[sdiy] Henry, 256 Bw limited!

[karl dalen]

I'm a bit puzzled, are you describing the Nyquist theorem and the ZHO?

Or are you only describing the ZHO in fixed sample rate DAC
as an rolloff effect like this, No?:

::the ZOH on the effective frequency response of the DAC, resulting in a ::mild roll-off of gain at the higher frequencies (a 3.9224 dB loss at the ::Nyquist frequency, corresponding to a gain of sinc(1/2) = 2/π). This ::droop is a consequence of the hold property of a conventional DAC,

But are the same ZHO effect the same for variable sample rate systems?
Assume 8 bit length, no less no more, then this sharp transition 
of bit to bit level adds harmonics (over/under shot swing) further
increases the spectrum. The faster the settling time between level
changes (no slew) the broader the bandwidth of the resulting wave!?
Well until frequency are so high it starts to modulate down but thats
not aliasing as per see in a fixed rate system since the rate are variable.(assume endless frequency response on DAC). 

I get the impression that the ZHO, if so, gets pushed upwards as
sample rate goes up as well? (aliasing of wave are harmonics). 

But where does Andrej muffling apply then?
Can you really hear a small 3.9db loss at Nyquist?

Does the ZHO effect explains Grants thoughts on bit widths?
(im unsure on what he actually wanted to point out).

What do you mean by gritty PPG? 
Wave to wave mismatch in table as in MSB integer toggling of bits in wave?
or gritty as in static cyclic single wave?

Reg
KD


>Antti Huovilainen <ajhuovil at cc.hut.fi>:
> It sort of works like that, but not exactly.
> A simplified explanation is that an abrupt transition in
> level, as happens for every sample when the wacetable
> oscillator has no interpolation, has a spectrum that falls
> off at 6dB/oct asymptotically. This falloff starts at the
> inverse of the transition repetition rate (this would
> frequency * wavetable length / 2 = nyquist frequency).
 
> Below that point, the spectrum is determined by the
> wavetable contents. This way you can have both very sharp
> sounding waveforms (square, sawtooth), and also mellow
> sounding (sine) when the filter cutoff is below the nyquist
> frequency.

> As there is no interpolation, the spectrum detail gets
> mirrored above nyquist (you can work out the maths, but it's
> generally not worth it). Take simple 8 sample waveform as
> example: The harmonics are a1, a2, a3 and a4. The resulting
> spectrum is then a1, a2, a3, a4, a4, a3, a2, a1, a1, a2, a3,
> a4, a4, a3 ...


> Superimposed on that mirrored spectrum is the 6dB/oct
> falloff rate. There is also some additional falloff near
> multiples of nyquist due to the step-like "interpolation"
> (the official term is zero order hold). The effect on sound
> is minor when the waveform is long as ear is not very good
> at determining exact spectrum shape at high frequencies.
> 
> 
> Now for the real reason some wavetable synths sound so
> gritty:
> PPG waveforms were simply miscalculated. If you take normal
> 128 entry 8 bit sine, it really sounds quite clean as long
> as filter removes the mirrored harmonics. PPG sine on the
> other hand evens looks gritty when the wavetable contents
> are viewed. This is either due to a bug in the software they
> used to calculate the wavetable contents or deliberate
> design decision. I'm betting on "happy accident".




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