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scipy.signal.

# periodogram

scipy.signal.periodogram(x, fs=1.0, window='boxcar', 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. If window is a string or tuple, it is passed to `get_window` to generate the window values, which are DFT-even by default. See `get_window` for a list of windows and required parameters. If window is array_like it will be used directly as the window and its length must be equal to the length of the axis over which the periodogram is computed. Defaults 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 each segment. If `detrend` is a string, it is passed as the type argument to the `detrend` function. If it is a function, it takes a segment and returns a detrended segment. 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. Defaults to True, but 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 V²/Hz and computing the squared magnitude spectrum (‘spectrum’) where Pxx has units of V², 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

  The ratio of the squared magnitude (`scaling='spectrum'`) divided by the spectral power density (`scaling='density'`) is the constant factor of `sum(abs(window)**2)*fs / abs(sum(window))**2`. If return_onesided is `True`, the values of the negative frequencies are added to values of the corresponding positive ones.

  Consult the Spectral Analysis section of the SciPy User Guide for a discussion of the scalings of the power spectral density and the magnitude (squared) spectrum.

  Added in version 0.12.0.

  Examples

      >>> import numpy as np
      >>> from scipy import signal
      >>> import matplotlib.pyplot as plt
      >>> rng = np.random.default_rng()

  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 += rng.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()

  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[25000:])
      0.000985320699252543

  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