.. _sphx_glr_auto_examples_plot_dft.py:


==========================
Discrete Fourier Transform
==========================

This example shows how you can approximate a time series using only some of its
Fourier coefficients using :class:`pyts.approximation.DFT`.




.. image:: /auto_examples/images/sphx_glr_plot_dft_001.png
    :align: center





.. code-block:: python


    import numpy as np
    import matplotlib.pyplot as plt
    from pyts.approximation import DFT

    # Parameters
    n_samples, n_features = 100, 48

    # Toy dataset
    rng = np.random.RandomState(41)
    X = rng.randn(n_samples, n_features)

    # DFT transformation
    n_coefs = 20
    norm_mean = False
    norm_std = False
    dft = DFT(n_coefs=n_coefs, norm_mean=norm_mean, norm_std=norm_std)
    X_dft = dft.fit_transform(X)

    # Compute the approximation for the first time series
    timestamps = np.arange(n_features) / n_features
    x_dft = np.zeros(n_features)
    for n in range(n_coefs // 2):
        x_dft += X_dft[0, 2 * n] * np.cos(2 * n * np.pi * timestamps) / n_features
        x_dft += X_dft[0, (2 * n) + 1] * np.sin(2 * n * np.pi * timestamps) / \
            n_features

    # Show the results for the first time series
    plt.figure(figsize=(12, 8))
    plt.plot(X[0], 'o-', label='Original')
    plt.plot(x_dft, 'o--', label='DFT - {0} coefs'.format(n_coefs))
    plt.legend(loc='best', fontsize=14)
    plt.show()

**Total running time of the script:** ( 0 minutes  0.024 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_dft.py <plot_dft.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_dft.ipynb <plot_dft.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_