scipy.signal.periodogram#
- scipy.signal.periodogram(x, fs=1.0, window='boxcar', nfft=None, detrend='constant', return_onesided=True, scaling='density', axis=-1)[source]#
Estimate power spectral density using a periodogram.
- Parameters:
- xarray_like
Time series of measurement values
- fsfloat, optional
Sampling frequency of the x time series. Defaults to 1.0.
- windowstr 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. Seeget_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’.- nfftint, optional
Length of the FFT used. If None the length of x will be used.
- detrendstr or function or False, optional
Specifies how to detrend each segment. If
detrend
is a string, it is passed as the type argument to thedetrend
function. If it is a function, it takes a segment and returns a detrended segment. Ifdetrend
is False, no detrending is done. Defaults to ‘constant’.- return_onesidedbool, 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 V**2/Hz and computing the squared magnitude spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’
- axisint, optional
Axis along which the periodogram is computed; the default is over the last axis (i.e.
axis=-1
).
- Returns:
- fndarray
Array of sample frequencies.
- Pxxndarray
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
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.
New 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