Bit of a Mathematical Question - Delay/Reverb Mod/Shift

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Eruerable

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My knowledge of transfer functions, from the control we got in chemical eng, is pretty much limited to LTI systems.

I am satisfied that LTI systems are commutative, doesn't matter which order they go.

Where I struggle is once we introduce modulation or pitch shifting of delays and reverbs into the mix. It seems to me that we now end up with LTV systems, yes?

I think I know that LTV systems aren't, by nature, commutative, but are they always non-commutative or is it case specific as to whether the order changes the product?
 
Modulation introduces a time variance. The amount of TV determines how badly commutability falls apart. The breaking of commutativity is absolute, but the amount of breakage may or may not be objectionable.
 
Eruerable said:
My knowledge of transfer functions, from the control we got in chemical eng, is pretty much limited to LTI systems.

I am satisfied that LTI systems are commutative, doesn't matter which order they go.

Where I struggle is once we introduce modulation or pitch shifting of delays and reverbs into the mix. It seems to me that we now end up with LTV systems, yes?

I think I know that LTV systems aren't, by nature, commutative, but are they always non-commutative or is it case specific as to whether the order changes the product?
Click to expand...

AFAIK, LTV blocks are always non-commutative, even when combined with LTI blocks. Whether the audible result reflects this depends on the specific preset. For instance, the order of a Chorus + EQ usually won't practically matter, even though it technically does.
 
LTV systems are not commutative. Whether or not the difference is audible is the question. In general it is not.
 
Thanks for the answers folks, and thanks for taking the time out to weigh in Cliff!
Ya'll also pre-empted my next question as to whether the changes introduced by the order are audible.

Cheers!
 
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I decided to do a quick test as to how noticeable the differences are, clip below.



  • The first group of 3 is unmodulated delay and unmodulated reverb.
  • The second group of 3 is modulated delay and modulated reverb.
  • The third group is unmodulated delay and shimmer reverb.
  • The fourth group is modulated delay and modulated shimmer reverb.

One of the clips in each set of 3 is a duplicate of one of the others.

The clip order in each set of 3 was randomised using a random number generator, so you don't know which order you're hearing first or which order you'll hear twice.

All clips were from the same looped piece of playing.

Delay was a 500ms digital, reverb was a 2s room, shimmer was an octave shift.


I'm quite surprised at how little perceptible difference the time-variance introduced, I thiiiink I hear a difference but I wouldn't be able to go so far as to blind guess which effect order they resulted from.
 
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Nice test, Eruerable. The differences really are subtle, to the point that, in most uses, I think they're freely interchangeable. In other words, makes no difference. Nice tones, too!
 
Thanks man! Agree, to me the difference is negligible. I was quite surprised at how little difference the shimmer makes, of all things I thought that might be noticeable.
 
Also consider that modulation LFOs will begin at random points in each clip. That could create audible differences, and you wouldn't be sure if effect order was entirely (or even partially) the reason.
 
Yeah I did think about that was well, becomes quite sensitive to where the LFO 'starts' but I couldn't think of any way to get around it.
 
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