

.. _sphx_glr_gallery_pylab_examples_spectrum_demo.py:


========================
Spectrum Representations
========================

The plots show different spectrum representations of a sine signal with
additive noise. A (frequency) spectrum of a discrete-time signal is calculated
by utilizing the fast Fourier transform (FFT).




.. image:: /gallery/pylab_examples/images/sphx_glr_spectrum_demo_001.png
    :align: center





.. code-block:: python

    import matplotlib.pyplot as plt
    import numpy as np


    np.random.seed(0)

    dt = 0.01  # sampling interval
    Fs = 1/dt  # sampling frequency
    t = np.arange(0, 10, dt)

    # generate noise:
    nse = np.random.randn(len(t))
    r = np.exp(-t/0.05)
    cnse = np.convolve(nse, r)*dt
    cnse = cnse[:len(t)]

    s = 0.1*np.sin(4*np.pi*t) + cnse  # the signal

    fig, axes = plt.subplots(nrows=3, ncols=2, figsize=(7, 7))

    # plot time signal:
    axes[0, 0].set_title("Signal")
    axes[0, 0].plot(t, s, color='C0')
    axes[0, 0].set_xlabel("Time")
    axes[0, 0].set_ylabel("Amplitude")

    # plot different spectrum types:
    axes[1, 0].set_title("Magnitude Spectrum")
    axes[1, 0].magnitude_spectrum(s, Fs=Fs, color='C1')

    axes[1, 1].set_title("Log. Magnitude Spectrum")
    axes[1, 1].magnitude_spectrum(s, Fs=Fs, scale='dB', color='C1')

    axes[2, 0].set_title("Phase Spectrum ")
    axes[2, 0].phase_spectrum(s, Fs=Fs, color='C2')

    axes[2, 1].set_title("Angle Spectrum")
    axes[2, 1].angle_spectrum(s, Fs=Fs, color='C2')

    axes[0, 1].remove()  # don't display empty ax

    fig.tight_layout()
    plt.show()

**Total running time of the script:** ( 0 minutes  0.188 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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