This documentation is for astroML version 0.2

This page

Links

astroML Mailing List

GitHub Issue Tracker

Videos

Scipy 2012 (15 minute talk)

Scipy 2013 (20 minute talk)

Citing

If you use the software, please consider citing astroML.

Example of a Fourier TransformΒΆ

Figure E.1

An example of approximating the continuous Fourier transform of a function using the fast Fourier transform.

../../_images/fig_fft_text_example_1.png
# Author: Jake VanderPlas
# License: BSD
#   The figure produced by this code is published in the textbook
#   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
#   For more information, see http://astroML.github.com
#   To report a bug or issue, use the following forum:
#    https://groups.google.com/forum/#!forum/astroml-general
import numpy as np
from matplotlib import pyplot as plt
from scipy import fftpack

from astroML.fourier import FT_continuous, sinegauss, sinegauss_FT

#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX.  This may
# result in an error if LaTeX is not installed on your system.  In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)

#------------------------------------------------------------
# Choose parameters for the wavelet
N = 10000
t0 = 5
f0 = 2
Q = 2

#------------------------------------------------------------
# Compute the wavelet on a grid of times
Dt = 0.01
t = t0 + Dt * (np.arange(N) - N / 2)
h = sinegauss(t, t0, f0, Q)

#------------------------------------------------------------
# Approximate the continuous Fourier Transform
f, H = FT_continuous(t, h)

rms_err = np.sqrt(np.mean(abs(H - sinegauss_FT(f, t0, f0, Q)) ** 2))

#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 3.75))
fig.subplots_adjust(hspace=0.25)

# plot the wavelet
ax = fig.add_subplot(211)
ax.plot(t, h.real, '-', c='black', label='$Re[h]$', lw=1)
ax.plot(t, h.imag, ':', c='black', label='$Im[h]$', lw=1)
ax.legend()

ax.set_xlim(2, 8)
ax.set_ylim(-1.2, 1.2)
ax.set_xlabel('$t$')
ax.set_ylabel('$h(t)$')

# plot the Fourier transform
ax = fig.add_subplot(212)
ax.plot(f, H.real, '-', c='black', label='$Re[H]$', lw=1)
ax.plot(f, H.imag, ':', c='black', label='$Im[H]$', lw=1)
ax.text(0.55, 1.5, "RMS Error = %.2g" % rms_err)
ax.legend()

ax.set_xlim(0.5, 3.5)
ax.set_ylim(-1.9, 1.9)
ax.set_xlabel('$f$')
ax.set_ylabel('$H(f)$')

plt.show()