#
# Copyright © 2015 jaidev <jaidev@newton>
#
# Distributed under terms of the MIT license.
"""
==============================================
Wideband Ambiguity Function of an Altes Signal
==============================================
For wideband signals, the narrow band ambiguity function is not appropriate for
wideband signals. So we consider a wide band ambiguity function. This function
is equivalent to the wavelet transform of a signal whose mother wavelet is the
signal itself.
Figure 4.25 from the tutorial.
"""
from tftb.generators import altes
from tftb.processing.ambiguity import wide_band
import matplotlib.pyplot as plt
import numpy as np
signal = altes(128, 0.1, 0.45)
waf, tau, theta = wide_band(signal, 0.1, 0.35, 64)
plt.contour(tau, theta, np.abs(waf)**2)
plt.xlabel("Delay")
plt.ylabel("Log(Scale)")
plt.title("Wide Band Ambiguity Function")
plt.show()
# Mellin transform computation of the analyzed signal
p = np.arange(2 * N)
MS = np.fft.fftshift(np.fft.ifft(ZS, axis=0))
beta = (p / float(N) - 1.0) / (2 * np.log(q))
# Inverse mellin and fourier transform.
Mmax = np.amax(np.ceil(X.shape[0] / 2.0 * a))
if isinstance(a, np.ndarray):
S = np.zeros((2 * Mmax, a.shape[0]), dtype=complex)
else:
S = np.zeros((2 * Mmax,), dtype=complex)
ptr = 0
DMS = np.exp(-2 * np.pi * 1j * beta * np.log(a)) * MS
DS = np.fft.fft(np.fft.fftshift(DMS), axis=0)
Mcurrent = np.ceil(a * X.shape[0] / 2)
t = np.arange(-Mcurrent, Mcurrent) - 1
itfmatx = np.exp(2 * 1j * np.pi * np.dot(t.reshape((256, 1)),
geo_f.reshape((1, 128))))
dilate_sig = np.zeros((2 * Mcurrent,), dtype=complex)
for kk in range(2 * int(Mcurrent)):
dilate_sig[kk] = trapz(itfmatx[kk, :] * DS[:N], geo_f)
S[(Mmax - Mcurrent):(Mmax + Mcurrent)] = dilate_sig
ptr += 1
S = S * np.linalg.norm(X) / np.linalg.norm(S)
return S
if __name__ == '__main__':
from tftb.generators import altes
sig = altes(256, 0.1, 0.45, 10000)
nha = ha.shape[0] / 2
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
detail = detail[int(np.floor(nha)):(detail.shape[0] -
np.round(nha))]
wt[ptr, :] = detail[time_instants]
tfr[ptr, :] = detail[time_instants] * np.conj(
detail[time_instants])
t = time_instants
f = f.T
# Normalization
SP = np.fft.fft(z, axis=0)
indmin = 1 + np.round(fmin * (signal.shape[0] - 2))
indmax = 1 + np.round(fmax * (signal.shape[0] - 2))
SPana = SP[indmin:(indmax + 1)]
tfr = np.real(tfr)
tfr = tfr * (np.linalg.norm(SPana)**2) / integrate_2d(tfr, t, f) / n_voices
return tfr, t, f, wt
if __name__ == '__main__':
from tftb.generators import altes
import matplotlib.pyplot as plt
sig = altes(64, 0.1, 0.45)
tfr, t, f = smoothed_pseudo_wigner(sig)
tfr = np.abs(tfr)**2
threshold = np.amax(tfr) * 0.05
tfr[tfr <= threshold] = 0.0
plt.imshow(tfr, aspect='auto', origin='bottomleft', extent=[0, 64, 0, 0.5])
plt.show()
wts = scale(waveparams, a, fmin, fmax, nscale)
for ptr in range(n_voices):
ha = wts[ptr, :]
nha = ha.shape[0] / 2
