[sdiy] FW: Kawai K3 - Bandlimited Waveforms

[ASSI]

On Monday 18 January 2010, Andre Majorel wrote:
> Are you talking about a fixed sample rate / variable phase
> increment wave table oscillator or a variable sample rate / fixed
> phase increment one ?

The former, specifically PPG and their heritage.  The phase 
quantization to 7bit can be viewed as a crude form of re-sampling or 
sample-rate conversion of the waveform.  The residual errors of this 
imperfect rate conversion are for most waveforms the predominant 
source of non-bandlimited noise (interpolation would improve that) and 
not so much the quantization of the amplitude to 8/12bit.  The latter 
noise can to first order be modeled as a sawtooth at 128*fw and LSB/2 
amplitude where fw is the frequency of the wave being played back.

A variable sample rate system doesn't have phase truncation errors and 
hence no aliasing produced by this kind of noise.  The reconstruction 
filter on the output would have to be more complicated if you'd wanted 
to perfect that aspect, however.

In both cases the quantization errors are synchronous to the sampling 
rate and periodic with the waveform frequency (or some integer factor 
of it), so all aliasing products happen to fall onto discrete 
frequencies.  In a variable rate system these move parallel to any 
pitch modulation, keeping their relation to the playback frequency.  
In a fixed rate system you can hear most aliasing products move 
"against" the pitch modulation as their distance from the fixed fs/2 
is changing.


Achim.
-- 
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