matplotlib.pyplot.psd(x, NFFT=None, Fs=None, Fc=None, detrend=None, window=None, noverlap=None, pad_to=None, sides=None, scale_by_freq=None, return_line=None, *, data=None, **kwargs)[source]

Plot the power spectral density.

The power spectral density \(P_{xx}\) by Welch's average periodogram method. The vector x is divided into NFFT length segments. Each segment is detrended by function detrend and windowed by function window. noverlap gives the length of the overlap between segments. The \(|\mathrm{fft}(i)|^2\) of each segment \(i\) are averaged to compute \(P_{xx}\), with a scaling to correct for power loss due to windowing.

If len(x) < NFFT, it will be zero padded to NFFT.

x1-D array or sequence

Array or sequence containing the data

Fsfloat, default: 2

The sampling frequency (samples per time unit). It is used to calculate the Fourier frequencies, freqs, in cycles per time unit.

windowcallable or ndarray, default: window_hanning

A function or a vector of length NFFT. To create window vectors see window_hanning, window_none, numpy.blackman, numpy.hamming, numpy.bartlett, scipy.signal, scipy.signal.get_window, etc. If a function is passed as the argument, it must take a data segment as an argument and return the windowed version of the segment.

sides{'default', 'onesided', 'twosided'}, optional

Which sides of the spectrum to return. 'default' is one-sided for real data and two-sided for complex data. 'onesided' forces the return of a one-sided spectrum, while 'twosided' forces two-sided.

pad_toint, optional

The number of points to which the data segment is padded when performing the FFT. This can be different from NFFT, which specifies the number of data points used. While not increasing the actual resolution of the spectrum (the minimum distance between resolvable peaks), this can give more points in the plot, allowing for more detail. This corresponds to the n parameter in the call to fft(). The default is None, which sets pad_to equal to NFFT

NFFTint, default: 256

The number of data points used in each block for the FFT. A power 2 is most efficient. This should NOT be used to get zero padding, or the scaling of the result will be incorrect; use pad_to for this instead.

detrend{'none', 'mean', 'linear'} or callable, default 'none'

The function applied to each segment before fft-ing, designed to remove the mean or linear trend. Unlike in MATLAB, where the detrend parameter is a vector, in Matplotlib is it a function. The mlab module defines detrend_none, detrend_mean, and detrend_linear, but you can use a custom function as well. You can also use a string to choose one of the functions: 'none' calls detrend_none. 'mean' calls detrend_mean. 'linear' calls detrend_linear.

scale_by_freqbool, default: True

Whether the resulting density values should be scaled by the scaling frequency, which gives density in units of Hz^-1. This allows for integration over the returned frequency values. The default is True for MATLAB compatibility.

noverlapint, default: 0 (no overlap)

The number of points of overlap between segments.

Fcint, default: 0

The center frequency of x, which offsets the x extents of the plot to reflect the frequency range used when a signal is acquired and then filtered and downsampled to baseband.

return_linebool, default: False

Whether to include the line object plotted in the returned values.

Pxx1-D array

The values for the power spectrum \(P_{xx}\) before scaling (real valued).

freqs1-D array

The frequencies corresponding to the elements in Pxx.


The line created by this function. Only returned if return_line is True.

Other Parameters:

Keyword arguments control the Line2D properties:

Property Description
agg_filter a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array
alpha float or None
animated bool
antialiased or aa bool
clip_box Bbox
clip_on bool
clip_path Patch or (Path, Transform) or None
color or c color
contains unknown
dash_capstyle {'butt', 'round', 'projecting'}
dash_joinstyle {'miter', 'round', 'bevel'}
dashes sequence of floats (on/off ink in points) or (None, None)
data (2, N) array or two 1D arrays
drawstyle or ds {'default', 'steps', 'steps-pre', 'steps-mid', 'steps-post'}, default: 'default'
figure Figure
fillstyle {'full', 'left', 'right', 'bottom', 'top', 'none'}
gid str
in_layout bool
label object
linestyle or ls {'-', '--', '-.', ':', '', (offset, on-off-seq), ...}
linewidth or lw float
marker marker style string, Path or MarkerStyle
markeredgecolor or mec color
markeredgewidth or mew float
markerfacecolor or mfc color
markerfacecoloralt or mfcalt color
markersize or ms float
markevery None or int or (int, int) or slice or List[int] or float or (float, float) or List[bool]
path_effects AbstractPathEffect
picker unknown
pickradius float
rasterized bool or None
sketch_params (scale: float, length: float, randomness: float)
snap bool or None
solid_capstyle {'butt', 'round', 'projecting'}
solid_joinstyle {'miter', 'round', 'bevel'}
transform matplotlib.transforms.Transform
url str
visible bool
xdata 1D array
ydata 1D array
zorder float

See also

Differs in the default overlap; in not returning the mean of the segment periodograms; in returning the times of the segments; and in plotting a colormap instead of a line.
Plots the magnitude spectrum.
Plots the spectral density between two signals.


For plotting, the power is plotted as \(10\log_{10}(P_{xx})\) for decibels, though Pxx itself is returned.


Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986)


In addition to the above described arguments, this function can take a data keyword argument. If such a data argument is given, the following arguments can also be string s, which is interpreted as data[s] (unless this raises an exception): x.

Objects passed as data must support item access (data[s]) and membership test (s in data).

Examples using matplotlib.pyplot.psd