what you're discussing here appears to me to be about perfect reconstruction in the context of Wavelets and Filter Banks. there is a theorem that's pretty easy to prove that if you have complementary high and low filterbanks with a common cutoff at 1/2 Nyquist, you can downsample both high and low-pass filterbank outputs by a factor of 1/2 and later combine the two down-sampled streams of samples to get perfect reconstruction of the original.� this result is not guaranteed if you **do** anything to either filter output in the filterbank. ---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? From: "gm" <g...@voxangelica.net> Date: Fri, November 9, 2018 4:19 pm To: music-dsp@music.columbia.edu -------------------------------------------------------------------------- > > hm, my application has also WOLA ... > > All I find is about up- and downsampling of time sequences and spectra > of the same length. > ... > > If anyone knows of an easy explanation of down- and up sampling spectra > it would be much appreciated. > > Am 09.11.2018 um 19:16 schrieb Ethan Duni: > .. >> The only applications I know of that tolerate time-domain aliasing in >> transforms are WOLA filter banks - which are explicitly designed to >> cancel these (severe!) artifacts in the surrounding time-domain >> processing. -- r b-j� � � � � � � � � � � � �r...@audioimagination.com "Imagination is more important than knowledge." � � � �
_______________________________________________ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
