Interactive 3D plot of complex signals for visual inspection

plot_complex.py

#!/usr/env/bin python
# -*- coding:utf-8 -*-


"""
Interactive plot for visual inspection:
Complex vectors are plotted as lines on a 3D space, such that 2 dimensions are
the real and imaginary components, and the third dimension goes through the
vector values (could be e.g. time or frequency).


Copyright 2021 aferro (ORCID: 0000-0003-3830-3595)

Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:

The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
"""


import numpy as np
import matplotlib.pyplot as plt
from seaborn import color_palette as palette


# ##############################################################################
# SIGNAL PROCESSING
# ##############################################################################
def unit_spiral(n_samples, n_cycles=1):
    """
    """
    x = np.linspace(0, 2 * np.pi * n_cycles, n_samples)
    result = np.zeros(n_samples, dtype=np.complex128)
    result.real = np.cos(x)
    result.imag = np.sin(x)
    return result


def dirac_delta(n_samples, idx):
    """
    """
    result = np.zeros(n_samples)
    result[idx] = 1
    return result


# ##############################################################################
# PLOTTER
# ##############################################################################
def plot_complex(*signals, domain=None, bg_color=(1, 1, 1, 0),
                 axis_alpha=0.1, signal_alpha=1.0,
                 axis_color="black"):
    """
    """
    lengths = [len(s) for s in signals]
    fig = plt.figure()
    ax = fig.add_subplot(111, projection="3d")
    ax.set_box_aspect((3, 1, 1))  # xy aspect ratio is 1:1, but stretches z
    ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    if domain is not None:
        ax.set_xlabel(domain)
    ax.set_ylabel("real")
    ax.set_zlabel("imaginary")
    ax.set_xticks([], [])
    ax.set_yticks([], [])
    ax.set_zticks([], [])
    ax.w_xaxis.set_pane_color(bg_color)
    ax.w_yaxis.set_pane_color(bg_color)
    ax.w_zaxis.set_pane_color(bg_color)
    # Draw zero-axis and unit circle for reference
    axis_line = np.zeros(max(lengths), dtype=np.float32)
    ax.plot3D(range(len(axis_line)), axis_line, axis_line, color=axis_color,
              alpha=axis_alpha)
    #
    unit_circle = unit_spiral(360, 1)
    ax.plot3D(np.zeros(360), unit_circle.real, unit_circle.imag,
              color=axis_color, alpha=axis_alpha)
    #
    scalar1 = np.linspace(0, 1, 5)
    ax.plot3D(np.zeros(5), scalar1, np.zeros(5), color=axis_color,
              alpha=axis_alpha)
    #
    for i, s in enumerate(signals):
        color = palette("colorblind")[i]
        ax.plot3D(range(len(s)), s.real, s.imag, color=color,
                  alpha=signal_alpha)
    #
    return fig


# ##############################################################################
# MAIN ROUTINE
# ##############################################################################
if __name__ == "__main__":
    N = 1000

    a = dirac_delta(N, 0)
    b = dirac_delta(N, 1)
    c = dirac_delta(N, 2)
    d = dirac_delta(N, 3)

    A = np.fft.fft(a)
    B = np.fft.fft(b)
    C = np.fft.fft(c)
    D = np.fft.fft(d)

    fig = plot_complex(A, B, C, D, domain="freq")
    fig.show()
    #
    import pdb; pdb.set_trace()