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 check_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)
