def check_wavelets(t0, f0, Q, t):
h = sinegauss(t, t0, f0, Q)
f, H = FT_continuous(t, h)
H2 = sinegauss_FT(f, t0, f0, Q)
assert_allclose(H, H2, atol=1E-8)
def check_IFT_continuous(a, t0, f0, method, f):
H = sinegauss_FT(f, t0, f0, a)
t, h = IFT_continuous(f, H, method=method)
assert_allclose(h, sinegauss(t, t0, f0, a), atol=1E-12)
N = 10000
t0 = 5
f0 = 2
Q = 2
#------------------------------------------------------------
# Compute the wavelet on a grid of times
Dt = 0.01
t = t0 + Dt * (np.arange(N) - N / 2)
h = sinegauss(t, t0, f0, Q)
#------------------------------------------------------------
# Approximate the continuous Fourier Transform
f, H = FT_continuous(t, h)
rms_err = np.sqrt(np.mean(abs(H - sinegauss_FT(f, t0, f0, Q))**2))
#------------------------------------------------------------
# Plot the results
fig = plt.figure()
fig.subplots_adjust(hspace=0.25)
# plot the wavelet
ax = fig.add_subplot(211)
ax.plot(t, h.real, '-', c='black', label='$Re[h]$', lw=1)
ax.plot(t, h.imag, ':', c='black', label='$Im[h]$', lw=1)
ax.legend(prop=dict(size=14))
ax.set_xlim(2, 8)
ax.set_ylim(-1.2, 1.2)
ax.set_xlabel('$t$')
def check_FT_continuous(a, t0, f0, method, t):
h = sinegauss(t, t0, f0, a)
f, H = FT_continuous(t, h, method=method)
assert_allclose(H, sinegauss_FT(f, t0, f0, a), atol=1E-12)
def test_FT_continuous(a, t0, f0, method):
t = np.linspace(-9, 10, 10000)
h = sinegauss(t, t0, f0, a)
f, H = FT_continuous(t, h, method=method)
assert_allclose(H, sinegauss_FT(f, t0, f0, a), atol=1E-12)
def check_IFT_continuous(a, t0, f0, method):
f = np.linspace(-9, 10, 10000)
H = sinegauss_FT(f, t0, f0, a)
t, h = IFT_continuous(f, H, method=method)
assert_allclose(h, sinegauss(t, t0, f0, a), atol=1E-12)
def test_wavelets(t0, f0, Q):
t = np.linspace(-10, 10, 10000)
h = sinegauss(t, t0, f0, Q)
f, H = FT_continuous(t, h)
H2 = sinegauss_FT(f, t0, f0, Q)
assert_allclose(H, H2, atol=1E-8)
def check_IFT_continuous(a, t0, f0, method, f):
H = sinegauss_FT(f, t0, f0, a)
t, h = IFT_continuous(f, H, method=method)
assert_allclose(h, sinegauss(t, t0, f0, a), atol=1E-12)
def check_wavelets(t0, f0, Q, t):
h = sinegauss(t, t0, f0, Q)
f, H = FT_continuous(t, h)
H2 = sinegauss_FT(f, t0, f0, Q)
assert_allclose(H, H2, atol=1E-8)
def check_FT_continuous(a, t0, f0, method, t):
h = sinegauss(t, t0, f0, a)
f, H = FT_continuous(t, h, method=method)
assert_allclose(H, sinegauss_FT(f, t0, f0, a), atol=1E-12)
N = 10000
t0 = 5
f0 = 2
Q = 2
#------------------------------------------------------------
# Compute the wavelet on a grid of times
Dt = 0.01
t = t0 + Dt * (np.arange(N) - N / 2)
h = sinegauss(t, t0, f0, Q)
#------------------------------------------------------------
# Approximate the continuous Fourier Transform
f, H = FT_continuous(t, h)
rms_err = np.sqrt(np.mean(abs(H - sinegauss_FT(f, t0, f0, Q)) ** 2))
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 3.75))
fig.subplots_adjust(hspace=0.25)
# plot the wavelet
ax = fig.add_subplot(211)
ax.plot(t, h.real, '-', c='black', label='$Re[h]$', lw=1)
ax.plot(t, h.imag, ':', c='black', label='$Im[h]$', lw=1)
ax.legend()
ax.set_xlim(2, 8)
ax.set_ylim(-1.2, 1.2)
ax.set_xlabel('$t$')
