Plotting power spectrum in python

Question

I have an array with 301 values  which were gathered from a movie clip with 301 frames  This means 1 value from 1 frame  The movie clip is running at 30 fps  so is in fact 10 sec long  Now I would like to get the power spectrum of this  signal    with the right Axis   I tried    X   fft S    2     pl plot abs X    pl show     I also tried    X   fft S    2     pl plot abs X   2   pl show     Though I don t think this is the real spectrum   the signal    The spectrum    The power spectrum      Can anyone provide some help with this   I would like to have a plot in Hz

User · Answer

Since FFT is symmetric over it s centre  half the values are just enough   import numpy as np import matplotlib pyplot as plt  fs   30 0 t   np arange 0 10 1 fs  x   np cos 2 np pi 10 t   xF   np fft fft x  N   len xF  xF   xF 0 N 2  fr   np linspace 0 fs 2 N 2   plt ion   plt plot fr abs xF   2

User · Answer

Numpy has a convenience function  np fft fftfreq to compute the frequencies associated with FFT components   from   future   import division import numpy as np import matplotlib pyplot as plt  data   np random rand 301  - 0 5 ps   np abs np fft fft data    2  time step   1   30 freqs   np fft fftfreq data size  time step  idx   np argsort freqs   plt plot freqs idx   ps idx       Note that the largest frequency you see in your case is not 30 Hz  but  In  7   max freqs  Out 7   14 950166112956811   You never see the sampling frequency in a power spectrum  If you had had an even number of samples  then you would have reached the Nyquist frequency  15 Hz in your case  although numpy would have calculated it as -15

User · Answer

From the numpy fft page http   docs scipy org doc numpy reference routines fft html      When the input a is a time-domain signal and A   fft a   np abs A  is   its amplitude spectrum and np abs A   2 is its power spectrum  The   phase spectrum is obtained by np angle A

User · Answer

You can also use scipy signal welch to estimate the power spectral density using Welch   s method  Here is an comparison between np fft fft and scipy signal welch   from scipy import signal import numpy as np import matplotlib pyplot as plt  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     np fft fft freqs   np fft fftfreq time size  1 fs  idx   np argsort freqs  ps   np abs np fft fft x    2 plt figure   plt plot freqs idx   ps idx   plt title  Power spectrum  np fft fft       signal welch f  Pxx spec   signal welch x  fs   flattop   1024  scaling  spectrum   plt figure   plt semilogy f  np sqrt Pxx spec   plt xlabel  frequency  Hz    plt ylabel  Linear spectrum  V RMS    plt title  Power spectrum  scipy signal welch    plt show

User · Answer

if rate is the sampling rate Hz   then np linspace 0  rate 2  n  is the frequency array of every point in fft  You can use rfft to calculate the fft in your data is real values   import numpy as np import pylab as pl rate   30 0 t   np arange 0  10  1 rate  x   np sin 2 np pi 4 t    np sin 2 np pi 7 t    np random randn len t   0 2 p   20 np log10 np abs np fft rfft x    f   np linspace 0  rate 2  len p   plot f  p      signal x contains 4Hz  amp  7Hz sin wave  so there are two peaks at 4Hz  amp  7Hz

[python] Plotting power spectrum in python

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