is the suggestion that the matplotlib
algorithm is correct in computing PSD amplitudes?
btw, increasing nFFT increases the number of points used in the FFT,
which
increases the spectral frequency resolution (smaller binwidth)
but for a limited data set
of N points, as is the case in the example, decreases the number of
data averages
thereby decreasing the spectral amplitude resolution
(accuracy). keep in mind that
just changing nFFT without making a corresponding change in overlap
will oversample
the data, thereby skewing the amplitudes.
in any case, the amplitude change is not approaching infinity, even if
you set nFFT to
6000, which is the length of the timeseries, the amplitudes are ~35dB,
adjust variable ymax
to see this.
to review issues of spectral/amplitude resolution, windowing/overlap,
etc, a good
reference is Random Data by Bendat &Piersol:
http://www.amazon.com/Random-Data-Analysis-Measurement-Procedures/dp/0471317330
i remain unconvinced that the PSD amplitudes are reasonable, which only
leaves Matlab
as an alternative... that's a hard pill to swallow... matplotlib is
clearly preferable.
[EMAIL PROTECTED] wrote:
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.
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)?
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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