_freq)
freqs_np, psd_np = elephant.spectral.welch_psd(data.magnitude,
fs=1 / sampling_period,
freq_res=freq_res)
self.assertTrue(np.all((freqs == freqs_np, psd == psd_np)))
# check of scipy.signal.welch() parameters
params = {
'window': 'hamming',
'nfft': 1024,
'detrend': 'linear',
'return_onesided': False,
'scaling': 'spectrum'
}
for key, val in params.items():
freqs, psd = elephant.spectral.welch_psd(data,
len_seg=1000,
overlap=0,
**{key: val})
freqs_spsig, psd_spsig = spsig.welch(data,
fs=1 / sampling_period,
nperseg=1000,
noverlap=0,
**{key: val})
self.assertTrue(np.all((freqs == freqs_spsig, psd == psd_spsig)))
# - generate multidimensional data for check of parameter `axis`
num_channel = 4
data_length = 5000
data_multidim = np.random.normal(size=(num_channel, data_length))
freqs, psd = elephant.spectral.welch_psd(data_multidim)
freqs_T, psd_T = elephant.spectral.welch_psd(data_multidim.T, axis=0)
self.assertTrue(np.all(freqs == freqs_T))
self.assertTrue(np.all(psd == psd_T.T))
def test_welch_psd_input_types(self):
# generate a test data
sampling_period = 0.001
data = n.AnalogSignalArray(np.array(np.random.normal(size=5000)),
sampling_period=sampling_period * pq.s,
units='mV')
# outputs from AnalogSignalArray input are of Quantity type (standard usage)
freqs_neo, psd_neo = elephant.spectral.welch_psd(data)
self.assertTrue(isinstance(freqs_neo, pq.quantity.Quantity))
self.assertTrue(isinstance(psd_neo, pq.quantity.Quantity))
# outputs from Quantity array input are of Quantity type
freqs_pq, psd_pq = elephant.spectral.welch_psd(data.magnitude *
data.units,
fs=1 / sampling_period)
self.assertTrue(isinstance(freqs_pq, pq.quantity.Quantity))
self.assertTrue(isinstance(psd_pq, pq.quantity.Quantity))
# outputs from Numpy ndarray input are NOT of Quantity type
freqs_np, psd_np = elephant.spectral.welch_psd(data.magnitude,
fs=1 / sampling_period)
self.assertFalse(isinstance(freqs_np, pq.quantity.Quantity))
self.assertFalse(isinstance(psd_np, pq.quantity.Quantity))
# check if the results from different input types are identical
self.assertTrue(np.all((freqs_neo == freqs_pq, psd_neo == psd_pq)))
self.assertTrue(np.all((freqs_neo == freqs_np, psd_neo == psd_np)))
def test_welch_cohere_input_types(self):
# generate a test data
sampling_period = 0.001
x = n.AnalogSignalArray(np.array(np.random.normal(size=5000)),
sampling_period=sampling_period * pq.s,
units='mV')
y = n.AnalogSignalArray(np.array(np.random.normal(size=5000)),
sampling_period=sampling_period * pq.s,
units='mV')
# outputs from AnalogSignalArray input are of Quantity type
# (standard usage)
freqs_neo, coherency_neo, phase_lag_neo =\
elephant.spectral.welch_cohere(x, y)
self.assertTrue(isinstance(freqs_neo, pq.quantity.Quantity))
self.assertTrue(isinstance(phase_lag_neo, pq.quantity.Quantity))
# outputs from Quantity array input are of Quantity type
freqs_pq, coherency_pq, phase_lag_pq =\
elephant.spectral.welch_cohere(x.magnitude*x.units,
y.magnitude*y.units, fs=1/sampling_period)
self.assertTrue(isinstance(freqs_pq, pq.quantity.Quantity))
self.assertTrue(isinstance(phase_lag_pq, pq.quantity.Quantity))
# outputs from Numpy ndarray input are NOT of Quantity type
freqs_np, coherency_np, phase_lag_np =\
elephant.spectral.welch_cohere(x.magnitude, y.magnitude,
fs=1/sampling_period)
self.assertFalse(isinstance(freqs_np, pq.quantity.Quantity))
self.assertFalse(isinstance(phase_lag_np, pq.quantity.Quantity))
# check if the results from different input types are identical
self.assertTrue(
np.all((freqs_neo == freqs_pq, coherency_neo == coherency_pq,
phase_lag_neo == phase_lag_pq)))
self.assertTrue(
np.all((freqs_neo == freqs_np, coherency_neo == coherency_np,
phase_lag_neo == phase_lag_np)))
