def test_default_bits(seed, sampling_rate, length):
"""Tests the determination of the default value for the bits argument of the constructor."""
pytest.importorskip("scipy")
mls = sumpf.MaximumLengthSequence(seed=seed, sampling_rate=sampling_rate, length=length)
bits = int(math.ceil(math.log2(length + 1)))
reference = sumpf.MaximumLengthSequence(bits=bits, seed=seed, sampling_rate=sampling_rate, length=length)
assert mls == reference
def test_seed(bits, seed, sampling_rate):
"""Tests if seeding the initial state of the MLS generator works as expected."""
pytest.importorskip("scipy")
length = 2 ** bits - 1
mls1 = sumpf.MaximumLengthSequence(bits=bits, seed=seed, sampling_rate=sampling_rate, length=length)
mls2 = sumpf.MaximumLengthSequence(bits, seed, sampling_rate, length)
mls3 = sumpf.MaximumLengthSequence(bits, seed + 1, sampling_rate, length)
assert mls1 is not mls2
assert mls1 == mls2
hypothesis.assume(mls2 != mls3) # if all generated MLS with different seeds are the same, this line will make the test fail
def test_constructor_defaults():
"""Tests the default values for the length and the bits arguments in the constructor."""
pytest.importorskip("scipy")
mls = sumpf.MaximumLengthSequence()
assert mls.bits() == 16
assert mls.sampling_rate() == 48000.0
assert mls.length() == 2 ** 16 - 1
mls = sumpf.MaximumLengthSequence(length=2 ** 13 - 1)
assert mls.bits() == 13
assert mls.sampling_rate() == 48000.0
assert mls.length() == 2 ** 13 - 1
mls = sumpf.MaximumLengthSequence(bits=10)
assert mls.bits() == 10
assert mls.sampling_rate() == 48000.0
assert mls.length() == 2 ** 10 - 1
def test_properties(bits, seed, sampling_rate, length):
"""Tests the methods for getting of derived parameters."""
pytest.importorskip("scipy")
mls = sumpf.MaximumLengthSequence(bits=bits, seed=seed, sampling_rate=sampling_rate, length=length)
assert mls.bits() == bits
assert mls.period_length() == 2 ** bits - 1
assert mls.periods() == mls.length() / mls.period_length()
assert set(mls.channels().flat) <= {-1.0, 1.0}
def test_magnitude(bits, seed, sampling_rate):
"""Tests if the magnitude of the MLS' spectrum is constant except for f=0."""
pytest.importorskip("scipy")
length = 2 ** bits - 1
mls = sumpf.MaximumLengthSequence(bits=bits, seed=seed, sampling_rate=sampling_rate, length=length)
spectrum = mls.fourier_transform()
reference = numpy.empty(spectrum.length())
reference[0] = 1.0
reference[1:] = math.sqrt(2 * spectrum.length())
assert spectrum.magnitude()[0] == pytest.approx(reference)
def test_auto_correlation(bits, seed, sampling_rate):
"""Tests if the auto-correlation of the MLS is an impulse."""
pytest.importorskip("scipy")
length = 2 ** bits - 1
mls = sumpf.MaximumLengthSequence(bits=bits, seed=seed, sampling_rate=sampling_rate, length=length)
spectrum = mls.fourier_transform()
auto_spectral_density = spectrum * spectrum.conjugate()
auto_correlation = auto_spectral_density.inverse_fourier_transform()
correction = 1.0 / (length - 1)
reference = numpy.empty(length - 1)
reference[0] = length - correction
reference[1:] = -1.0 - correction
assert auto_correlation.channels()[0] == pytest.approx(reference)
def test_periodicity(bits, seed, sampling_rate, length):
"""Tests if a signal with repeated MLS can be generated as expected."""
pytest.importorskip("scipy")
mls = sumpf.MaximumLengthSequence(bits=bits, seed=seed, sampling_rate=sampling_rate, length=2 ** bits - 1)
assert mls.period_length() == mls.length()
periodic = sumpf.MaximumLengthSequence(bits=bits, seed=seed, sampling_rate=sampling_rate, length=length)
assert periodic.period_length() == mls.length()
i = 0
start = 0
stop = mls.length()
while stop <= periodic.length():
assert (periodic.channels()[:, start:stop] == mls.channels()).all()
start = stop
stop += mls.length()
i += 1
if start != periodic.length():
remainder = periodic.length() - start
if remainder == 1:
assert periodic.channels()[0, start] == mls.channels()[0, 0]
else:
assert (periodic.channels()[0, start:] == mls.channels()[0, 0:remainder]).all()
assert periodic.periods() == pytest.approx(i + remainder / mls.length())
else:
assert periodic.periods() == i