Hello - This discussion reminded me of something I have been curious about - has anyone has seen the techniques described in this paper being used in real world with audio ?
http://arxiv.org/pdf/0902.0026.pdf @MISC{Tropp09beyondnyquist:, author = {Joel A. Tropp and Jason N. Laska and Marco F. Duarte and Justin K. Romberg and Richard G. Baraniuk}, title = { Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals}, year = {2009} } Apparently related approaches are being used with single pixel cameras. > Message: 3 > Date: Thu, 27 Mar 2014 00:33:08 -0400 > From: Doug Houghton <doug_hough...@sympatico.ca> > To: "A discussion list for music-related DSP" > <music-dsp@music.columbia.edu> > Subject: Re: [music-dsp] Nyquist??"Shannon sampling theorem > Message-ID: <blu0-smtp55a662ba3f5bf784f51648ff...@phx.gbl> > Content-Type: text/plain; charset="iso-8859-1"; Format="flowed" > > consider this from a wiki page > > "A bandlimited signal can be fully reconstructed from its samples, provided > that the sampling rate exceeds twice the maximum frequency in the > bandlimited signal. This minimum sampling frequency is called the Nyquist > rate. This result, usually attributed to Nyquist and Shannon, is known as > the Nyquist-Shannon sampling theorem. > > An example of a simple deterministic bandlimited signal is a sinusoid of the > form . If this signal is sampled at a rate so that we have the samples , > for all integers , we can recover completely from these samples. Similarly, > sums of sinusoids with different frequencies and phases are also bandlimited > to the highest of their frequencies." > > > > The example may imply that the "bandlimited signal" to satisfy the theory is > at it's most a complex sum of various sinusoids at different frequencies > phases, amplitudes. > > > > > -------------- next part -------------- > A non-text attachment was scrubbed... > Name: not available > Type: image/png > Size: 899 bytes > Desc: not available > URL: > <http://music.columbia.edu/pipermail/music-dsp/attachments/20140327/33c9b6ca/attachment.png> > -------------- next part -------------- > A non-text attachment was scrubbed... > Name: not available > Type: image/png > Size: 572 bytes > Desc: not available > URL: > <http://music.columbia.edu/pipermail/music-dsp/attachments/20140327/33c9b6ca/attachment-0001.png> > -------------- next part -------------- > A non-text attachment was scrubbed... > Name: not available > Type: image/png > Size: 445 bytes > Desc: not available > URL: > <http://music.columbia.edu/pipermail/music-dsp/attachments/20140327/33c9b6ca/attachment-0002.png> > -------------- next part -------------- > A non-text attachment was scrubbed... > Name: not available > Type: image/png > Size: 198 bytes > Desc: not available > URL: > <http://music.columbia.edu/pipermail/music-dsp/attachments/20140327/33c9b6ca/attachment-0003.png> > -------------- next part -------------- > A non-text attachment was scrubbed... > Name: not available > Type: image/png > Size: 354 bytes > Desc: not available > URL: > <http://music.columbia.edu/pipermail/music-dsp/attachments/20140327/33c9b6ca/attachment-0004.png> > > ------------------------------ > > -- > dupswapdrop -- the music-dsp mailing list and website: subscription info, > FAQ, source code archive, list archive, book reviews, dsp links > http://music.columbia.edu/cmc/music-dsp > http://music.columbia.edu/mailman/listinfo/music-dsp > > End of music-dsp Digest, Vol 123, Issue 44 > ****************************************** -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
