Antialias for waveshaping - needed?

[Music Engineer]

hmm - when the wagon starts, they move forward, then stop, move backward, stop again, move forward again, stop, etc. - or not? it's some time ago that i have seen that kind of movie.

Are you guys serious?

[...]

The wheel is obviously moving all the same way, and not suddenly changing direction. The appearance of changing direction, and of different directions for the different parts (the 5 bolts vs. 6 spokes) is aliasing.

huh? obviously, i didn't mean, that the wheel literally changes direction but only apparently.

[AdmiralQuality]

Right. I just can't believe some here haven't noticed or thought about this before. I guess the Western movie is dead.

[Music Engineer]

Right. I just can't believe some here haven't noticed or thought about this before. I guess the Western movie is dead.

i used to watch bonanza as a child. but that's looong ago.

[Tzarls]

Ah, ok, now I get it.

[Borogove]

So.. how much oversampling is needed?

It depends on the particular waveshaping function in use.

For a polynomial waveshaper, IIRC, each component of the input signal will get an overtone at the highest power of the polynomial - so a cubic like x - (Kx^3) (a popular sigmoid limiter) with input components up to 10KHz will produce 30Khz output components. Now, that rule of thumb doesn't say anything about the amplitude of those components, so in practice you may not need to go that far with the oversampling.

Waveshapers that aren't expressed as polynomials don't have easy rules of thumb like that, but intuitively you can imagine that the more jagged and complex the shaping function is, the greater the bandwidth expansion can be.

[stratum]

So.. how much oversampling is needed?

It depends on the particular waveshaping function in use.

For a polynomial waveshaper, IIRC, each component of the input signal will get an overtone at the highest power of the polynomial - so a cubic like x - (Kx^3) (a popular sigmoid limiter) with input components up to 10KHz will produce 30Khz output components. Now, that rule of thumb doesn't say anything about the amplitude of those components, so in practice you may not need to go that far with the oversampling.

Waveshapers that aren't expressed as polynomials don't have easy rules of thumb like that, but intuitively you can imagine that the more jagged and complex the shaping function is, the greater the bandwidth expansion can be.

What you would do if you were to model a modern high gain guitar amp? If you use a single wave shaping function that is almost like:

y = x>0 ? 1 : -1

(well almost).

Of course one can use more than one wave shaping function to approximate a response like that, but that still would require many waveshaping and lowpass filtering stages to be cascaded. To further complicate the subject actual guitar amps have in fact more than one gain stage but the one that is hit by a strongest signal is often the last one and would behave almost like the formula above. If we also consider the actual responses of various circuit elements and their interaction with their surrounding the picture is further complicated but discussing that would be offtopic for this thread, obviously.

In my experience the one that works best is the simplest: One wave shaping stage and a sufficiently high sampling rate. But that might be due to my lack of ability to design well behaving filters that can be cascaded with nonlinear waveshaping functions without causing anomalies, I am not quite sure.

[AdmiralQuality]

y = x>0 ? 1 : -1

Hard clipping with infinite gain? All the oversampling in the world won't hide the aliasing you'll get from that!

[Borogove]

What you would do if you were to model a modern high gain guitar amp? If you use a single wave shaping function that is almost like:

y = x>0 ? 1 : -1

(well almost).

This aliases like hell - think of it as taking each pure/sinusoidal partial in the waveform and replacing it with a much louder (naïve) square wave with fundamental at that frequency, with overtones falling off at only -6dB/octave.

Hard clipping with infinite gain? All the oversampling in the world won't hide the aliasing you'll get from that!

"You are technically correct -- the best kind of correct!"

Fortunately, since it's massively distorting, you kind of don't care about the aliasing, but you can run the numbers anyway. Say your input has significant content at 10KHz (but not much above that), and you want audible aliases down 36dB. 6 octaves of falloff gets you that, so 8x oversampling should do you. (10K + 6 octaves is 640KHz, reflections start at 8 x 44K = 352K, 640K reflected at 352K -> 64KHz is the -36dB point).

[stratum]

y = x>0 ? 1 : -1

Hard clipping with infinite gain? All the oversampling in the world won't hide the aliasing you'll get from that!

That's not the actual function that I use, but actual guitar amps have lots of gain, so the end result will be something like that even though I guess an aliasing free software implementation will be a bit tricky. A softclipping function hit by a strong signal is not supposed to be very different from the formula above I guess, regardless of the actual shape of the clipping function. That's what actual guitar amp circuits roughly do, frankly. So there isn't even a trace of soft clipping in an actual tube amp of the "modern" variety (as long as you use the modern sounding highgain channel and max the gain knob, that is). Some of them even have a pair of diodes as the clipping circuit to achieve the same result with less complex circuitry.

[stratum]

"You are technically correct -- the best kind of correct!"

Fortunately, since it's massively distorting, you kind of don't care about the aliasing, but you can run the numbers anyway.

That has to be correct, because in spite of all that aliasing, it doesn't sound bad as long as pre and post distortion EQ's are right - but the overdriven chords sound a bit strange if your ears are trained to distinguish the way they sound from analog amps because of playing actual (analog) guitar amps for some time.

[AdmiralQuality]

y = x>0 ? 1 : -1

Hard clipping with infinite gain? All the oversampling in the world won't hide the aliasing you'll get from that!

That's not the actual function that I use, but actual guitar amps have lots of gain, so the end result will be something like that even though I guess an aliasing free software implementation will be a bit tricky. A softclipping function hit by a strong signal is not supposed to be very different from the formula above I guess, regardless of the actual shape of the clipping function. That's what actual guitar amp circuits roughly do, frankly. So there isn't even a trace of soft clipping in an actual tube amp of the "modern" variety (as long as you use the modern sounding highgain channel and max the gain knob, that is). Some of them even have a pair of diodes as the clipping circuit to achieve the same result with less complex circuitry.

I'm not going to bother to argue that with you, just going to say I disagree. Have fun!

[stratum]

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I'm not going to bother to argue that with you, just going to say I disagree. Have fun!

I'm not arguing, I have just told you what I know about these amps. Given that I have actually built a few of them I am well qualified to make the above statements about them. You may be right about aliasing, after all I am the one who have asked the question about how much oversampling would be needed so I am not claiming anything about it other than the fact that the result is perceptually OK. So have fun.

[AdmiralQuality]

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I'm not going to bother to argue that with you, just going to say I disagree. Have fun!

I'm not arguing, I have just told you what I know about these amps. You may be right about aliasing, after all I am the one who have asked the question so I am not claiming anything about it either other than the fact that the result is perceptually OK. So have fun.

Real-world amps don't have infinite gain. That algorithm above would make the noise floor sound like noise at full blast. Good chance of exploding some speakers with that too as it creates an absolutely worst case signal. Hence the fun...

[stratum]

Real-world amps don't have infinite gain. That algorithm above would make the noise floor sound like noise at full blast.

Of course they do not have infinite gain, it was just a formula exaggarated in a way so that it could help to state what I wanted to state. I have also stated that I actually do not use that formula so don't be concerned too much about it. That exact formula is not a part of any argument, or a part of any computer program intented to model any amp, it was just tool to say something easily, but apparently it was misunderstood. I had never thought that anyone would take it literally.

[AdmiralQuality]

OK