def test_notch_filters():
"""Test notch filters."""
# let's use an ugly, prime sfreq for fun
sfreq = 487.0
sig_len_secs = 20
t = np.arange(0, int(sig_len_secs * sfreq)) / sfreq
freqs = np.arange(60, 241, 60)
# make a "signal"
a = rng.randn(int(sig_len_secs * sfreq))
orig_power = np.sqrt(np.mean(a ** 2))
# make line noise
a += np.sum([np.sin(2 * np.pi * f * t) for f in freqs], axis=0)
# only allow None line_freqs with 'spectrum_fit' mode
assert_raises(ValueError, notch_filter, a, sfreq, None, 'fft')
assert_raises(ValueError, notch_filter, a, sfreq, None, 'iir')
methods = ['spectrum_fit', 'spectrum_fit', 'fft', 'fft', 'iir']
filter_lengths = ['auto', 'auto', 'auto', 8192, 'auto']
line_freqs = [None, freqs, freqs, freqs, freqs]
tols = [2, 1, 1, 1]
for meth, lf, fl, tol in zip(methods, line_freqs, filter_lengths, tols):
with catch_logging() as log_file:
with warnings.catch_warnings(record=True):
b = notch_filter(a, sfreq, lf, fl, method=meth, verbose=True)
if lf is None:
out = log_file.getvalue().split('\n')[:-1]
if len(out) != 2 and len(out) != 3: # force_serial: len(out) == 3
raise ValueError('Detected frequencies not logged properly')
out = np.fromstring(out[-1], sep=', ')
assert_array_almost_equal(out, freqs)
new_power = np.sqrt(sum_squared(b) / b.size)
assert_almost_equal(new_power, orig_power, tol)
def test_notch_filters():
"""Test notch filters
"""
# let's use an ugly, prime sfreq for fun
sfreq = 487.0
sig_len_secs = 20
t = np.arange(0, int(sig_len_secs * sfreq)) / sfreq
freqs = np.arange(60, 241, 60)
# make a "signal"
rng = np.random.RandomState(0)
a = rng.randn(int(sig_len_secs * sfreq))
orig_power = np.sqrt(np.mean(a ** 2))
# make line noise
a += np.sum([np.sin(2 * np.pi * f * t) for f in freqs], axis=0)
# only allow None line_freqs with 'spectrum_fit' mode
assert_raises(ValueError, notch_filter, a, sfreq, None, "fft")
assert_raises(ValueError, notch_filter, a, sfreq, None, "iir")
methods = ["spectrum_fit", "spectrum_fit", "fft", "fft", "iir"]
filter_lengths = [None, None, None, 8192, None]
line_freqs = [None, freqs, freqs, freqs, freqs]
tols = [2, 1, 1, 1]
for meth, lf, fl, tol in zip(methods, line_freqs, filter_lengths, tols):
with catch_logging() as log_file:
b = notch_filter(a, sfreq, lf, filter_length=fl, method=meth, verbose="INFO")
if lf is None:
out = log_file.getvalue().split("\n")[:-1]
if len(out) != 2:
raise ValueError("Detected frequencies not logged properly")
out = np.fromstring(out[1], sep=", ")
assert_array_almost_equal(out, freqs)
new_power = np.sqrt(sum_squared(b) / b.size)
assert_almost_equal(new_power, orig_power, tol)
def test_notch_filters(method, filter_length, line_freq, tol):
"""Test notch filters."""
# let's use an ugly, prime sfreq for fun
rng = np.random.RandomState(0)
sfreq = 487
sig_len_secs = 21
t = np.arange(0, int(round(sig_len_secs * sfreq))) / sfreq
# make a "signal"
a = rng.randn(int(sig_len_secs * sfreq))
orig_power = np.sqrt(np.mean(a**2))
# make line noise
a += np.sum([np.sin(2 * np.pi * f * t) for f in line_freqs], axis=0)
# only allow None line_freqs with 'spectrum_fit' mode
for kind in ('fir', 'iir'):
with pytest.raises(ValueError, match='freqs=None can only be used wi'):
notch_filter(a, sfreq, None, kind)
with catch_logging() as log_file:
b = notch_filter(a,
sfreq,
line_freq,
filter_length,
method=method,
verbose=True)
if line_freq is None:
out = [
line.strip().split(':')[0]
for line in log_file.getvalue().split('\n') if line.startswith(' ')
]
assert len(out) == 4, 'Detected frequencies not logged properly'
out = np.array(out, float)
assert_array_almost_equal(out, line_freqs)
new_power = np.sqrt(sum_squared(b) / b.size)
assert_almost_equal(new_power, orig_power, tol)
def test_notch_filters():
"""Test notch filters."""
