.. _book_fig_chapter10_fig_fft_example:


Fast Fourier Transform Example
------------------------------
Figure 10.5

The discrete Fourier transform (bottom panel) for two noisy data sets shown in
the top panel. For 512 evenly sampled times t (dt = 0.977), points are drawn
from h(t) = a + sin(t)G(t), where G(t) is a Gaussian N(mu = 0,sigma = 10).
Gaussian noise with sigma = 0.05 (top data set) and 0.005 (bottom data set)
is added to signal h(t). The value of the offset a is 0.15 and 0, respectively.
The discrete Fourier transform is computed as described in Section 10.2.3.
For both noise realizations, the correct frequency f = (2pi)-1 ~ 0.159 is
easily discernible in the bottom panel. Note that the height of peaks is the
same for both noise realizations. The large value of abs(H(f = 0)) for data
with larger noise is due to the vertical offset.



.. image:: ../images/chapter10/fig_fft_example_1.png
    :scale: 100
    :align: center


.. raw:: html
    
    <div class="toggle_trigger"><a href="#">

**Code output:**

.. raw:: html

    </a></div>
    <div class="toggle_container">

.. literalinclude:: fig_fft_example.txt

.. raw:: html

    </div>
    <div class="toggle_trigger" id="start_open"><a href="#">

**Python source code:**

.. raw:: html

    </a></div>
    <div class="toggle_container">

.. literalinclude:: fig_fft_example.py
    :lines: 17-

.. raw:: html

    </div>
    <div align="right">

:download:`[download source: fig_fft_example.py] <fig_fft_example.py>`

.. raw:: html
    
    </div>