Non-linear/Linear Distortion?

While studying synths at the moment, I keep coming across the concepts of nonlinear and linear distortion. I have searched quite a bit on the net recently trying to find some clear explanation of the differences between the two, but instead I have found many people arguing about which is which as well as some very long and drawn out explanations that leave me more confused than when I started researching the topic, can anyone out there provide me with a decent explanation? or at least direct me to a site that can help

 

I don't know what is meant by 'linear distortion'.

A 'linear circuit' is composed of signal additions, or of multiplications by constants. Examples of linear circuits are mixers and most digital filters.

A 'nonlinear circuit' is any circuit that contains anything else. Examples of nonlinear circuits are ring modulators (multiplication of two signals), saturators (the multiplication factor depends on the signal's amplitude), and clippers.

Does this help?

 

There's one more important digital linear operation: delay. A digital (or analog) delay also qualifies as a linear operation. So digital filters, which are built out of combinations of delays, multiplies and adds, also qualify as linear operations.

And two more important analog linear operations that can't be perfectly replicated in digital systems: integration and differentiation.

The formal definition of a linear operation: that addition commutes (?) across the operation. A fancy way of saying that the following identities are true:

LinearOperation(signalA + signalB)

produces the same signal as:

LinearOperation(signalA) + LinearOperation(signalB)

and

LinearOperation(signal*100)

produces the same signal as

100*LinearOperation(signal)

A concrete example:

LowPassFilter(vocalSignal + guitarSignal)

will produce the same result as

LowPassFilter(vocalSignal) + LowPassFilter(guitarSignal)

as long as we're using the same lowpass filter.

Linear distortion: primarily, non-flat frequency response, or phase distortion. For some reason nobody seems to take an interest in the kind of linear distortion that makes things really really loud. But that is -- strictly speaking -- linear distortion as well.

Phase distortion: the result of an audio system that delays signals at different frequencies by different amounts. Human hearing is relatively insensitive to phase distortion in steady state signals, so the effect is often ignored, but phase distortion can audibly affect the sound of transient signals (e.g short duration signals, like clicks, and the attack of a sound).

Audiophiles like systems that don't have phase distortion, because they are supposed to have a perciptible "clarity" to them that run-of-the-mill audio systems do not. Allegedly, inear phase systems (with no phase distortion) sound quite startlingly "real", rather than recorded. Of course this only makes a difference if every single component between what gets recorded and what comes out of the speaker is phase preserving. I can't say that I've ever heard the effect myself. But I don't doubt that it's true.

Non-linear distortion: for practical purposes, any effect on an audio signal that isn't addition, multiplication, delay. Example: signal clipping.

One of the consequences of non-linear distortion is that frequency response of the system is volume-dependent. e.g. Clipping: a quiet signal doesn't clip, so the frequency response is pretty good; a louder version of the same signal does clip, so the frequency response is totally different.

Clipping is not a non-linear operation because:

Clipping(1000*inputSignal)

isn't the same as

1000*Clipping(inputSignal)

Why is that theoretically important? The mathematics of linear operations (where the above relationship is true) are much easier to deal with than the mathematics of non-linear operations (which is very difficult, usually). Generally speaking, the mathematics of linear systems, where all operations are linear, are fairly well understood; but the mathematics of non-linear systems is difficult, and often impossible to deal with.

Why is that practically important? Most digital audio theory is based around linear operations. Concepts like "frequency response" really apply to purely linear systems. Things that involve non-linear operations, like, for example guitar amp emulations, are very difficult (impossible, even) to implement properly in digital systems, without introducing strange digital side-effects.

Hope that enlightens rather than confuses. Feel free to ask for clarification.

fwiw, phase distortion is pretty much ignored by reaktorists. None of the Reaktor digital filters are phase preserving, and honestly, it probably doesn't matter that they aren't, except in very rare circumstances.

 

Whoa thanks so much that was really informative, thanks for taking the time to write all that it is very much appreciated

 

Thank you Robin! This helps much!

Thomas

 

So what would the difference be between say a distortion pedal for an electric guitar as aposed to distortion created by waveshaping in synthesis?

 

Digital aliasing is a serious problem with digital waveshapers. (See this thread: http://www.native-instruments.com/forum_us/showthread.php?t=46859 for a discussion, and a partial solution).

Analog pedals don't have a problem with aliasing, so waveshaping in the analog domain is easier to do. But it really depends on what kind of distortion you want to try to produce, how much you want to produce, what kind of subtleties you're looking to produce, and how good your ears are.

I'm not really that familiar with effect pedal distortion units. I use my amp to overdrive (and very lightly at that, since I play jazz). Good overdrive for jazz guitar is pretty demainding: even a hint of inharmonic content tends to turn big pretty jazz chords into mush.

There are lots of contributing factors to the sound of amp overdrive: tube-or-transitor distortion; non-linear speaker behavior; natural compression caused by power-supply sag. All non-linear, and all difficult to reproduce digitally. Amp modellers try to do all of these, and produce indifferntly good results, I think (never found a digital amp modeller that doesn't break up earlier than a real tube amp does).

I would imagine that pedals try to replicate at some of the dynamics of amp distortion/overdrive, in addition to just-plain waveshaping. Or not. I'm not really sure. If not, then see the thread I posted earlier.