# let's use an ugly, prime sfreq for fun
sfreq = 487.0
sig_len_secs = 20
t = np.arange(0, int(sig_len_secs * sfreq)) / sfreq
freqs = np.arange(60, 241, 60)
# make a "signal"
a = rng.randn(int(sig_len_secs * sfreq))
orig_power = np.sqrt(np.mean(a ** 2))
# make line noise
a += np.sum([np.sin(2 * np.pi * f * t) for f in freqs], axis=0)
# only allow None line_freqs with 'spectrum_fit' mode
assert_raises(ValueError, notch_filter, a, sfreq, None, 'fft')
assert_raises(ValueError, notch_filter, a, sfreq, None, 'iir')
methods = ['spectrum_fit', 'spectrum_fit', 'fft', 'fft', 'iir']
filter_lengths = ['auto', 'auto', 'auto', 8192, 'auto']
line_freqs = [None, freqs, freqs, freqs, freqs]
tols = [2, 1, 1, 1]
for meth, lf, fl, tol in zip(methods, line_freqs, filter_lengths, tols):
with catch_logging() as log_file:
with warnings.catch_warnings(record=True):
b = notch_filter(a, sfreq, lf, fl, method=meth, verbose=True)
if lf is None:
out = log_file.getvalue().split('\n')[:-1]
if len(out) != 2 and len(out) != 3: # force_serial: len(out) == 3
raise ValueError('Detected frequencies not logged properly')
out = np.fromstring(out[-1], sep=', ')
assert_array_almost_equal(out, freqs)
new_power = np.sqrt(sum_squared(b) / b.size)
assert_almost_equal(new_power, orig_power, tol)
def test_csd_on_artificial_data():
"""Test computing CSD on artificial data. """
epochs = _get_data(mode='sin')
sfreq = epochs.info['sfreq']
# Computing signal power in the time domain
signal_power = sum_squared(epochs._data)
signal_power_per_sample = signal_power / len(epochs.times)
# Computing signal power in the frequency domain
data_csd_mt, freqs_mt = csd_array(epochs._data, sfreq, mode='multitaper')
data_csd_fourier, freqs_fft = csd_array(epochs._data,
sfreq,
mode='fourier')
fourier_power = np.abs(data_csd_fourier[0, 0]) * sfreq
mt_power = np.abs(data_csd_mt[0, 0]) * sfreq
assert_true(abs(fourier_power - signal_power) <= 0.5)
assert_true(abs(mt_power - signal_power) <= 1)
# Power per sample should not depend on time window length
for tmax in [0.2, 0.8]:
tslice = np.where(epochs.times <= tmax)[0]
for add_n_fft in [0, 30]:
t_mask = (epochs.times >= 0) & (epochs.times <= tmax)
n_samples = sum(t_mask)
n_fft = n_samples + add_n_fft
data_csd_fourier, _ = csd_array(epochs._data[:, :, tslice],
sfreq,
mode='fourier',
fmin=0,
fmax=np.inf,
n_fft=n_fft)
first_samp = data_csd_fourier[0, 0]
fourier_power_per_sample = np.abs(first_samp) * sfreq / n_fft
assert_true(
abs(signal_power_per_sample -
fourier_power_per_sample) < 0.003)
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 5]:
for add_n_fft in [0, 30]:
mt_bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
data_csd_mt, _ = csd_array(epochs._data[:, :, tslice],
sfreq,
mt_bandwidth=mt_bandwidth,
n_fft=n_fft)
mt_power_per_sample = np.abs(data_csd_mt[0, 0]) *\
sfreq / n_fft
# The estimate of power gets worse for small time windows when
# more tapers are used
if n_tapers == 5 and tmax == 0.2:
delta = 0.05
else:
delta = 0.004
assert_true(
abs(signal_power_per_sample - mt_power_per_sample) < delta)
def test_compute_epochs_csd_on_artificial_data():
"""Test computing CSD on artificial data
"""
epochs, epochs_sin = _get_data()
sfreq = epochs_sin.info['sfreq']
# Computing signal power in the time domain
signal_power = sum_squared(epochs_sin._data)
signal_power_per_sample = signal_power / len(epochs_sin.times)
# Computing signal power in the frequency domain
data_csd_fourier = compute_epochs_csd(epochs_sin, mode='fourier')
