I didn't say infinite power, but infinite power density at the sine wave frequemcy.
Being per Hz doesn't mean that one computes the PSD using a 1 Hz band! It means that one divides the power in the band by the width of the band, which can be anything one chooses. The formula for S(f) of a sine wave is a delta function! Joseph Park <[EMAIL PROTECTED]> Sent by: [EMAIL PROTECTED] 26/10/2007 11:50 AM To cc matplotlib-users@lists.sourceforge.net Subject Re: [Matplotlib-users] PSD amplitudes spectral density is by convention a 1Hz binwidth, not an arbitrary one, units of A^2/Hz. perhaps if you manually compute the spectral density of a sine wave, you will easily see that they don't have infinite power, R is the autocorrelation of the Asin(wt): Back to the original question: Is there evidence that the matplotlib PSD spectral amplitudes are accurate? say by comparison with Matlab results, or a synthetic signal as in the example, or from considerations of basic DSP as in the references? [EMAIL PROTECTED] wrote: There is certainly differences (usually of a factor of PI) in the various definitions used for PSDs, but a simple sign wave has an infinite power density at the sine wave frequency. Are we agreed on that? Use of windowing will modify this comment somewhat (so it probably won't really go to infinity) but the basic fact remains. The units of a PSD are amp^2/Hz. The MS of a signal between two frequencies should equal the area under the PSD between those frequencies (with allowance for different definitions/factors of PI). As I said, for a sign wave the frequency band can be made arbitrarily small about the sine wave frequency, but the power between these bands remains constant. Therefore the PSD goes to infinity. Otherwise it isn't a density. Joseph Park <[EMAIL PROTECTED]> Sent by: [EMAIL PROTECTED] 26/10/2007 10:49 AM To cc matplotlib-users@lists.sourceforge.net Subject Re: [Matplotlib-users] PSD amplitudes 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. 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. -- ______________________________________________________________________ This email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________ ##---------------------------------------------------------------------------- ## 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() ------------------------------------------------------------------------- This SF.net email is sponsored by: Splunk Inc. Still grepping through log files to find problems? Stop. Now Search log events and configuration files using AJAX and a browser. Download your FREE copy of Splunk now >> http://get.splunk.com/_______________________________________________ Matplotlib-users mailing list Matplotlib-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-users UNITED GROUP This email message is the property of United Group. The information in this 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. -- ______________________________________________________________________ This email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________ ------------------------------------------------------------------------- This SF.net email is sponsored by: Splunk Inc. Still grepping through log files to find problems? Stop. Now Search log events and configuration files using AJAX and a browser. Download your FREE copy of Splunk now >> http://get.splunk.com/_______________________________________________ Matplotlib-users mailing list Matplotlib-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-users UNITED GROUP This email message is the property of United Group. The information in this 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. -- ______________________________________________________________________ This email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________ ------------------------------------------------------------------------- This SF.net email is sponsored by: Splunk Inc. Still grepping through log files to find problems? Stop. Now Search log events and configuration files using AJAX and a browser. Download your FREE copy of Splunk now >> http://get.splunk.com/_______________________________________________ Matplotlib-users mailing list Matplotlib-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-users UNITED GROUP This email message is the property of United Group. The information in this 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. -- ______________________________________________________________________ This email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________ ------------------------------------------------------------------------- This SF.net email is sponsored by: Splunk Inc. Still grepping through log files to find problems? Stop. Now Search log events and configuration files using AJAX and a browser. Download your FREE copy of Splunk now >> http://get.splunk.com/ _______________________________________________ Matplotlib-users mailing list Matplotlib-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-users UNITED GROUP This email message is the property of United Group. The information in this 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.
<<image/jpeg>>
------------------------------------------------------------------------- This SF.net email is sponsored by: Splunk Inc. Still grepping through log files to find problems? Stop. Now Search log events and configuration files using AJAX and a browser. Download your FREE copy of Splunk now >> http://get.splunk.com/
_______________________________________________ Matplotlib-users mailing list Matplotlib-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-users
