 codex/hot-wire-spatial-transfer.py

"""Uniform hot-wire line-average power transfer.

Tested with Python 3.14, NumPy 2.3.5 and Matplotlib 3.10.7.
The horizontal coordinate is length / spatial wavelength along the wire, not
frequency / sample rate. Run via Make in the mirrored media working directory.
"""
from pathlib import Path

import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import numpy as np


def power_transfer(length_over_wavelength):
    """Squared transfer of a uniform line average; np.sinc(x)=sin(pi*x)/(pi*x)."""
    return np.sinc(np.asarray(length_over_wavelength))**2


def main():
    x = np.linspace(0, 2.5, 2001)
    fig, ax = plt.subplots(figsize=(8, 4.6), facecolor='white')
    ax.set_facecolor('white')
    ax.plot(x, power_transfer(x), color='#165f87', linewidth=2.4)
    points = [(.25, r'$\lambda_s=4\ell$', (.52, .91)),
              (.50, r'$\lambda_s=2\ell$', (.82, .53)),
              (1., r'$\lambda_s=\ell$', (1.35, .19))]
    for xx, label, text in points:
        yy = float(power_transfer(xx))
        ax.plot(xx, yy, 'o', color='#a74716', markersize=6)
        ax.annotate(f'{label}\nPower fraction {yy:.3f}', xy=(xx, yy), xytext=text,
                    fontsize=10, ha='left', arrowprops={'arrowstyle':'-', 'color':'#666666'})
    ax.set(xlim=(0, 2.5), ylim=(-.025, 1.04),
           xlabel=r'Wire length / spatial wavelength, $\ell/\lambda_s$',
           ylabel=r'Power transfer $|H|^2$',
           title='Spatial averaging by an ideal finite-length hot wire')
    ax.set_xticks([0, .25, .5, 1, 1.5, 2, 2.5])
    ax.grid(alpha=.20)
    ax.spines[['top', 'right']].set_visible(False)
    fig.text(.5, .025, 'Uniform linear averaging model; electronics are assumed ideal.',
             ha='center', fontsize=10)
    fig.subplots_adjust(left=.11, right=.98, bottom=.19, top=.88)
    fig.savefig(Path.cwd()/'hot-wire-spatial-transfer.png', dpi=110, facecolor='white')
    plt.close(fig)


if __name__ == '__main__':
    main()