data_csd_mt = compute_epochs_csd(epochs_sin, mode='multitaper')
fourier_power = np.abs(data_csd_fourier.data[0, 0]) * sfreq
mt_power = np.abs(data_csd_mt.data[0, 0]) * sfreq
assert_true(abs(fourier_power - signal_power) <= 0.5)
assert_true(abs(mt_power - signal_power) <= 1)
# Power per sample should not depend on time window length
for tmax in [0.2, 0.4, 0.6, 0.8]:
for add_n_fft in [30, 0, 30]:
t_mask = (epochs_sin.times >= 0) & (epochs_sin.times <= tmax)
n_samples = sum(t_mask)
n_fft = n_samples + add_n_fft
data_csd_fourier = compute_epochs_csd(epochs_sin,
mode='fourier',
tmin=None,
tmax=tmax,
fmin=0,
fmax=np.inf,
n_fft=n_fft)
fourier_power_per_sample = np.abs(data_csd_fourier.data[0, 0]) *\
sfreq / data_csd_fourier.n_fft
assert_true(
abs(signal_power_per_sample -
fourier_power_per_sample) < 0.003)
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 3, 5]:
for add_n_fft in [30, 0, 30]:
mt_bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
data_csd_mt = compute_epochs_csd(epochs_sin,
mode='multitaper',
tmin=None,
tmax=tmax,
fmin=0,
fmax=np.inf,
mt_bandwidth=mt_bandwidth,
n_fft=n_fft)
mt_power_per_sample = np.abs(data_csd_mt.data[0, 0]) *\
sfreq / data_csd_mt.n_fft
# The estimate of power gets worse for small time windows when
# more tapers are used
if n_tapers == 5 and tmax == 0.2:
delta = 0.05
else:
delta = 0.004
assert_true(
abs(signal_power_per_sample - mt_power_per_sample) < delta)
def test_csd_multitaper():
"""Test computing cross-spectral density using multitapers."""
epochs = _generate_coherence_data()
sfreq = epochs.info['sfreq']
_test_fourier_multitaper_parameters(epochs, csd_multitaper,
csd_array_multitaper)
# Compute CSDs using various parameters
times = [(None, None), (1, 9)]
as_arrays = [False, True]
adaptives = [False, True]
parameters = product(times, as_arrays, adaptives)
for (tmin, tmax), as_array, adaptive in parameters:
if as_array:
csd = csd_array_multitaper(epochs.get_data(), sfreq, epochs.tmin,
adaptive=adaptive, fmin=9, fmax=23,
tmin=tmin, tmax=tmax,
ch_names=epochs.ch_names)
else:
csd = csd_multitaper(epochs, adaptive=adaptive, fmin=9, fmax=23,
tmin=tmin, tmax=tmax)
if tmin is None and tmax is None:
assert csd.tmin == 0 and csd.tmax == 9.98
else:
assert csd.tmin == tmin and csd.tmax == tmax
csd = csd.mean([9.9, 14.9, 21.9], [10.1, 15.1, 22.1])
_test_csd_matrix(csd)
# Test equivalence with PSD
psd, psd_freqs = psd_multitaper(epochs, fmin=1e-3,
normalization='full') # omit DC
csd = csd_multitaper(epochs)
assert_allclose(psd_freqs, csd.frequencies)
csd = np.array([np.diag(csd.get_data(index=ii))
for ii in range(len(csd))]).T
assert_allclose(psd[0], csd)
# For the next test, generate a simple sine wave with a known power
times = np.arange(20 * sfreq) / sfreq # 20 seconds of signal
signal = np.sin(2 * np.pi * 10 * times)[None, None, :] # 10 Hz wave
signal_power_per_sample = sum_squared(signal) / len(times)
# Power per sample should not depend on time window length
for tmax in [12, 18]:
t_mask = (times <= tmax)
n_samples = sum(t_mask)
n_fft = len(times)
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 5]:
bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
csd_mt = csd_array_multitaper(signal, sfreq, tmax=tmax,
bandwidth=bandwidth,
n_fft=n_fft).sum().get_data()
mt_power_per_sample = np.abs(csd_mt[0, 0]) * sfreq / n_fft
assert abs(signal_power_per_sample - mt_power_per_sample) < 0.001
def test_csd_multitaper():
"""Test computing cross-spectral density using multitapers."""
