File:Ram-Lak kernel.svg

#! /usr/bin/env python3
# -*- coding:utf8 -*-

import matplotlib.pyplot as plt
import numpy as np
from math import *

def ramlak(N):
    y = np.zeros(N)
    y[0] = 0.25
    fodd = np.arange(1, N, 2)
    fodd = np.minimum(fodd, N - fodd)
    y[1:N:2] = (-1. / (pi * pi)) / (fodd * fodd)
    return y

N = 18
xlim = -8, 8
kernel = ramlak(N)

plt.figure(figsize=(5, 3.5))
plt.plot(np.arange(-N//2, N - N//2),
         np.roll(kernel, N//2),
         "o-", label="Ram-Lak")

xa = np.linspace(*xlim, 801)
ya = np.divide(-pi**-2, xa * xa, out=None, where=(xa!=0))
ya[xa==0] = float(nan)
plt.plot(xa, ya, "--", color="#bbbbbb", zorder=1.9, label=r"$-1/(x \pi)^2$")

annotate_args = {"va":"center", "ha":"left", "xytext":(12, 0), "zorder":1.8,
    "textcoords":"offset points", "fontsize":14,
    "bbox":{"fc":"white", "ec":"none"} }
plt.annotate(r"$\frac{1}{4}$", (0, kernel[0]), **annotate_args)
plt.annotate(r"$\frac{-1}{\pi^2}$", (1, kernel[1]), **annotate_args)
annotate_args.update({"va":"top", "ha":"center", "xytext":(0, -8)})
plt.annotate(r"$\frac{-1}{(3\pi)^2}$", (3, kernel[3]), **annotate_args)
plt.annotate(r"$\frac{-1}{(5\pi)^2}$", (5, kernel[5]), **annotate_args)
plt.annotate(r"$\frac{-1}{(7\pi)^2}$", (7, kernel[7]), **annotate_args)

plt.grid(True)
plt.xlim(*xlim)
plt.ylim(-0.13, 0.28)
plt.legend(loc="upper left", framealpha=1, borderaxespad=1.0, borderpad=0.6)
plt.tight_layout()
plt.savefig("Ram-Lak kernel.svg")