Hi everyone, I'm trying to figure out the "window presum FFT" technique (seems to also go by the name "polyphase FFT", "time domain aliasing/folding" as well as "weighted overlap and add" even though the latter is often simply used as a synonym for the basic "windowed overlap and add" method). I've found it mentioned and/or explained in quite a few posts/papers/books...
http://www.dsprelated.com/showmessage/123311/1.php http://www.dsprelated.com/showmessage/45449/1.php http://eetimes.com/design/embedded/4007611/DSP-Tricks-Building-a-practical-spectrum-analyzer http://contentdm.lib.byu.edu/cdm/singleitem/collection/ETD/id/16 http://groups.yahoo.com/group/softrock40/message/1299 http://www.rfel.com/download/D02003-Polyphase%20DFT%20data%20sheet.pdf http://dev.vinux-project.org/time-aliased-hann http://www.rfel.com/download/w03006-comparison_of_fft_and_polydft_transient_response.pdf http://www.eurasip.org/Proceedings/Eusipco/Eusipco2005/defevent/papers/cr1183.pdf ...but unfortunately all of these however seem to "stop" at the analysis stage (i.e. "we've gotten a more precise spectrum and that's all we need"). I've wraped my head around the idea itself and the analysis procedure, I (think) I know how and why it works but I don't understand how is one supposed to go about the synthesis stage. IOW how does one get back to the (non aliased) time domain data. For example, in the simplest case where the window is twice the size of the FFT: - we take in 2N time domain samples - window them (with a 2N sized window) - fold them to N time domain samples (i.e. simply add the first and second half of the input data) - take an N point FFT - do some processing with the "more precise spectrum" - take an N point IFFT - and now what? :) we've got N time domain samples that correspond to the folded input samples...I can't imagine it would sound good if this is simply window-overlap-added and sent to output as is... ps. I've seen this article http://archive.chipcenter.com/dsp/DSP000315F1.html often being mentioned as "explaining it all" but unfortunately the site no longer exists... -- "What Huxley teaches is that in the age of advanced technology, spiritual devastation is more likely to come from an enemy with a smiling face than from one whose countenance exudes suspicion and hate." Neil Postman -- 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