epochs = _generate_coherence_data()
sfreq = epochs.info['sfreq']
_test_fourier_multitaper_parameters(epochs, csd_multitaper,
csd_array_multitaper)
# Compute CSDs using various parameters
times = [(None, None), (1, 9)]
as_arrays = [False, True]
adaptives = [False, True]
parameters = product(times, as_arrays, adaptives)
for (tmin, tmax), as_array, adaptive in parameters:
if as_array:
csd = csd_array_multitaper(epochs.get_data(), sfreq, epochs.tmin,
adaptive=adaptive, fmin=9, fmax=23,
tmin=tmin, tmax=tmax,
ch_names=epochs.ch_names)
else:
csd = csd_multitaper(epochs, adaptive=adaptive, fmin=9, fmax=23,
tmin=tmin, tmax=tmax)
if tmin is None and tmax is None:
assert csd.tmin == 0 and csd.tmax == 9.98
else:
assert csd.tmin == tmin and csd.tmax == tmax
csd = csd.mean([9.9, 14.9, 21.9], [10.1, 15.1, 22.1])
_test_csd_matrix(csd)
# Test equivalence with PSD
psd, psd_freqs = psd_multitaper(epochs, fmin=1e-3,
normalization='full') # omit DC
csd = csd_multitaper(epochs)
assert_allclose(psd_freqs, csd.frequencies)
csd = np.array([np.diag(csd.get_data(index=ii))
for ii in range(len(csd))]).T
assert_allclose(psd[0], csd)
# For the next test, generate a simple sine wave with a known power
times = np.arange(20 * sfreq) / sfreq # 20 seconds of signal
signal = np.sin(2 * np.pi * 10 * times)[None, None, :] # 10 Hz wave
signal_power_per_sample = sum_squared(signal) / len(times)
# Power per sample should not depend on time window length
for tmax in [12, 18]:
t_mask = (times <= tmax)
n_samples = sum(t_mask)
n_fft = len(times)
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 5]:
bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
csd_mt = csd_array_multitaper(signal, sfreq, tmax=tmax,
bandwidth=bandwidth,
n_fft=n_fft).sum().get_data()
mt_power_per_sample = np.abs(csd_mt[0, 0]) * sfreq / n_fft
assert abs(signal_power_per_sample - mt_power_per_sample) < 0.001
def test_csd_on_artificial_data():
"""Test computing CSD on artificial data. """
# Ignore deprecation warnings for this test
epochs = _generate_simple_data()
sfreq = epochs.info['sfreq']
# Computing signal power in the time domain
signal_power = sum_squared(epochs._data)
signal_power_per_sample = signal_power / len(epochs.times)
# Computing signal power in the frequency domain
with warnings.catch_warnings(record=True): # deprecation
csd_mt = csd_array(epochs._data, sfreq, mode='multitaper').get_data()
csd_fourier = csd_array(epochs._data, sfreq, mode='fourier').get_data()
fourier_power = np.abs(csd_fourier[0, 0]) * sfreq
mt_power = np.abs(csd_mt[0, 0]) * sfreq
assert abs(fourier_power - signal_power) <= 0.5
assert abs(mt_power - signal_power) <= 1
# Power per sample should not depend on time window length
for tmax in [0.2, 0.8]:
tslice = np.where(epochs.times <= tmax)[0]
for add_n_fft in [0, 30]:
t_mask = (epochs.times >= 0) & (epochs.times <= tmax)
n_samples = sum(t_mask)
n_fft = n_samples + add_n_fft
with warnings.catch_warnings(record=True): # deprecation
csd_fourier = csd_array(epochs._data[:, :, tslice], sfreq,
mode='fourier', fmin=0, fmax=np.inf,
n_fft=n_fft).get_data()
first_samp = csd_fourier[0, 0]
fourier_power_per_sample = np.abs(first_samp) * sfreq / n_fft
assert abs(signal_power_per_sample -
fourier_power_per_sample) < 0.003
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 5]:
mt_bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
with warnings.catch_warnings(record=True): # deprecation
csd_mt = csd_array(
epochs._data[:, :, tslice], sfreq,
mt_bandwidth=mt_bandwidth, n_fft=n_fft
).get_data()
mt_power_per_sample = np.abs(csd_mt[0, 0]) * sfreq / n_fft
# The estimate of power gets worse for small time windows when more
# tapers are used
if n_tapers == 5 and tmax == 0.2:
delta = 0.05
else:
delta = 0.004
assert abs(signal_power_per_sample -
mt_power_per_sample) < delta