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
detail = detail[int(np.floor(nha)):(detail.shape[0] - np.round(nha))]
wt[ptr, :] = detail[time_instants]
tfr[ptr, :] = detail[time_instants] * np.conj(detail[time_instants])
t = time_instants
f = f.T
# Normalization
SP = np.fft.fft(z, axis=0)
indmin = 1 + np.round(fmin * (signal.shape[0] - 2))
indmax = 1 + np.round(fmax * (signal.shape[0] - 2))
SPana = SP[indmin:(indmax + 1)]
tfr = np.real(tfr)
tfr = tfr * (np.linalg.norm(SPana) ** 2) / integrate_2d(tfr, t, f) / n_voices
return tfr, t, f, wt
if __name__ == '__main__':
from tftb.generators import altes
import matplotlib.pyplot as plt
sig = altes(64, 0.1, 0.45)
tfr, t, f = smoothed_pseudo_wigner(sig)
tfr = np.abs(tfr) ** 2
threshold = np.amax(tfr) * 0.05
tfr[tfr <= threshold] = 0.0
plt.imshow(tfr, aspect='auto', origin='bottomleft', extent=[0, 64, 0, 0.5])
plt.show()
def setUp(self):
self.signal = altes(128, 0.1, 0.45)
self.tfr, self.tau, self.theta = ambiguity.wide_band(self.signal)
def setUp(self):
self.signal = altes(128, 0.1, 0.45)
self.tfr, self.tau, self.theta = ambiguity.wide_band(self.signal)
# Copyright © 2015 jaidev <jaidev@newton>
#
# Distributed under terms of the MIT license.
"""
==============================================
Wideband Ambiguity Function of an Altes Signal
==============================================
For wideband signals, the narrow band ambiguity function is not appropriate for
wideband signals. So we consider a wide band ambiguity function. This function
is equivalent to the wavelet transform of a signal whose mother wavelet is the
signal itself.
Figure 4.25 from the tutorial.
"""
from tftb.generators import altes
from tftb.processing.ambiguity import wide_band
import matplotlib.pyplot as plt
import numpy as np
signal = altes(128, 0.1, 0.45)
waf, tau, theta = wide_band(signal, 0.1, 0.35, 64)
plt.contour(tau, theta, np.abs(waf) ** 2)
plt.xlabel("Delay")
plt.ylabel("Log(Scale)")
plt.title("Wide Band Ambiguity Function")
plt.show()
p = np.arange(2 * N)
MS = np.fft.fftshift(np.fft.ifft(ZS, axis=0))
beta = (p / float(N) - 1.0) / (2 * np.log(q))
# Inverse mellin and fourier transform.
Mmax = np.amax(np.ceil(X.shape[0] / 2.0 * a))
if isinstance(a, np.ndarray):
S = np.zeros((2 * Mmax, a.shape[0]), dtype=complex)
else:
S = np.zeros((2 * Mmax, ), dtype=complex)
ptr = 0
DMS = np.exp(-2 * np.pi * 1j * beta * np.log(a)) * MS
DS = np.fft.fft(np.fft.fftshift(DMS), axis=0)
Mcurrent = np.ceil(a * X.shape[0] / 2)
t = np.arange(-Mcurrent, Mcurrent) - 1
itfmatx = np.exp(2 * 1j * np.pi * np.dot(t.reshape(
(256, 1)), geo_f.reshape((1, 128))))
dilate_sig = np.zeros((2 * Mcurrent, ), dtype=complex)
for kk in range(2 * int(Mcurrent)):
dilate_sig[kk] = trapz(itfmatx[kk, :] * DS[:N], geo_f)
S[(Mmax - Mcurrent):(Mmax + Mcurrent)] = dilate_sig
ptr += 1
S = S * np.linalg.norm(X) / np.linalg.norm(S)
return S
if __name__ == '__main__':
from tftb.generators import altes
sig = altes(256, 0.1, 0.45, 10000)
