File:Dirichlet kernels.svg
Summary
| Description |
English: Plots of the first few Dirichlet kernels made with matplotlib. This function has a period of 2π. |
||
| Date | |||
| Source | Dirichlet.png | ||
| Author |
|
||
| Other versions |
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Source code
Source Code in python: |
|---|
from __future__ import division # In case someone wants to use Python 2
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns # Just for the colors
mpl.rcParams['axes.labelsize'] = 20
mpl.rcParams['axes.titlesize'] = 22
mpl.rcParams['legend.fontsize'] = 18
mpl.rcParams['xtick.labelsize'] = 14
mpl.rcParams['ytick.labelsize'] = 14
mpl.rcParams['lines.linewidth'] = 3
def dirichlet(n, x):
return np.where(x!=0, np.sin((n + .5)*x)/np.sin(.5*x), 2*n + 1)
points = 2**10 + 1
kernels = 4
x_min = -np.pi
x_max = np.pi
x_vals = np.linspace(x_min, x_max, num=points)
n_vals = np.arange(1, kernels + 1)
D = dirichlet(np.resize(n_vals, (points, kernels)).T,
np.resize(x_vals, (kernels, points)))
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
for kernel, n in zip(D, n_vals):
ax.plot(x_vals, kernel,
label=r'$\frac{\sin((' + str(n) + r'+1/2)x)}{\sin(x/2)}$')
ax.xaxis.set_ticks(np.pi*np.arange(-4, 5)/4)
ax.xaxis.set_ticklabels([r'$-\pi$', r'$-\frac{3\pi}{4}$', r'$-\frac{\pi}{2}$',
r'$-\frac{\pi}{4}$', r'$0$', r'$\frac{\pi}{4}$',
r'$\frac{\pi}{2}$', r'$\frac{3\pi}{4}$', r'$\pi$'])
ax.legend()
ax.set_xlim([x_min, x_max])
ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$D_n(x)$')
ax.xaxis.grid(color='gray')
ax.yaxis.grid(color='gray')
plt.tight_layout()
plt.savefig('dirichlet.svg')
|