def test_csd_on_artificial_data():
"""Test computing CSD on artificial data. """
# Ignore deprecation warnings for this test
epochs = _generate_simple_data()
sfreq = epochs.info['sfreq']
# Computing signal power in the time domain
signal_power = sum_squared(epochs._data)
signal_power_per_sample = signal_power / len(epochs.times)
# Computing signal power in the frequency domain
with warnings.catch_warnings(record=True): # deprecation
csd_mt = csd_array(epochs._data, sfreq, mode='multitaper').get_data()
csd_fourier = csd_array(epochs._data, sfreq, mode='fourier').get_data()
fourier_power = np.abs(csd_fourier[0, 0]) * sfreq
mt_power = np.abs(csd_mt[0, 0]) * sfreq
assert abs(fourier_power - signal_power) <= 0.5
assert abs(mt_power - signal_power) <= 1
# Power per sample should not depend on time window length
for tmax in [0.2, 0.8]:
tslice = np.where(epochs.times <= tmax)[0]
for add_n_fft in [0, 30]:
t_mask = (epochs.times >= 0) & (epochs.times <= tmax)
n_samples = sum(t_mask)
n_fft = n_samples + add_n_fft
with warnings.catch_warnings(record=True): # deprecation
csd_fourier = csd_array(epochs._data[:, :, tslice], sfreq,
mode='fourier', fmin=0, fmax=np.inf,
n_fft=n_fft).get_data()
first_samp = csd_fourier[0, 0]
fourier_power_per_sample = np.abs(first_samp) * sfreq / n_fft
assert abs(signal_power_per_sample -
fourier_power_per_sample) < 0.003
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 5]:
mt_bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
with warnings.catch_warnings(record=True): # deprecation
csd_mt = csd_array(
epochs._data[:, :, tslice], sfreq,
mt_bandwidth=mt_bandwidth, n_fft=n_fft
).get_data()
mt_power_per_sample = np.abs(csd_mt[0, 0]) * sfreq / n_fft
# The estimate of power gets worse for small time windows when more
# tapers are used
if n_tapers == 5 and tmax == 0.2:
delta = 0.05
else:
delta = 0.004
assert abs(signal_power_per_sample -
mt_power_per_sample) < delta
def test_csd_on_artificial_data():
"""Test computing CSD on artificial data. """
epochs = _get_data(mode='sin')
sfreq = epochs.info['sfreq']
# Computing signal power in the time domain
signal_power = sum_squared(epochs._data)
signal_power_per_sample = signal_power / len(epochs.times)
# Computing signal power in the frequency domain
data_csd_mt, freqs_mt = csd_array(epochs._data, sfreq,
mode='multitaper')
data_csd_fourier, freqs_fft = csd_array(epochs._data, sfreq,
mode='fourier')
fourier_power = np.abs(data_csd_fourier[0, 0]) * sfreq
mt_power = np.abs(data_csd_mt[0, 0]) * sfreq
assert_true(abs(fourier_power - signal_power) <= 0.5)
assert_true(abs(mt_power - signal_power) <= 1)
# Power per sample should not depend on time window length
for tmax in [0.2, 0.8]:
tslice = np.where(epochs.times <= tmax)[0]
for add_n_fft in [0, 30]:
t_mask = (epochs.times >= 0) & (epochs.times <= tmax)
n_samples = sum(t_mask)
n_fft = n_samples + add_n_fft
data_csd_fourier, _ = csd_array(epochs._data[:, :, tslice],
sfreq, mode='fourier',
fmin=0, fmax=np.inf, n_fft=n_fft)
first_samp = data_csd_fourier[0, 0]
fourier_power_per_sample = np.abs(first_samp) * sfreq / n_fft
assert_true(abs(signal_power_per_sample -
fourier_power_per_sample) < 0.003)
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 5]:
for add_n_fft in [0, 30]:
mt_bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
data_csd_mt, _ = csd_array(epochs._data[:, :, tslice],
sfreq, mt_bandwidth=mt_bandwidth,
n_fft=n_fft)
mt_power_per_sample = np.abs(data_csd_mt[0, 0]) *\
sfreq / n_fft
# The estimate of power gets worse for small time windows when
# more tapers are used
if n_tapers == 5 and tmax == 0.2:
delta = 0.05
else:
delta = 0.004
assert_true(abs(signal_power_per_sample -
mt_power_per_sample) < delta)
def test_csd_multitaper():
"""Test computing cross-spectral density using multitapers."""
