`scipy.signal._spectral_py:periodogram`

source: /scipy/signal/_spectral_py.py:365

Signature

def periodogram(x, fs = 1.0, window = boxcar, nfft = None, detrend = constant, return_onesided = True, scaling = density, axis = -1)

Summary

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.

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 tutorial_SpectralAnalysis section of the user_guide for a discussion of the scalings of the power spectral density and the magnitude (squared) spectrum.

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]')

✗

Text(0, 0.5, '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:])

✗

np.float64(0.001007816358315675)

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]')

✗

Text(0, 0.5, '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())

✗

np.float64(1.999065127333741)

Aliases

scipy.signal.periodogram