def test_welch_cohere_multidim_input(self):
# generate multidimensional data
num_channel = 4
data_length = 5000
sampling_period = 0.001
x_np = np.array(np.random.normal(size=(num_channel, data_length)))
y_np = np.array(np.random.normal(size=(num_channel, data_length)))
# Since row-column order in AnalogSignalArray is different from the
# convention in NumPy/SciPy, `data_np` needs to be transposed when its
# used to define an AnalogSignalArray
x_neo = n.AnalogSignalArray(x_np.T,
units='mV',
sampling_period=sampling_period * pq.s)
y_neo = n.AnalogSignalArray(y_np.T,
units='mV',
sampling_period=sampling_period * pq.s)
x_neo_1dim = n.AnalogSignalArray(x_np[0],
units='mV',
sampling_period=sampling_period *
pq.s)
y_neo_1dim = n.AnalogSignalArray(y_np[0],
units='mV',
sampling_period=sampling_period *
pq.s)
# check if the results from different input types are identical
freqs_np, coherency_np, phase_lag_np =\
elephant.spectral.welch_cohere(x_np, y_np, fs=1/sampling_period)
freqs_neo, coherency_neo, phase_lag_neo =\
elephant.spectral.welch_cohere(x_neo, y_neo)
freqs_neo_1dim, coherency_neo_1dim, phase_lag_neo_1dim =\
elephant.spectral.welch_cohere(x_neo_1dim, y_neo_1dim)
self.assertTrue(np.all(freqs_np == freqs_neo))
self.assertTrue(np.all(coherency_np.T == coherency_neo))
self.assertTrue(np.all(phase_lag_np.T == phase_lag_neo))
self.assertTrue(np.all(coherency_neo_1dim == coherency_neo[:, 0]))
self.assertTrue(np.all(phase_lag_neo_1dim == phase_lag_neo[:, 0]))
def test_welch_cohere_behavior(self):
# generate data by adding white noise and a sinusoid
data_length = 5000
sampling_period = 0.001
signal_freq = 100.0
noise1 = np.random.normal(size=data_length) * 0.01
noise2 = np.random.normal(size=data_length) * 0.01
signal1 = [
np.cos(2 * np.pi * signal_freq * t)
for t in np.arange(0, data_length *
sampling_period, sampling_period)
]
signal2 = [
np.sin(2 * np.pi * signal_freq * t)
for t in np.arange(0, data_length *
sampling_period, sampling_period)
]
x = n.AnalogSignalArray(np.array(signal1 + noise1),
units='mV',
sampling_period=sampling_period * pq.s)
y = n.AnalogSignalArray(np.array(signal2 + noise2),
units='mV',
sampling_period=sampling_period * pq.s)
# consistency between different ways of specifying segment length
freqs1, coherency1, phase_lag1 = elephant.spectral.welch_cohere(
x, y, len_seg=data_length // 5, overlap=0)
freqs2, coherency2, phase_lag2 = elephant.spectral.welch_cohere(
x, y, num_seg=5, overlap=0)
self.assertTrue(
np.all((coherency1 == coherency2, phase_lag1 == phase_lag2,
freqs1 == freqs2)))
# frequency resolution and consistency with data
freq_res = 1.0 * pq.Hz
freqs, coherency, phase_lag = elephant.spectral.welch_cohere(
x, y, freq_res=freq_res)
self.assertAlmostEqual(freq_res, freqs[1] - freqs[0])
self.assertAlmostEqual(freqs[coherency.argmax()],
signal_freq,
places=2)
self.assertAlmostEqual(phase_lag[coherency.argmax()],
np.pi / 2,
places=2)
freqs_np, coherency_np, phase_lag_np =\
elephant.spectral.welch_cohere(x.magnitude, y.magnitude,
fs=1/sampling_period, freq_res=freq_res)
self.assertTrue(
np.all((freqs == freqs_np, coherency == coherency_np,
phase_lag == phase_lag_np)))
# - check the behavior of parameter `axis` using multidimensional data
num_channel = 4
data_length = 5000
x_multidim = np.random.normal(size=(num_channel, data_length))
y_multidim = np.random.normal(size=(num_channel, data_length))
freqs, coherency, phase_lag =\
elephant.spectral.welch_cohere(x_multidim, y_multidim)
freqs_T, coherency_T, phase_lag_T =\
elephant.spectral.welch_cohere(x_multidim.T, y_multidim.T, axis=0)
self.assertTrue(np.all(freqs == freqs_T))
self.assertTrue(np.all(coherency == coherency_T.T))
self.assertTrue(np.all(phase_lag == phase_lag_T.T))