epochs = _generate_coherence_data()
sfreq = epochs.info['sfreq']
_test_fourier_multitaper_parameters(epochs, csd_multitaper,
csd_array_multitaper)
# Compute CSDs using various parameters
times = [(None, None), (1, 9)]
as_arrays = [False, True]
adaptives = [False, True]
parameters = product(times, as_arrays, adaptives)
for (tmin, tmax), as_array, adaptive in parameters:
if as_array:
csd = csd_array_multitaper(epochs.get_data(),
sfreq,
epochs.tmin,
adaptive=adaptive,
fmin=9,
fmax=23,
tmin=tmin,
tmax=tmax)
else:
csd = csd_multitaper(epochs,
adaptive=adaptive,
fmin=9,
fmax=23,
tmin=tmin,
tmax=tmax)
csd = csd.mean([9.9, 14.9, 21.9], [10.1, 15.1, 22.1])
_test_csd_matrix(csd)
# For the next test, generate a simple sine wave with a known power
times = np.arange(20 * sfreq) / sfreq # 20 seconds of signal
signal = np.sin(2 * np.pi * 10 * times)[None, None, :] # 10 Hz wave
signal_power_per_sample = sum_squared(signal) / len(times)
# Power per sample should not depend on time window length
for tmax in [12, 18]:
t_mask = (times <= tmax)
n_samples = sum(t_mask)
n_fft = len(times)
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 5]:
bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
csd_mt = csd_array_multitaper(signal,
sfreq,
tmax=tmax,
bandwidth=bandwidth,
n_fft=n_fft).sum().get_data()
mt_power_per_sample = np.abs(csd_mt[0, 0]) * sfreq / n_fft
assert abs(signal_power_per_sample - mt_power_per_sample) < 0.001
def test_compute_epochs_csd_on_artificial_data():
"""Test computing CSD on artificial data
"""
epochs, epochs_sin = _get_data()
sfreq = epochs_sin.info['sfreq']
# Computing signal power in the time domain
signal_power = sum_squared(epochs_sin._data)
signal_power_per_sample = signal_power / len(epochs_sin.times)
# Computing signal power in the frequency domain
data_csd_fourier = compute_epochs_csd(epochs_sin, mode='fourier')
data_csd_mt = compute_epochs_csd(epochs_sin, mode='multitaper')
fourier_power = np.abs(data_csd_fourier.data[0, 0]) * sfreq
mt_power = np.abs(data_csd_mt.data[0, 0]) * sfreq
assert_almost_equal(fourier_power, signal_power, delta=0.5)
assert_almost_equal(mt_power, signal_power, delta=1)
# Power per sample should not depend on time window length
for tmax in [0.2, 0.4, 0.6, 0.8]:
for add_n_fft in [30, 0, 30]:
t_mask = (epochs_sin.times >= 0) & (epochs_sin.times <= tmax)
n_samples = sum(t_mask)
n_fft = n_samples + add_n_fft
data_csd_fourier = compute_epochs_csd(epochs_sin, mode='fourier',
tmin=None, tmax=tmax, fmin=0,
fmax=np.inf, n_fft=n_fft)
fourier_power_per_sample = np.abs(data_csd_fourier.data[0, 0]) *\
sfreq / data_csd_fourier.n_fft
assert_almost_equal(signal_power_per_sample,
fourier_power_per_sample, delta=0.003)
# Power per sample should not depend on number of tapers
for n_tapers in [1, 2, 3, 5]:
for add_n_fft in [30, 0, 30]:
mt_bandwidth = sfreq / float(n_samples) * (n_tapers + 1)
data_csd_mt = compute_epochs_csd(epochs_sin, mode='multitaper',
tmin=None, tmax=tmax, fmin=0,
fmax=np.inf,
mt_bandwidth=mt_bandwidth,
n_fft=n_fft)
mt_power_per_sample = np.abs(data_csd_mt.data[0, 0]) *\
sfreq / data_csd_mt.n_fft
# The estimate of power gets worse for small time windows when
# more tapers are used
if n_tapers == 5 and tmax == 0.2:
delta = 0.05
else:
delta = 0.004
assert_almost_equal(signal_power_per_sample,
mt_power_per_sample, delta=delta)
def test_csd_fourier():
"""Test computing cross-spectral density using short-term Fourier."""
