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# Authors : Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Eric Larson <larson.eric.d@gmail.com>
#
# License : BSD-3-Clause
import pytest
import numpy as np
from scipy import linalg
from numpy.testing import assert_almost_equal, assert_array_almost_equal
from mne.time_frequency import stft, istft, stftfreq
from mne.time_frequency._stft import stft_norm2
@pytest.mark.parametrize('T', (127, 128, 255, 256, 1337))
@pytest.mark.parametrize('wsize', (128, 256))
@pytest.mark.parametrize('tstep', (4, 64))
@pytest.mark.parametrize('f', (7., 23.)) # should be close to fftfreqs
def test_stft(T, wsize, tstep, f):
"""Test stft and istft tight frame property."""
sfreq = 1000. # Hz
if True: # just to minimize diff
# Test with low frequency signal
t = np.arange(T).astype(np.float64)
x = np.sin(2 * np.pi * f * t / sfreq)
x = np.array([x, x + 1.])
X = stft(x, wsize, tstep)
xp = istft(X, tstep, Tx=T)
freqs = stftfreq(wsize, sfreq=sfreq)
max_freq = freqs[np.argmax(np.sum(np.abs(X[0]) ** 2, axis=1))]
assert X.shape[1] == len(freqs)
assert np.all(freqs >= 0.)
assert np.abs(max_freq - f) < 1.
assert_array_almost_equal(x, xp, decimal=6)
# norm conservation thanks to tight frame property
assert_almost_equal(np.sqrt(stft_norm2(X)),
[linalg.norm(xx) for xx in x], decimal=6)
# Test with random signal
x = np.random.randn(2, T)
wsize = 16
tstep = 8
X = stft(x, wsize, tstep)
xp = istft(X, tstep, Tx=T)
freqs = stftfreq(wsize, sfreq=1000)
max_freq = freqs[np.argmax(np.sum(np.abs(X[0]) ** 2, axis=1))]
assert X.shape[1] == len(freqs)
assert np.all(freqs >= 0.)
assert_array_almost_equal(x, xp, decimal=6)
# norm conservation thanks to tight frame property
assert_almost_equal(np.sqrt(stft_norm2(X)),
[linalg.norm(xx) for xx in x],
decimal=6)
# Try with empty array
x = np.zeros((0, T))
X = stft(x, wsize, tstep)
xp = istft(X, tstep, T)
assert xp.shape == x.shape
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