# Fw: PSD amplitudes

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 <jpark@…1765…>

Sent by: matplotlib-users-bounces@lists.sourceforge.net
26/10/2007 06:50 AM

To

Subject

[Matplotlib-users] PSD amplitudes

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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______________________________________________________________________`##----------------------------------------------------------------------------

## 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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