Find the RMS from a PSD

Hello matplotlib users.

I’m new to signal processing and I’ve read that RMS could be found from a PSD. I’m interested in as I would further like to know energy in a signal through it’s frequencies.

My problem is I don’t find how to calculate the RMS from the PSD output. It seems it’s a matter of scale (frequencies bandwith is taken in account already).

I wrote a test case with a simple sinus. I should be able to find the same RMS value from the PSD method and direct RMS over signal method.

Could you please have a look and tell me how to find good RMS value from PSD output?



-- coding: utf-8 --

import matplotlib, platform

if platform.system() == ‘Linux’ :


import pylab

import scipy



samplerate = 48000

nfft = 1024*2

graph = False

#create 1 sec sinus signal

t = scipy.arange(0, 1 , 1/float(samplerate))

signal = .25scipy.sin(2scipy.pi*(samplerate/10.)*t)

print len(signal)

#RMS of an array

def RMS(data):

rms = data**2

rms = scipy.sqrt(rms.sum()/len(data))

return rms

#PSD of an array. I want this to return the RMS

def RMSfromPSD(data) :

y, x = pylab.psd(data, NFFT = nfft, Fs = samplerate)

##Calculate the RMS

#The energy returned by PSD depends on FFT size

freqbandwith = x[1]

y = y*freqbandwith

#The energy returned by PSD depends on Samplerate

y = y/float(samplerate)

#Summing the power in freq domain to get RMS

rms = scipy.sqrt(y.sum())

return rms

print “RMS method”, RMS(signal)

print “RMS using PSD method”, RMSfromPSD(signal)


if graph == True :




pylab.psd(signal, nfft, samplerate)