If you lower the resolution (ie increase nFFT) in your program you will
see that the PSD does indeed increase. I think it may be on the way to
infinity.
Joseph Park <[EMAIL PROTECTED]>
Sent by: [EMAIL PROTECTED]
26/10/2007 10:05 AM
To
matplotlib-users@lists.sourceforge.net
cc
Subject
Re: [Matplotlib-users] PSD amplitudes
Shouldn't the PSD for a simple sine wave tend to infinity
the spectral resolution will impact the amplitude, if you
are not dealing with a density. by definition a spectral density
has applied the bandwidth resolution correction. the PSD amplitude
should correspond to the RMS amplitude of the sine wave. in the
example a 1VRMS amplitude sine wave (time domain) should have a
PSD power of 20*log(1V) = 0dB. The windowing function will impact
this ideal number a bit, but certainly not by 25dB.
[EMAIL PROTECTED] wrote:
Are you sure that the answer should be zero? Shouldn't the PSD for a
simple sine wave tend to infinity (depending on the resolution)?
Joseph Park <[EMAIL PROTECTED]>
Sent by: [EMAIL PROTECTED]
26/10/2007 06:50 AM
To
matplotlib-users@lists.sourceforge.net
cc
Subject
[Matplotlib-users] PSD amplitudes
Please try the attached script.
The answer should be ~0 dB for each of the frequencies.
Most likely a simple scaling issue/parameter of which i'm ignorant.
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##----------------------------------------------------------------------------
## Name: psd_scale.py
##
## Purpose: Test Power Spectral Density of 1Vrms data
## Depends on Python SciPy and NumPy
##
## Author: J Park
##
## Created: 10/17/07
##
## Modified:
##----------------------------------------------------------------------------
try:
from numpy import * # www.numpy.org numpy.scipy.org
except ImportError:
print "Failed to import numpy."
try:
import pylab as mp # matplotlib.sourceforge.net
from matplotlib.font_manager import fontManager, FontProperties
except ImportError:
print "Failed to import pylab."
# Default Parameters
nFFT = 1024
overlap = 512
freqSample = 100.
PlotAll = False
WriteOutput = False
##----------------------------------------------------------------------------
## Main module
def main():
deltaF = freqSample/nFFT # Frequency resolution in Hz
deltaT = 1./freqSample # Sample interval
print 'Sample interval %e (s)' % (deltaT)
print 'Frequency resolution %e (Hz)' % (deltaF)
# Setup Plots
#
----------------------------------------------------------------------
mp.figure(1)
mp.title ( "PSD" )
mp.ylabel( "(dB)" )
mp.xlabel( "Frequency (Hz)" )
legendFont = FontProperties(size='small')
ymin = 0
ymax = 30
xmin = 0
xmax = 50
xticks = 5
yticks = 5
if PlotAll:
mp.figure(2)
mp.title ( "Input Timeseries" )
mp.ylabel( "Amplitude" )
mp.xlabel( "time (s)" )
# Create some synthetic data with unity RMS amplitude = 0 dB
#
----------------------------------------------------------------------
t = mp.arange(0., 60., deltaT) # 60 seconds at deltaT interval
A = 1.414
y0 = A * sin( 2. * math.pi * 5 * t )
y1 = A * sin( 2. * math.pi * 10 * t )
y2 = A * sin( 2. * math.pi * 20 * t )
y3 = A * sin( 2. * math.pi * 30 * t )
y4 = A * sin( 2. * math.pi * 40 * t )
y5 = A * sin( 2. * math.pi * 45 * t )
dataList = [ y0, y1, y2, y3, y4, y5 ]
for data in dataList:
inputDataLen = len( data )
numAverages = math.floor( inputDataLen / (overlap) ) - 1
normalizedRandomError = 1./math.sqrt( numAverages )
print "%d points" % ( inputDataLen ),
print "%d averages" % (numAverages),
print "normalized random error %.3f" % ( normalizedRandomError )
mp.figure(1)
(Pxx, freqs) = mp.psd( data,
NFFT = nFFT,
Fs = freqSample,
noverlap = overlap,
lw = 2,
label = '' )
Pxx_dB = 10.*log10(Pxx)
if PlotAll:
mp.figure(2)
mp.plot(t, data, label='' )
# Write Output data
#
----------------------------------------------------------------------
if WriteOutput:
PxxLen = len(Pxx)
OutputFile = "PSD.dat"
fdOutFile = open( OutputFile, 'a' )
fdOutFile.write( "Freq\t\tPower(dB)\n" )
for i in range(PxxLen):
fdOutFile.write( "%.4e\t%.3f\n" % ( freqs[i], Pxx_dB[i] ) )
fdOutFile.close()
print "Wrote ", PxxLen, " points to ", OutputFile
# Show the Plot
#
----------------------------------------------------------------------
mp.figure(1)
mp.axis([xmin, xmax, ymin, ymax])
mp.xticks( arange(xmin, xmax+1, xticks) )
mp.yticks( arange(ymin, ymax , yticks) )
mp.title('')
mp.xlabel('Frequency (Hz)')
mp.ylabel(r'$\tt{dB re V^2/Hz}$')
#mp.legend( loc='upper right', prop=legendFont )
if WriteOutput:
plotFileName = "PSD.png"
mp.savefig( plotFileName )
print "Wrote png image to ", plotFileName
if PlotAll:
mp.figure(2)
#mp.legend( loc='lower left', prop=legendFont )
mp.show()
print "Normal Exit"
## Main module
##----------------------------------------------------------------------------
##----------------------------------------------------------------------------
## Provide for cmd line invocation
if __name__ == "__main__":
main()
-------------------------------------------------------------------------
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email is confidential and may be legally privileged. It is intended solely for
the addressee. Access to this email by anyone else is unauthorised. If you are
not the intended recipient, you may not disclose, copy or distribute this
email, nor take or omit to take any action in reliance on it. United Group
accepts no liability for any damage caused by this email or any attachments due
to viruses, interference, interception, corruption or unauthorised access.
If you have received this email in error, please notify United Group
immediately by email to the sender's email address and delete this document.-------------------------------------------------------------------------
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