The better Multi-Osc

[martinvicanek]

Updated harmonic oscillators with phase drift fixed:
viewtopic.php?f=3&t=2871&p=15437#p15437

Updated classical waveforms oscillators with phase drift fixed:
viewtopic.php?f=3&t=2871&p=15534#p15534

[KG_is_back]

Very nice! Cool how you take advantage of the integer overflow. At first I thought it would reduce the frequency precision, but then I've done the math. The frequency coefficient gets rounded (looses last few decimal digits) if you set the cutoff at (1/256)*nyquist ( =81Hz @44kHz samplerate). For the original floating point the rounding depends on the phase of the oscillator - when the phase gets over 0.5 (oscillator is half cycle through) the oscillator starts to loose precision at any samplerate above 0.5*Nyquist. Smaller the phase, smaller the loss. However, that means the rounding errors are inconsistent and the actual frequency of the oscillator (vs. the one you feed in) is less predictable.

With fixed point arithmetic you can be sure that there are 2**31 possible frequencies ( 2**32 if we count negative too).
If you use freq > 2^-7 then you can be sure the oscillator will not drift ever. For freq < 2^-7 it is not as hard to figure out the real frequency of the osc - for every negative power of two below -7 you loose one binary digit.

[tulamide]

@Martin and @KG:

Just so that you know. If you could listen to a discussion between Stephen Hawking and Albert Einstein - that's how I feel right now

And a question: Should I implement the new sine osc in the multi-osc, or is it a special case?

[martinvicanek]

@KG, I am not at all worried about low frequencies losing a bit or two - that's still very accurate even for the LFO range. No, the point is that in the new design, the internal oscillator state is incremented in steps given by the frequency and nothing else. The phase is added when all is done - there is no influence of the phase on the internal state, no rounding errors there. Hence if you take two instances of the oscillator and drive them with the same frequency, they will maintain a constant phase relationship forever. (well at least until the Andromeda galaxy collides with our Milky Way, or until our sun becomes a red giant and swallows the earth - whatever comes first haha).
@tulamide, yes, please replace the oscillators with the updated versions whenever you get round to it.

[KG_is_back]

I am not at all worried about low frequencies losing a bit or two - that's still very accurate even for the LFO range.

Actually it can be an issue in some applications. Like if you need Oscillator to run continuously over long periods of time ( ~days). Like keeping track if AC distribution net is not drifting or something. Saw this in a documentary - if electricity demand drops/rises suddenly the frequency of AC drops/rises too by minuscule amounts - the electricity companies have to monitor that very carefully and adjust power plants energy output accordingly. This becomes even bigger issue with wind-farms, which are completely irradic.

(well at least until the Andromeda galaxy collides with our Milky Way, or until our sun becomes a red giant and swallows the earth - whatever comes first haha

Andromeda galaxy hits us (Milkyway) in about 3.75 billion years, while sun becomes red giant in cca.4-5billion years. However, as sun get brighter and brighter earth might get inhabitable in under 2 billion Y. The real threat are the solar storms. I think in 19th century one hit us and it basically took out most of telegraph net. Solar storms regularly take down satellites and a big one could potentially fry all electronics on earth including power grid (and most definitely on the orbit). The worst part about it is, well... ever heard of butterfly effect? because that's basically how solar storms form. We can have like 8minute warning ahead if we are lucky - good luck throwing your computer and TV into nearest Faraday cage in that time

[tulamide]

@tulamide, yes, please replace the oscillators with the updated versions whenever you get round to it.

Done! Also made a second module, so one can use either bandlimited or naive versions (where applicable, I think it is not needed for sine and noise correct? If not, what would the naive version of the sine be?)

[martinvicanek]

Correct, and thanks! A sine is bandlimited by definition, there is no "naive" sine. In a way, white noise is the complete opposite: it has full bandwith, and the more it aliases, the better.

[KG_is_back]

In a way, white noise is the complete opposite: it has full bandwith, and the more it aliases, the better.

well, that is more of a philosophical question. White noise is defined as "noise with equal energy in every frequency band of the same width". In mathematical world it would have overall infinite energy (because continuous bandwidth extends to infinity). That implies, if you would sample such noise into sampled-signal, the aliases would add-up to infinity or you'd filter them out and the magnitude frequency response would no longer be truly flat (if you'd use brickwall-lowpass at nyquist the response would be flat in DC-Nyquist range and zero above, which is also the case of this "white noise" generator).
There is no "white noise" in real world either, since (as far as we can tell) real world can't "interpret" infinite frequency (Planc length is most likely the maximum possible wavelength in the universe, higher frequency waves would most likely collapse into black holes or something).

[Perfect Human Interface]

There is no "white noise" in real world either, since (as far as we can tell) real world can't "interpret" infinite frequency

Indeed, it's purely a mathematical concept. Interesting how the universe seems to both support and yet limit infinities.

Although remarkable how similar rain or river rapids can sound to noise, audibly speaking.

[KG_is_back]

lthough remarkable how similar rain or river rapids can sound to noise, audibly speaking.

Yeah, it's simply a limitation of human perception. In both situations the water drops are created by very complicated process and one they hit the surface, they create "randomly" spaced short bursts of sound. Our brain is incapable of recognising the pattern thus considering it random "noise".

Sound is a very good example where model of reality that our brain uses does not correspond with reality. In reality sound is wave, which can equivalently be described as time-varying air pressure or as sum of (co)sine-waves with different frequencies. However, our auditory system does not detect it in that way. Our ears consist of cca.7000 sensory cells (per ear), where each one detects narrow part of the spectrum and transmits "envelope" of that spectrum into the brain. In our brain we "see" (hear) what you can see on a FFT analyser - a frequency graph that changes over time.
Our brain observes time and frequency ( > 20Hz) as two unrelated phenomena, while in reality they are just two ways to describe the same thing. This leads to some weird perception illusions when signal shifts from "time domain" (perceived as value changing in time) into "frequency domain" (perceived as periodic event with frequency).
Good example of this is binaural beat. If you send a two sine-waves each into one ear, with slightly different frequency, your brain can't make sense of that. If the frequency difference is big enough you will hear two "frequencies" one in each ear. But once you choose the differece to be smaller ( <50Hz) you will hear <50Hz "frequency" inside your head (your brain assumes is a single sine wave driven by some weird LFO with <50Hz frequency). It get's even weirder - you can hear this beating downto cca.5Hz ( =you perceive sub-sonic event as a sonic one), where you have a mixed impression of "frequency" (sound with 5Hz) and "beating" (the original sine wave driven by 5Hz LFO).

Similarly, our brains have similar misconception about waves and moving objects. Waves on water seem to "travel" while the water is only slightly moving in circles. This effect of something both "moving" and "not moving" seems slightly paradoxic and confusing. It is even worse with quantum-mechanics which is completely out of human intuition and comprehension.