def direct_shift(x, a, period=None):
n = len(x)
if period is None:
k = fftfreq(n) * 1j * n
else:
k = fftfreq(n) * 2j * pi / period * n
return ifft(fft(x) * exp(k * a)).real
def test_definition(self):
x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
assert_array_almost_equal(9 * fftfreq(9), x)
assert_array_almost_equal(9 * pi * fftfreq(9, pi), x)
x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1]
assert_array_almost_equal(10 * fftfreq(10), x)
assert_array_almost_equal(10 * pi * fftfreq(10, pi), x)
def direct_itilbert(x, h=1, period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2 * pi
w = fftfreq(n) * h * 2 * pi / period * n
w = -1j * tanh(w)
return ifft(w * fx)
def direct_tilbert(x, h=1, period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2 * pi
w = fftfreq(n) * h * 2 * pi / period * n
w[0] = 1
w = 1j / tanh(w)
w[0] = 0j
return ifft(w * fx)
def direct_diff(x, k=1, period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2 * pi
w = fftfreq(n) * 2j * pi / period * n
if k < 0:
w = 1 / w**k
w[0] = 0.0
else:
w = w**k
if n > 2000:
w[250:n - 250] = 0.0
return ifft(w * fx).real
def direct_hilbert(x):
fx = fft(x)
n = len(fx)
w = fftfreq(n) * n
w = 1j * sign(w)
return ifft(w * fx)