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# scipy.signal.periodogram

`scipy.signal.``periodogram`(x, fs=1.0, window=None, nfft=None, detrend='constant', return_onesided=True, scaling='density', axis=-1)

  Estimate power spectral density using a periodogram.

  Parameters:

  x : array_like

  > Time series of measurement values

  fs : float, optional

  > Sampling frequency of the x time series. Defaults to 1.0.

  window : str or tuple or array_like, optional

  > Desired window to use. See `get_window` for a list of windows and required parameters. If window is an array it will be used directly as the window. Defaults to None; equivalent to ‘boxcar’.

  nfft : int, optional

  > Length of the FFT used. If None the length of x will be used.

  detrend : str or function or False, optional

  > Specifies how to detrend x prior to computing the spectrum. If `detrend` is a string, it is passed as the `type` argument to `detrend`. If it is a function, it should return a detrended array. If `detrend` is False, no detrending is done. Defaults to ‘constant’.

  return_onesided : bool, optional

  > If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Note that for complex data, a two-sided spectrum is always returned.

  scaling : { ‘density’, ‘spectrum’ }, optional

  > Selects between computing the power spectral density (‘density’) where Pxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’

  axis : int, optional

  > Axis along which the periodogram is computed; the default is over the last axis (i.e. `axis=-1`).

  Returns:

  f : ndarray

  > Array of sample frequencies.

  Pxx : ndarray

  > Power spectral density or power spectrum of x.

  See also

  `welch`
    Estimate power spectral density using Welch’s method
  `lombscargle`
    Lomb-Scargle periodogram for unevenly sampled data

  Notes

  New in version 0.12.0.

  Examples

      >>> from scipy import signal
      >>> import matplotlib.pyplot as plt
      >>> np.random.seed(1234)

  Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by 0.001 V**2/Hz of white noise sampled at 10 kHz.

      >>> fs = 10e3
      >>> N = 1e5
      >>> amp = 2*np.sqrt(2)
      >>> freq = 1234.0
      >>> noise_power = 0.001 * fs / 2
      >>> time = np.arange(N) / fs
      >>> x = amp*np.sin(2*np.pi*freq*time)
      >>> x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape)

  Compute and plot the power spectral density.

      >>> f, Pxx_den = signal.periodogram(x, fs)
      >>> plt.semilogy(f, Pxx_den)
      >>> plt.ylim([1e-7, 1e2])
      >>> plt.xlabel('frequency [Hz]')
      >>> plt.ylabel('PSD [V**2/Hz]')
      >>> plt.show()

  (Source code)

  If we average the last half of the spectral density, to exclude the peak, we can recover the noise power on the signal.

      >>> np.mean(Pxx_den[256:])
      0.0018156616014838548

  Now compute and plot the power spectrum.

      >>> f, Pxx_spec = signal.periodogram(x, fs, 'flattop', scaling='spectrum')
      >>> plt.figure()
      >>> plt.semilogy(f, np.sqrt(Pxx_spec))
      >>> plt.ylim([1e-4, 1e1])
      >>> plt.xlabel('frequency [Hz]')
      >>> plt.ylabel('Linear spectrum [V RMS]')
      >>> plt.show()

  The peak height in the power spectrum is an estimate of the RMS amplitude.

      >>> np.sqrt(Pxx_spec.max())
      2.0077340678640727