epochs = _generate_coherence_data()
sfreq = epochs.info['sfreq']
_test_fourier_multitaper_parameters(epochs, csd_fourier, csd_array_fourier)
# Compute CSDs using various parameters
times = [(None, None), (1, 9)]
as_arrays = [False, True]
parameters = product(times, as_arrays)
for (tmin, tmax), as_array in parameters:
if as_array:
csd = csd_array_fourier(epochs.get_data(),
sfreq,
epochs.tmin,
fmin=9,
fmax=23,
tmin=tmin,
tmax=tmax,
ch_names=epochs.ch_names)
else:
csd = csd_fourier(epochs, fmin=9, fmax=23, tmin=tmin, tmax=tmax)
if tmin is None and tmax is None:
assert csd.tmin == 0 and csd.tmax == 9.98
else:
assert csd.tmin == tmin and csd.tmax == tmax
csd = csd.mean([9.9, 14.9, 21.9], [10.1, 15.1, 22.1])
_test_csd_matrix(csd)
# For the next test, generate a simple sine wave with a known power
times = np.arange(20 * sfreq) / sfreq # 20 seconds of signal
signal = np.sin(2 * np.pi * 10 * times)[None, None, :] # 10 Hz wave
signal_power_per_sample = sum_squared(signal) / len(times)
# Power per sample should not depend on time window length
for tmax in [12, 18]:
t_mask = (times <= tmax)
n_samples = sum(t_mask)
# Power per sample should not depend on number of FFT points
for add_n_fft in [0, 30]:
n_fft = n_samples + add_n_fft
csd = csd_array_fourier(signal, sfreq, tmax=tmax,
n_fft=n_fft).sum().get_data()
first_samp = csd[0, 0]
fourier_power_per_sample = np.abs(first_samp) * sfreq / n_fft
assert abs(signal_power_per_sample -
fourier_power_per_sample) < 0.001
def test_notch_filters():
"""Test notch filters
"""
tempdir = _TempDir()
log_file = op.join(tempdir, 'temp_log.txt')
# let's use an ugly, prime sfreq for fun
sfreq = 487.0
sig_len_secs = 20
t = np.arange(0, int(sig_len_secs * sfreq)) / sfreq
freqs = np.arange(60, 241, 60)
# make a "signal"
rng = np.random.RandomState(0)
a = rng.randn(int(sig_len_secs * sfreq))
orig_power = np.sqrt(np.mean(a**2))
# make line noise
a += np.sum([np.sin(2 * np.pi * f * t) for f in freqs], axis=0)
# only allow None line_freqs with 'spectrum_fit' mode
assert_raises(ValueError, notch_filter, a, sfreq, None, 'fft')
assert_raises(ValueError, notch_filter, a, sfreq, None, 'iir')
methods = ['spectrum_fit', 'spectrum_fit', 'fft', 'fft', 'iir']
filter_lengths = [None, None, None, 8192, None]
line_freqs = [None, freqs, freqs, freqs, freqs]
tols = [2, 1, 1, 1]
for meth, lf, fl, tol in zip(methods, line_freqs, filter_lengths, tols):
if lf is None:
set_log_file(log_file, overwrite=True)
b = notch_filter(a,
sfreq,
lf,
filter_length=fl,
method=meth,
verbose='INFO')
if lf is None:
set_log_file()
with open(log_file) as fid:
out = fid.readlines()
if len(out) != 2:
raise ValueError('Detected frequencies not logged properly')
out = np.fromstring(out[1], sep=', ')
assert_array_almost_equal(out, freqs)
new_power = np.sqrt(sum_squared(b) / b.size)
assert_almost_equal(new_power, orig_power, tol)
def test_csd_fourier():
"""Test computing cross-spectral density using short-term Fourier."""
