Why doesn't order matter for (linear) effects?

[sujayakar314]

I was thinking about it, and why is it that all of the linear (EQ, delay, etc.) effects blocks are commutative (order doesn't matter)? It sounds right (in both senses), but it shouldn't HAVE to be the case.

 

[javajunkie]

I was thinking about it, and why is it that all of the linear (EQ, delay, etc.) effects blocks are commutative (order doesn't matter)? It sounds right (in both senses), but it shouldn't HAVE to be the case.

Because 1 + 3 + 5 = 9 and 5+1+3 = 9. If I understand correctly.

 

[GiRa]

javajunkie's example gives the idea. If you want to dive more in to it search for Linear Time Invariant systems.

 

[godprobe]

add red light to green light, you get yellow light
add green light to red light, you get yellow light

spin both lights around a circle, you still get a yellow light
delay one, and they won't always line up to make yellow anymore
"invert the phase" (swap the clockwise/counter-clockwise rotation) of one and they'll line up with the same frequency as before... but it looks different

 

[Ochanomizu]

BTW, which effects are classed as "linear" and which ones are classed as "non-linear"? Feel free to just point me in the right direction...


Cheers

 

[sujayakar314]

I was thinking about it, and why is it that all of the linear (EQ, delay, etc.) effects blocks are commutative (order doesn't matter)? It sounds right (in both senses), but it shouldn't HAVE to be the case.

Because 1 + 3 + 5 = 9 and 5+1+3 = 9. If I understand correctly.

Adding numbers is certainly commutative, but applying functions does not have to be. If "the mother of" and "the father of" are functions on a set of people, "the mother of the father of Jim" is different than "the father of the mother of Jim."

javajunkie's example gives the idea. If you want to dive more in to it search for Linear Time Invariant systems.

So after reading up some more, every linear audio effect we use in the Axe-Fx is characterized by an impulse response, then? So the commutativity of convolution makes order not matter here. Furthermore, does that mean that the time-invariance of the system is what gives it its commutativity?

BTW, which effects are classed as "linear" and which ones are classed as "non-linear"? Feel free to just point me in the right direction...


Cheers

I think all of them are except for the Amp Sim, Drives, and Compressors/Gates as long as any internal drive isn't used. I have no idea if the Pitch and Synth blocks are linear in this sense.

 

[Jay Mitchell]

Adding numbers is certainly commutative, but applying functions does not have to be.

If they are linear functions that do not vary with time, it does "have to be."

So after reading up some more, every linear audio effect we use in the Axe-Fx is characterized by an impulse response, then?

Yes.

So the commutativity of convolution makes order not matter here.

Yes.

Furthermore, does that mean that the time-invariance of the system is what gives it its commutativity?

Yes. Although time-varying functions (e.g., those based on modulated delays) are, strictly speaking, not commutative, for the most part the effect of changing their order with other linear functions are subtle.

I think all of them are except for the Amp Sim, Drives, and Compressors/Gates as long as any internal drive isn't used.

Correct.

I have no idea if the Pitch and Synth blocks are linear in this sense.

Neither of these are linear, as they both add frequencies that were not present in the original signal.

 

[javajunkie]

I believe the tremolo block is not LTI as well.

 

[FractalAudio]

Technically chorus, flanger, phaser are not LTI but in practice the order doesn't matter (much anyways) since they are "wide-sense stationary".

 

[Bakerman]

I believe the tremolo block is not LTI as well.

Its level is time-variant of course, but I think it's linear otherwise. IOW its placement can affect what you hear from a reverb or delay* but wouldn't really matter with other LTIs or chorus/flanger/phaser.

*Unless delay time is an integer multiple of tremolo cycle time--then order still doesn't matter.

 

[javajunkie]

I believe the tremolo block is not LTI as well.

Its level is time-variant of course, but I think it's linear otherwise. IOW its placement can affect what you hear from a reverb or delay* but wouldn't really matter with other LTIs or chorus/flanger/phaser.

*Unless delay time is an integer multiple of tremolo cycle time--then order still doesn't matter.

hmmm, I remember us placing a trem block in front and behind a cab. I could be remembering wrong but order did matter in that case. I'll try and find the post. Maybe my memory is faltering.

 

[sujayakar314]

Thanks all for your expertise.