def test_fourier4_normal(self):
"""normal ft of exp(-b*t)*unit_step(t)==1/(1.j*w + b)"""
func = fourier4
func_ = fourier4_
a = 2.3
args = (a, )
s = 1.5
ft = FourierTransform(func, args=args, inv=False, func_is_real=True)
assert_allclose(ft(s)[0], func_(s, *args), atol=0)
def test_fourier2_normal(self):
"""normal ft of rect(t/tau)==tau * sinc(tau*W/(2*pi))"""
#note that inverse of fourier2 will fail due to oscillations
func = fourier2
func_ = fourier2_
a = 2.3
args = (a, )
s = 1.5
ft = FourierTransform(func, args=args, inv=False, func_is_real=True)
assert_allclose(ft(s)[0], func_(s, *args), atol=0)
def test_fourier4_inverse(self):
"""inverse ft of 1/(1.j*w + b)==exp(-b*t)*unit_step(t)"""
func_ = fourier4
func = fourier4_
a = 2.3
args = (a, )
s = 1.5
ft = FourierTransform(
func,
args=args,
inv=True,
)
assert_allclose(ft(s)[0], func_(s, *args), atol=0)
def test_fourier1_inverse(self):
"""inverse ft of 2 * a / (a**2 + x**2)==exp(- a * abs(x))"""
func_ = fourier1
func = fourier1_
a = 2.3
args = (a, )
s = 1.5
ft = FourierTransform(func,
args=args,
inv=True,
func_is_real=True,
real_part_even=True)
assert_allclose(ft(s)[0], func_(s, *args), atol=0)
def test_fourier1_normal_at_zero(self):
"""normal ft of exp(- a * abs(x)) == 2 * a / (a**2 + x**2)"""
func = fourier1
func_ = fourier1_
a = 2.3
args = (a, )
s = 0
ft = FourierTransform(func,
args=args,
inv=False,
func_is_real=True,
real_part_even=True)
assert_allclose(ft(s)[0], func_(s, *args), atol=0)
def fourier_inverse(self, f, tvar, args, **opt):
ft = FourierTransform(f, args, inv=True, **opt)
val, err = ft(tvar)
return val, err
def fourier(self, f, tvar, args, **opt):
ft = FourierTransform(f, args, **opt)
val, err = ft(tvar)
return val, err