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<p class="MsoNormal">Hi all,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I have a question about how FieldTrip normalizes the output of a spectral analyses using ft_freqanalysis.<o:p></o:p></p>
<p class="MsoNormal">This is important for me, because I need the absolute value of the spectrum for a publication.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I was scanning through the code trying to find the normalization steps.<o:p></o:p></p>
<p class="MsoNormal">In particular, I don’t understand the following steps:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l1 level1 lfo2"><![if !supportLists]><span style="mso-list:Ignore">1.)<span style="font:7.0pt "Times New Roman"">
</span></span><![endif]>The tapers (e.g. hanning) are normalized prior to the multiplication with the data by the following code:<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:18.0pt;text-indent:18.0pt"><i>tap = tap./norm(tap, 'fro');
</i> (line 195 in the function fr_specest_mtmfft)<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:18.0pt;text-indent:18.0pt">What is the rationale of dividing through this special norm of the taper itself?<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:18.0pt;text-indent:18.0pt"><o:p> </o:p></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l1 level1 lfo2"><![if !supportLists]><span style="mso-list:Ignore">2.)<span style="font:7.0pt "Times New Roman"">
</span></span><![endif]>After calculating the fft, the specrum is scaled (i.e. in the function fr_specest_mtmfft) by:<o:p></o:p></p>
<p class="MsoListParagraph"><i><span lang="DE">dum = dum .* sqrt(2 ./ endnsample); (line 251)<o:p></o:p></span></i></p>
<p class="MsoListParagraph">Later on, to get to the power spectrum, the abs of the spectrum is taken and squared<o:p></o:p></p>
<p class="MsoListParagraph"><i>powdum = abs(spectrum(acttap,:,foiind(ifoi),acttboi)) .^2;</i> (line 629 in ft_frequanalysis)<o:p></o:p></p>
<p class="MsoListParagraph"><o:p> </o:p></p>
<p class="MsoListParagraph">This puzzles me, because scanning through the literature, the power spectrum should be given by<o:p></o:p></p>
<p class="MsoListParagraph"><span lang="DE">(2*abs(X)^2) ./ </span>(nfft^2) -> unit: V^2 (X=signal, nfft = number of data points)<o:p></o:p></p>
<p class="MsoListParagraph">and the PSD by<o:p></o:p></p>
<p class="MsoListParagraph">(2*abs(X)^2) ./ (nfft*Fs) -> unit: V^2/Hz (X=signal, nfft = number of data points, Fs=sampling rate)<o:p></o:p></p>
<p class="MsoListParagraph"><o:p> </o:p></p>
<p class="MsoListParagraph">Alternatively, one can get the amplitude spectrum from the power spectrum by taking the square root of the PSD:<o:p></o:p></p>
<p class="MsoListParagraph">sqrt(PSD) -> unit: V/sqrt(Hz)<o:p></o:p></p>
<p class="MsoListParagraph">which is still different from<o:p></o:p></p>
<p class="MsoListParagraph">(2*abs(X)) ./ (nfft*Fres) -> unit: V/Hz ? (Fres = frequency resolution = Fs/nfft)<o:p></o:p></p>
<p class="MsoListParagraph"><o:p> </o:p></p>
<p class="MsoListParagraph">The result of these equations are different from what comes out of the FieldTrip code.<o:p></o:p></p>
<p class="MsoListParagraph">So what is the unit of the spectrum in FieldTrip? <o:p>
</o:p></p>
<p class="MsoListParagraph">What is the rationale of scaling the complex spectrum by sqrt(2/nfft) ?
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Furthermore, is the unit for the different spectral estimation methods the same? That is, using mtmfft, mtmconvol, wavelet,…?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">It would help me a lot if someone could clarify these points.
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thanks in advance,<o:p></o:p></p>
<p class="MsoNormal">Thomas<o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:9.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt">-----<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt">Dr. Thomas Wunderle<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt"><a href="http://www.ncbi.nlm.nih.gov/feed/rss.cgi?ChanKey=PubMedNews"><span style="color:windowtext;text-decoration:none">Ernst Strüngmann Institute
</span><span lang="DE" style="color:windowtext;text-decoration:none">(ESI) for Neuroscience</span></a></span><span lang="DE" style="font-family:"Arial","sans-serif""><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt"><a href="http://www.ncbi.nlm.nih.gov/feed/rss.cgi?ChanKey=PubMedNews"><span style="color:windowtext;text-decoration:none">in Cooperation with Max Planck Society
</span></a></span><span style="font-size:9.0pt"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:9.0pt">Deutschordenstrasse 46</span><span lang="DE"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:9.0pt">60528 Frankfurt am Main, Germany</span><span lang="DE"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:9.0pt"><a href="http://www.esi-frankfurt.de/"><span style="color:blue">www.esi-frankfurt.de</span></a></span><span lang="DE"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:9.0pt"><a href="mailto:thomas.wunderle@esi-frankfurt.de"><span style="color:blue">thomas.wunderle@esi-frankfurt.de</span></a></span><span lang="DE"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:9.0pt">Tel: +49 69 96769 516<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:9.0pt">Fax: +49 69 96769 555<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:9.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:10.0pt;color:gray">Sitz der Gesellschaft: Frankfurt am Main<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:10.0pt;color:gray">Registergericht: Amtsgericht Frankfurt - HRB 84266<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:10.0pt;color:gray">Geschäftsführer: Prof. Dr. Pascal Fries<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="DE"><o:p> </o:p></span></p>
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