def check_czt(x):
# Check that czt is the equivalent of normal fft
y = fft(x)
y1 = czt(x)
assert_allclose(y1, y, rtol=1e-13)
# Check that interpolated czt is the equivalent of normal fft
y = fft(x, 100 * len(x))
y1 = czt(x, 100 * len(x))
assert_allclose(y1, y, rtol=1e-12)
def test_czt_math(impulse, m, w, a):
# z-transform of an impulse is 1 everywhere
assert_allclose(czt(impulse[2:], m=m, w=w, a=a), np.ones(m), rtol=1e-10)
# z-transform of a delayed impulse is z**-1
assert_allclose(czt(impulse[1:], m=m, w=w, a=a),
czt_points(m=m, w=w, a=a)**-1,
rtol=1e-10)
# z-transform of a 2-delayed impulse is z**-2
assert_allclose(czt(impulse, m=m, w=w, a=a),
czt_points(m=m, w=w, a=a)**-2,
rtol=1e-10)
def test_nonsense_size(size):
# Numpy and Scipy fft() give ValueError for 0 output size, so we do, too
with pytest.raises(ValueError, match='Invalid number of CZT'):
CZT(size, 3)
with pytest.raises(ValueError, match='Invalid number of CZT'):
ZoomFFT(size, 0.2, 3)
with pytest.raises(ValueError, match='Invalid number of CZT'):
CZT(3, size)
with pytest.raises(ValueError, match='Invalid number of CZT'):
ZoomFFT(3, 0.2, size)
with pytest.raises(ValueError, match='Invalid number of CZT'):
czt([1, 2, 3], size)
with pytest.raises(ValueError, match='Invalid number of CZT'):
zoom_fft([1, 2, 3], 0.2, size)
def test_large_prime_lengths():
np.random.seed(0) # Deterministic randomness
for N in (101, 1009, 10007):
x = np.random.rand(N)
y = fft(x)
y1 = czt(x)
assert_allclose(y, y1, rtol=1e-12)
def test_int_args():
# Integer argument `a` was producing all 0s
assert_allclose(abs(czt([0, 1], m=10, a=2)), 0.5 * np.ones(10), rtol=1e-15)
assert_allclose(czt_points(11, w=2), 1 / (2**np.arange(11)), rtol=1e-30)
def test_0_rank_input():
with pytest.raises(IndexError, match='tuple index out of range'):
czt(5)
with pytest.raises(IndexError, match='tuple index out of range'):
zoom_fft(5, 0.5)
def test_empty_input():
with pytest.raises(ValueError, match='Invalid number of CZT'):
czt([])
with pytest.raises(ValueError, match='Invalid number of CZT'):
zoom_fft([], 0.5)
def test_czt_vs_fft():
np.random.seed(123)
random_lengths = np.random.exponential(100000, size=10).astype('int')
for n in random_lengths:
a = np.random.randn(n)
assert_allclose(czt(a), fft(a), rtol=1e-11)