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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