Dear Stefan,
Dear aRtsians,
As a first thing, let me intoduce myself.
My name is Frank "#bang" Haferkorn. The nickname "#bang" stand for
"hashbang". Those who program bash-skripts now what its about. I am a
physicist with a specialization to acoustics/signaltheory.
So think I I well hosted at the arts-project
I discussed the following problem with Stefan for a while.
At the current kde release 2.1.1 all ofthe Synth_WAVE_* modules calculate
their values by evaluating the phase information (pos) and calculating using
a mostly simple algorithm to determin the wanted amplitude.
For example is the rule for calcuilating a saw wave:
saw = 2*(pos-0.5)
This is an algorithm for an ideal saw-wave.
As the spectra is limited by half the sample frequency, this will fail and
resume in lower frequencies mirrowed into the resulting signal.
HINT: Try to genarate 1,5kHz , 8kHz and a 15kHz Sinus Waves. Analyse the
signal with big scaling factor, in order to analyse groups of periods . The
smaller frequency look good, but the nearer the frequency gets to half the
sample frequency (here 22,1kHz). You see ramps of the Envelopes of the
Saw-Wave-Signal.
These Ramps in the Envelope-Wave give the distorting noise (as of mirror
frequencies)
Stefan tried to clear this with creating new a Modules under Synth_Osc_Saw
etc.
let's hear a translation of his own words.
In My Optinon is the problem easy. If you "sample" a real ramp, then it isn't
limited in the frequency domain. That's the reason of the aliasing.
I recently have tried to implement a band-limited ramp (saw-wave)
Herein we can't use de aRrts typical diffrence betwen the Modul that creates
the waveform and a generic function generator.as the Waveform changes with
the frequency. So the new modul shall get the name Synth_OSC_SAW. It is the
synth_FREQUENCY and a Synth_WAVE_SAW a single module
Stefans solution works like this.
generating an ideal ramp in frequency domain with an explicit formula in
order to gerate the FFT Koefficients with an ideal ramp.
remove the frequencies over the Bandwidth over F_grenz = SR/2with a Blackman
Window
inverse transformation into the time domnain (IFFT)
the resulting Wavetable is the sampled band-limited ramp (saw-wave) with
SR/2, so that the Wavetablesynthesis (here without every Interpolation) is
satisfying
Problems with the implementation:
IFFT is not performant, so changing the frequency is cpu-costy
at the moment only realized for saw-wave
frequency-sliding and modulating won't work as of block-calculation
But that might be the way we have about to go in order to get rid of the
aliasing
It is also possible, to implement it with (FIR/IIR-filter or earlier
calculated band-limited tables instead of IFFT. This has to be implemented
into other waveforms except sinus
My solution is different. but has the same effects at fewer cpu-costs
It should be necessary to implementa new module property:
The new module Functionality OVERSAMPLING has to come with:
Module wide Oversampling (=increasing of the samplerate)
this leads to a module wide increasing of samplerate at runtime
needs interpolation ofall nonconstant inputs and downsampling of all outputs
by any factor x^2
A module with oversampling-factor different 1 performs a RUNTIME:
oversampling/interpolating the increased samplerate from all non constant
input-channels
downsampling/bandwidth-filter and sampleratereduction for all output chanells
performing the sample stepping increased (by the oversampling factor)
TODO, if accepted.
If the above precedere is accepted, Stefan could do a simple Oversampling
module with copying the last samples (=hold) instead of interpolating. amd
integration (=averaging) for downsampling. (Sorry,Idon't know thearts
intrinsics right now.)
I will then implement the proper over/downsampling, I mentioned similar
software earlier to Stefan.
That are the resultsto the arts projects
New Oversampling, also useful for ather time critical feedback operations
Move all Synth_WAVE... to the new Synth_CALC... . in sourcecode.
Redo the Synth_WAVE as module-files with oversampling using the now called
Synth_CALC modules.
