Animated aliasing waves

aliasing_waves.py

import numpy as np
import matplotlib.pyplot as plt

# Knobs to twiddle:
# 1. sine frequencies: `f1`, `f2`
# 2. spacing between vectical bars: `rect_spacing`
# (You can also change `rect_width`, but the frequency/spacing are more interesting)

f1 = 7.5  # Twiddle with the red sine frequency!
f2 = 7.0  # Slightly different frequency

xx = np.linspace(0, 5, 500)
# Make 2 sine waves, offset vertically, with different frequencies
A = 0.5  # Make it about half the height of the plot
y1 = A * np.sin(2 * np.pi * f1 * xx) + 1.2 * A
y2 = A * np.sin(2 * np.pi * f2 * xx) - 1.2 * A

fig, ax = plt.subplots(1, 1, figsize=(8, 4))

# Plot the red sine waves
ax.plot(xx, y1, "r", lw=2)
ax.plot(xx, y2, "r", lw=2)

rect_spacing = 0.16

num_rects = 20
x_rects = np.arange(0, num_rects * rect_spacing, rect_spacing)

rect_width = 11 # Possible knob to twiddle, but only values ~10-13 seem interesting
height = 1.5
# zorder makes sure the these are on top of the sine wave lines
rects = ax.vlines(x_rects, -height, height, lw=rect_width, color="k", zorder=5) 

ymax = 0.8 * height
xmax = 5
ax.set_ylim((-ymax, ymax))
ax.set_xlim((0, xmax))
ax.set_axis_off()

# Get the [(x, y), ...] positions of the vectical rectangles
segments = rects.get_segments()

# For interactive version with a slider, which works in jupyter notebooks
# import ipywidgets
# xstart = 0
# @ipywidgets.interact(xstart=(xx[0]-2, xx[-1], rect_spacing/10))
# def move_rects(xstart=-2):
#     global segments
#     rects.set_paths([np.array([xstart, 0]) + a for a in segments])


# For saved animation:
from matplotlib.animation import FuncAnimation


def init():
    ax.set_ylim((-ymax, ymax))
    ax.set_xlim((0, xmax))
    return (rects,)


# Receives the value from the `frames` iterable
def update(x_start):
    # move the `segments` slightly to the right by adding `frame` to the x values
    rects.set_paths([np.array([x_start, 0]) + a for a in segments])
    return (rects,)


interval_ms = 100
x_start_positions = np.linspace(-2, 3, 200)
ani = FuncAnimation(
    fig,
    update,
    frames=x_start_positions,
    init_func=init,
    blit=True,
    interval=interval_ms,
);
# Save as a gif, noting what frequency was used
ani.save(f"aliasing_freqs_{f1}_{f2}_width_{rect_width}_dx_{rect_spacing}.gif");