Hello, can someone clear up some confusion for me? This article on the Chirp Z transform (using FFT) appears to show the algorithm creating better precision by zooming in on a narrow band of frequencies. For example, the two peaks being separated in the diagrams. Link to article: http://www.embedded.com/columns/technicalinsights/17301593?_requestid=286320 I read other posts on here and elsewhere stating that the chirp-Z does not create extra precision, but simply acts the same as zero-padding (only cheaper for big pads) - or perhaps the 'zoom-FFT'. Can someone verify that this actually gives better precision, rather than simply interpolate the standard FFT? Thanks. Also, I see some Java code here: http://www.dsprelated.com/showmessage/13193/1.php (C version: http://www.mat.ucsb.edu/projects/allosphere/browser/AlloBrain/AlloBrainSource/lp.quadmap/dsp/src/ChirpZ.h?rev=194 ) This has a two dimensional array as input and doesn't appear to relate to the article, is the input also real/imaginary? Cheers, Dave.
Chirp Z tranform precision.
Started by ●September 15, 2009
Reply by ●September 15, 20092009-09-15
On Sep 15, 2:22 pm, "contact" <cont...@invalid.com> wrote:> Hello, can someone clear up some confusion for me? > > This article on the Chirp Z transform (using FFT) appears to show the > algorithm creating better precision by zooming in on a narrow band of > frequencies. For example, the two peaks being separated in the diagrams. > Link to article:http://www.embedded.com/columns/technicalinsights/17301593?_requestid... > > I read other posts on here and elsewhere stating that the chirp-Z does not > create extra precision, but simply acts the same as zero-padding (only > cheaper for big pads) - or perhaps the 'zoom-FFT'. > > Can someone verify that this actually gives better precision, rather than > simply interpolate the standard FFT? > Thanks. > ...Participants in comp.dsp have already remarked on this issue. See the reader comments at the end of the linked article. Dale B. Dalrymple
Reply by ●September 16, 20092009-09-16
"Dale Dalrymple" <dbd@ieee.org> wrote in message news:5798666f-f323-444e-b644-b76c02659b0d@x5g2000prf.googlegroups.com...> On Sep 15, 2:22 pm, "contact" <cont...@invalid.com> wrote: >> Hello, can someone clear up some confusion for me? >> >> This article on the Chirp Z transform (using FFT) appears to show the >> algorithm creating better precision by zooming in on a narrow band of >> frequencies. For example, the two peaks being separated in the diagrams. >> Link to >> article:http://www.embedded.com/columns/technicalinsights/17301593?_requestid... >> >> I read other posts on here and elsewhere stating that the chirp-Z does >> not >> create extra precision, but simply acts the same as zero-padding (only >> cheaper for big pads) - or perhaps the 'zoom-FFT'. >> >> Can someone verify that this actually gives better precision, rather than >> simply interpolate the standard FFT? >> Thanks. >> ... > > Participants in comp.dsp have already remarked on this issue. See the > reader comments at the end of the linked article. > > Dale B. DalrympleI didn't see those, thanks Dale. I guess the Uncertainty Principle can't be cheated. The article is highly rated as well - typical. Can anyone answer my second question: I want to fully understand the process and the code linked below (which appears in a previous 'comp.dsp' chirp-Z thread) has a multi-dimensional input, is that previously FFT'ed sample data? Java Chirp-Z thread: http://www.dsprelated.com/showmessage/13193/1.php Thanks, Dave
Reply by ●September 16, 20092009-09-16
contact wrote:> I want to fully understand the process and the code linked below > (which appears in a previous 'comp.dsp' chirp-Z thread) has a > multi-dimensional input, is that previously FFT'ed sample data? > Java Chirp-Z thread: > http://www.dsprelated.com/showmessage/13193/1.phpNo, the input of czt() is complex-valued but in the time domain (transform duality aside). To treat real input, provide an array of pairs a[n] = [x[n],0]. Martin -- Quidquid latine scriptum est, altum videtur.