Thanks for that Vadim, your pdf is quite helpful. I guess the kicker with this approach is that we require knowledge of all of the signal's derivatives on each side of every discontinuity? I also appreciate your comment that min-phase BLEP disturbs the phase relationships and so gives quite different time-domain shapes (which makes a big difference if there are any non-linearities downstream, as I think people have discussed on the list before).
>As to the latency, practical window sizes have order of magnitude of a few samples which is a quite acceptable. That's lower than I would expect - you get good aliasing performance with that short of a filter? Even at, say, a fundamental frequency in the high single-digit kHz? Could you maybe say a bit about how the BLEP method compares to a more brute-force approach like doing "naive" hard sync in a (heavily) oversampled domain, and then downsampling? Is there mileage to be had by combining oversampling with BLEP? E On Thu, Jun 25, 2015 at 1:34 AM, Vadim Zavalishin < vadim.zavalis...@native-instruments.de> wrote: > On 24-Jun-15 21:30, Ethan Duni wrote: > >> Could you expand a bit on exactly what it means to apply the BLEP method >> to >> the discontinuities? I have a general grasp of the basic idea but I'm a >> bit >> fuzzy on exactly what this means in practice. If you're getting a >> truly band limited signal, then isn't the result infinite in time extent? >> In which case how do you use this for dynamic synthesis in practice? If >> the >> idea is to stitch together these BLEP'd segments to represent, say, a >> hard-synced sawtooth or something, then don't you end up needing huge >> latency? >> > > By integrating the Dirac delta we obtain a Heaviside step function (a > discontinuity of the 0th order). Integrating again we obtain a > discontinuity of the 1st order and so on. The bandlimited version of the > 0th order discontinuity is the integral sine Si(x). The bandlimited > versions of discontinuities of higher orders are integrals of Si(x), which > have analytical expressions via Si(x). The BLEP method replaces a > discontinuity of each derivative by its respective bandlimited version. > More detail can be found e.g. here > > http://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/SineSync.pdf > > In practice the BLEPs need to be timelimited by windowing. But neither can > we compute an infinite sum of those at a single point anyway (except in > special cases), which is another tradeoff. As to the latency, practical > window sizes have order of magnitude of a few samples which is a quite > acceptable. > > > -- > Vadim Zavalishin > Reaktor Application Architect | R&D > Native Instruments GmbH > +49-30-611035-0 > > www.native-instruments.com > -- > 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 > -- 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
