[SciPy-User] Find the RMS from a PSD

[E]

Hello scipy 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?

Thanks

#!/usr/bin/python
# -*- coding: utf-8 -*-

import matplotlib, platform
if platform.system() == 'Linux' :
	matplotlib.use("gtk")
import pylab
import scipy



## PSD vs RMS

#Parameters
samplerate = 48000
nfft = 1024*2
graph = False

#create 1 sec sinus signal
t = scipy.arange(0, 1 , 1/float(samplerate))
signal = .25*scipy.sin(2*scipy.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)



#Graph
if graph == True :
	pylab.subplot(211)
	pylab.plot(t,signal)
	pylab.subplot(212)
	pylab.psd(signal, nfft, samplerate)
	pylab.show()
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