epochs = _generate_coherence_data()
sfreq = epochs.info['sfreq']
_test_fourier_multitaper_parameters(epochs, csd_fourier, csd_array_fourier)
# Compute CSDs using various parameters
times = [(None, None), (1, 9)]
as_arrays = [False, True]
parameters = product(times, as_arrays)
for (tmin, tmax), as_array in parameters:
if as_array:
csd = csd_array_fourier(epochs.get_data(), sfreq, epochs.tmin,
fmin=9, fmax=23, tmin=tmin, tmax=tmax,
ch_names=epochs.ch_names)
else:
csd = csd_fourier(epochs, fmin=9, fmax=23, tmin=tmin, tmax=tmax)
if tmin is None and tmax is None:
assert csd.tmin == 0 and csd.tmax == 9.98
else:
assert csd.tmin == tmin and csd.tmax == tmax
csd = csd.mean([9.9, 14.9, 21.9], [10.1, 15.1, 22.1])
_test_csd_matrix(csd)
# For the next test, generate a simple sine wave with a known power
times = np.arange(20 * sfreq) / sfreq # 20 seconds of signal
signal = np.sin(2 * np.pi * 10 * times)[None, None, :] # 10 Hz wave
signal_power_per_sample = sum_squared(signal) / len(times)
# Power per sample should not depend on time window length
for tmax in [12, 18]:
t_mask = (times <= tmax)
n_samples = sum(t_mask)
# Power per sample should not depend on number of FFT points
for add_n_fft in [0, 30]:
n_fft = n_samples + add_n_fft
csd = csd_array_fourier(signal, sfreq, tmax=tmax,
n_fft=n_fft).sum().get_data()
first_samp = csd[0, 0]
fourier_power_per_sample = np.abs(first_samp) * sfreq / n_fft
assert abs(signal_power_per_sample -
fourier_power_per_sample) < 0.001
def test_notch_filters():
"""Test notch filters
"""
tempdir = _TempDir()
log_file = op.join(tempdir, 'temp_log.txt')
# let's use an ugly, prime sfreq for fun
sfreq = 487.0
sig_len_secs = 20
t = np.arange(0, int(sig_len_secs * sfreq)) / sfreq
freqs = np.arange(60, 241, 60)
# make a "signal"
rng = np.random.RandomState(0)
a = rng.randn(int(sig_len_secs * sfreq))
orig_power = np.sqrt(np.mean(a ** 2))
# make line noise
a += np.sum([np.sin(2 * np.pi * f * t) for f in freqs], axis=0)
# only allow None line_freqs with 'spectrum_fit' mode
assert_raises(ValueError, notch_filter, a, sfreq, None, 'fft')
assert_raises(ValueError, notch_filter, a, sfreq, None, 'iir')
methods = ['spectrum_fit', 'spectrum_fit', 'fft', 'fft', 'iir']
filter_lengths = [None, None, None, 8192, None]
line_freqs = [None, freqs, freqs, freqs, freqs]
tols = [2, 1, 1, 1]
for meth, lf, fl, tol in zip(methods, line_freqs, filter_lengths, tols):
if lf is None:
set_log_file(log_file, overwrite=True)
b = notch_filter(a, sfreq, lf, filter_length=fl, method=meth,
verbose='INFO')
if lf is None:
set_log_file()
with open(log_file) as fid:
out = fid.readlines()
if len(out) != 2:
raise ValueError('Detected frequencies not logged properly')
out = np.fromstring(out[1], sep=', ')
assert_array_almost_equal(out, freqs)
new_power = np.sqrt(sum_squared(b) / b.size)
assert_almost_equal(new_power, orig_power, tol)
def test_sum_squared():
"""Test optimized sum of squares
"""
X = np.random.randint(0, 50, (3, 3))
assert_equal(np.sum(X**2), sum_squared(X))
def test_sum_squared():
"""Test optimized sum of squares."""
X = np.random.RandomState(0).randint(0, 50, (3, 3))
assert np.sum(X**2) == sum_squared(X)
def test_sum_squared():
"""Test optimized sum of squares."""
X = np.random.RandomState(0).randint(0, 50, (3, 3))
assert_equal(np.sum(X ** 2), sum_squared(X))
