On 11-Jun-15 11:00, Sampo Syreeni wrote:
I don't know how useful the resulting Fourier transforms would be to the original poster, though: their structure is weird to say the least. Under the Fourier transform polynomials map to linear combinations of the derivatives of various orders of the delta distribution, and their spectrum has as its support the single point x=0.
So they can be considered "kind of" bandlimited, although as I noted in my other post, it seems to result in DC offsets in their restored versions, if sinc is windowed. It probably can be shown that in the context of BLEP these DC offsets will cancel each other (possibly under some additional restrictions). So, this seems to agree with my previous guesses and ideas.
You also mentioned (or I understood you so) that the exp(at) (a - real, t - from -infty to +infty) is not bandlimited (whereas my conjecture, based on the derivative rolloff speed, was that it's bandlimited if a is below the Nyquist). Could you tell us how does its spectrum look like?
Thanks, Vadim -- 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
