<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Hi Sameer,<DIV><BR class="khtml-block-placeholder"></DIV><DIV>If you are resampling your data for the purposes of speeding up the ICA algorithm, then you just take the (de-)mixing matrix and apply to your original data. Although I would recommend the following normalization of the mixing matrix (in the following A is the mixing matrix and W = inv(A) is the de-mixing matrix):</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>[nchan, nsrcs] = size(A);</DIV><DIV>for i=1:nsrcs</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>A(:,i) = A(:,i)./norm(A(:,i),2);</DIV><DIV>end</DIV><DIV>W = inv(A);</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>this way you ensure that your mixing (and de-mixing) matrix do not contain information about the power of the components but merely about spatial projections (and the spatial correlations of these), so that when you apply W to your data (at the original sampling rate), you can treat the variance (power) of the components s = Wx as "correct".</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Some further comments to bear in mind: since in estimating the ICA on the downsampled data you in effect assume that the high-frequency content (above the Nyquist limit of your resampling frequency) is not relevant. Hence you might as well continue working with the downsampled data. However, if there IS stuff going on in the high-frequency bands that is important (e.g., part of a string artifact signal which has a broad band spectrum), then the ICA model estimated on the downsampled data will effectively be "wrong" and will not be able to successfully separate your data into independent components. This may be an unlikely scenario for very high frequencies, but the considerations should guide you in choosing a resampling rate that is not "too low".</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Regards,</DIV><DIV>Christian</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR><DIV><DIV>On 22 Feb 2007, at 18:29, Sameer Walawalkar wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hello,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">How exactly does resampling work? If I resample data to 300 Hz from 1KHz, will the resulting data structure have encoded information for going back to 1KHz?</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">This is so that I could resample down, do ICA, remove components, and then get back to 1KHz. (Clearly, I dont understnad the resampling algorithm).</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">thanks,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">sameer</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV> </BLOCKQUOTE></DIV><BR><DIV> <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; -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; -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; "><DIV>----------------------------------------------------------------------</DIV><DIV>Christian Hesse, PhD, MIEEE</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">F.C. Donders Centre for Cognitive Neuroimaging </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">P.O. Box 9101 </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">NL-6500 HB Nijmegen </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The Netherlands</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Tel.: +31 (0)24 36 68293</DIV><DIV>Fax: +31 (0)24 36 10989</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Email: <A href="mailto:c.hesse@fcdonders.ru.nl">c.hesse@fcdonders.ru.nl</A></DIV><DIV>Web: <A href="http://www.fcdonders.ru.nl">www.fcdonders.ru.nl</A></DIV><DIV>----------------------------------------------------------------------</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><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><BR class="Apple-interchange-newline"></SPAN></SPAN></SPAN></SPAN></SPAN> </DIV><BR></DIV></BODY></HTML>