Merge pull request #94 from jaidevd/jd-fix-fig4.4567

Add Wigner-Ville contour plots to the gallery

doc/_gallery/plot_4_1_1_pwv_atoms.py

@@ -0,0 +1,33 @@
+#! /usr/bin/env python
+# -*- coding: utf-8 -*-
+# vim:fenc=utf-8
+#
+# Copyright © 2015 jaidev <jaidev@newton>
+#
+# Distributed under terms of the MIT license.
+
+"""
+==================================================
+Pseudo Wigner-Ville Distribution of Gaussian Atoms
+==================================================
+
+This example shows the Pseudo Wigner-Ville distribution of four Gaussian atoms
+located at the corners of a rectangle in the time-frequency plane. The
+`PseudoWignerVilleDistribution` class uses frequency smoothing, which
+attenuates the interferences oscillating along the time axis.
+
+Figure 4.5 from the tutorial.
+"""
+
+import numpy as np
+from tftb.generators import atoms
+from tftb.processing import PseudoWignerVilleDistribution
+
+x = np.array([[32, .15, 20, 1],
+             [96, .15, 20, 1],
+             [32, .35, 20, 1],
+             [96, .35, 20, 1]])
+g = atoms(128, x)
+spec = PseudoWignerVilleDistribution(g)
+spec.run()
+spec.plot(kind="contour", scale="log", show_tf=True)

doc/_gallery/plot_4_1_1_wv_analytic_signal.py

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+#! /usr/bin/env python
+# -*- coding: utf-8 -*-
+# vim:fenc=utf-8
+#
+# Copyright © 2015 jaidev <jaidev@newton>
+#
+# Distributed under terms of the MIT license.
+
+"""
+====================================================
+Wigner Ville Distribution of Analytic Gaussian Atoms
+====================================================
+
+This example shows the WVD of and analytic Gaussian atom. As seen in Figure
+4.6, the WVD of a real valued signal may present interference terms and
+spectral aliasing. One of the ways to fix this is to use an analytic signal,
+which divides the spectral domain into two parts: real and imaginary. Thus, the
+number of interference terms is also halved. Secondly, analytic signals have no
+negative components, so the terms present in the negative half plane also
+vanish.
+
+Figure 4.7 from the tutorial.
+"""
+
+import numpy as np
+from tftb.generators import atoms
+from tftb.processing import WignerVilleDistribution
+
+x = np.array([[32, .15, 20, 1],
+             [96, .32, 20, 1]])
+g = atoms(128, x)
+spec = WignerVilleDistribution(g)
+spec.run()
+spec.plot(show_tf=True, kind="contour", scale="log")

doc/_gallery/plot_4_1_1_wv_atoms.py

@@ -0,0 +1,32 @@
+#! /usr/bin/env python
+# -*- coding: utf-8 -*-
+# vim:fenc=utf-8
+#
+# Copyright © 2015 jaidev <jaidev@newton>
+#
+# Distributed under terms of the MIT license.
+
+"""
+===========================================
+Wigner-Ville Distribution of Gaussian Atoms
+===========================================
+
+This example shows the WV distribution of four Gaussian atoms, each localized
+at the corner of a rectangle in the time-frequency plane. The distribution does
+show the four signal terms, as well as six interference terms.
+
+Figure 4.4 from the tutorial.
+"""
+
+import numpy as np
+from tftb.generators import atoms
+from tftb.processing import WignerVilleDistribution
+
+x = np.array([[32, .15, 20, 1],
+             [96, .15, 20, 1],
+             [32, .35, 20, 1],
+             [96, .35, 20, 1]])
+g = atoms(128, x)
+spec = WignerVilleDistribution(g)
+spec.run()
+spec.plot(kind="contour", show_tf=True, scale="log")

doc/_gallery/plot_4_1_1_wv_real_signal.py

@@ -0,0 +1,31 @@
+#! /usr/bin/env python
+# -*- coding: utf-8 -*-
+# vim:fenc=utf-8
+#
+# Copyright © 2015 jaidev <jaidev@newton>
+#
+# Distributed under terms of the MIT license.
+
+"""
+================================================================================
+Sampling Effects on the Wigner-Ville Distribution of a Real Valued Gaussian Atom
+================================================================================
+
+This example shows the Wigner-Ville distribution of a real valued Gaussian
+atom. If a signal is sampled at the Nyquist rate, the WVD is affected by
+spectral aliasing and many additional interferences. To fix this, either the
+signal may be oversampled, or an analytical signal may be used.
+
+Figure 4.6 from the tutorial.
+"""
+
+import numpy as np
+from tftb.generators import atoms
+from tftb.processing import WignerVilleDistribution
+
+x = np.array([[32, .15, 20, 1],
+             [96, .32, 20, 1]])
+g = atoms(128, x)
+spec = WignerVilleDistribution(np.real(g))
+spec.run()
+spec.plot(kind="contour", show_tf=True, scale="log")