On 11-Jun-15 19:58, Sampo Syreeni wrote:
On 2015-06-11, vadim.zavalishin wrote:
Not really, if the windowing is done right. The DC offsets have more
to do with the following integration step.
I'm not sure which integration step you are referring to.
The typical framework starts with BLITs, implemented as interpolated
wavetable lookup, and then goes via a discrete time summation to derive
BLEPs. Right?
I prefer analytical expressions for BLEPs of 0 and higher orders :)
So the main problem tends to be with the summation,
because it's a (borderline) unstable operation.
I don't think so. The analytical expressions give beautiful answers
without any ill-conditioning.
So we don't know, if exp is bandlimited or not. This brings us back to
my idea to try to extend the definition of "bandlimitedness", by
replacing the usage of Fourier transform by the usage of a sequence of
windowed sinc convolutions.
The trouble is that once you go with such a local description, you start
to introduce elements of shift-variance.
How's that? This condition (transparency of the convolution of the
original signal with sinc in continuous time domain) is equivalent to
the normal definition of bandlimitedness via the Fourier transform, as
long as Fourier transform exists. The thing is, by understanding the
convolution integral in the generalized Cesaro sense (or just ignoring
the 0th and higher-order "DC offsets" arising in this convolution) we
might attempt to extend the class of applicable signals. This seems
relatively straightforward for polynomials. As the next step we can
attempt to use polynomials of infinite order, particularly the Taylor
expansions, where the BLEP conversion question will arise. The answer to
the latter might be given by the rolloff speed of the Taylor series
terms (derivative rolloff).
Regards,
Vadim
--
Vadim Zavalishin
Reaktor Application Architect | R&D
Native Instruments GmbH
+49-30-611035-0
www.native-instruments.com
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