<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Hi Thomas,<DIV><DIV><BLOCKQUOTE type="cite"><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="country-region"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="place"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="Street"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="address"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PersonName"><DIV class="Section1"><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Following up on this conversation. It seems that the ‘induced activity’ contains both phase-locked and non-phase-locked activity, whereby the ‘evoked’ activity contains only phase-locked activity. Is it then kosher to separate these components by linear subtraction? For example, if we first compute the ‘induced’ activity by averaging power over individual trials, and from that subtract the ‘evoked activity’ (calculated based on average response) to get the induced activity without any phase-locked activity?</SPAN></SPAN></FONT></P></DIV></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></SPAN></BLOCKQUOTE><DIV><BR class="khtml-block-placeholder"></DIV>It is not correct to subtract because computing the induced and evoked power spectra involves squaring signal amplitudes (a non-linear operation), and hence, taking your terminology to refer to the instantaneous amplitudes of the signal components (this applies to any time-frequency tile)</DIV><DIV><BLOCKQUOTE type="cite"><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="country-region"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="place"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="Street"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="address"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PersonName"><DIV class="Section1"><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "><SPAN style=""><SPAN style="">Induced = Phase + Non-Phase</SPAN></SPAN></SPAN></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">And</SPAN><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Evoked = Phase</SPAN><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Then</SPAN><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Non-Phase = Induced – Evoked</SPAN><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "><BR></SPAN></O:P></SPAN></FONT></P></DIV></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></SPAN></BLOCKQUOTE><DIV>what you actually get from spectral or time-frequency analysis is the power of your MEASURED signal</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Induced^2 = (Phase + Non-Phase)^2 = Phase^2 + 2*Phase*Non-Phase + Non-Phase^2</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Evoked^2 = Phase^2</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Then</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Induced^2 - Evoked^2 = 2*Phase*Non-Phase + Non-Phase^2 AND NOT Non-Phase^2<BR><BLOCKQUOTE type="cite"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="country-region"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="place"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="Street"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="address"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PersonName"><DIV class="Section1"><P class="MsoNormal"><SPAN style=""><O:P style=""></O:P></SPAN></P></DIV></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></BLOCKQUOTE></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>This bit of high-school algebra shows quite clearly that even if you had a perfect estimate of Evoked and Induced power (which you of course in practice do not have due to a finite number of trials, amplitude non-stationarities, artifacts and noise) it is not possible to obtain an estimate of Non-Phase^2 using time-frequency analysis, averaging and subtraction.</DIV></DIV></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Cheers,</DIV><DIV>Christian</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR><DIV> <SPAN class="Apple-style-span" style="border-collapse: separate; 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font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; 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Donders Centre for Cognitive Neuroimaging </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">P.O. 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