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The difference between linear and nonlinear distortion

If a piece of equipment changes the shape of this sine wave, or any signal, then distortion is created. Distortion generates additional frequencies that were not present in the original signal. Sometimes distortion can add 'warmth' often it is distinctly unpleasant...

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This is a puzzle that came my way recently. A colleague asked me what the difference is between linear and nonlinear distortion?

"Hmm...", I said, "Distortion is inherently a nonlinearity imposed on the signal, so there can be no such thing as linear distortion". Well maybe I wasn't quite right about that, but it is a matter of terminology rather than science.

Let's investigate...

Firstly, what is distortion anyway? Distortion is any change in the shape of a signal's waveform. So to take an example, the waveform might be a simple sine wave, which is the simplest sound you can possibly get, consisting of only one frequency.

If a piece of equipment changes the shape of this sine wave, or any signal, then distortion is created. Distortion generates additional frequencies that were not present in the original signal. Sometimes distortion can add 'warmth' often it is distinctly unpleasant.

I would liken this to a funfair hall of mirrors. When you stand in front of a flat full-length mirror, you get an accurate reflection of what you look like. But a funfair mirror bends and distorts the reflection in all kinds of ways. The funfair mirror is bent, which causes the distortion of the image. We can call the flat mirror 'linear', meaning a straight line. The funfair mirror is 'nonlinear', causing distortion.

So now we know that linear means undistorted, nonlinear means distorted. So how come there is such a thing as linear distortion? Surely that is a contradiction in terms?

Well I took a look into this and I found that some people use the term 'linear distortion' to mean any change to the signal that doesn't change the shape of the individual sine wave components of a signal.

This could mean an irregularity in the frequency response, or it could mean a change in the relative phase (timing) of the various frequencies. It can make the individual sine wave components bigger or smaller, or shift them in time, but it doesn't bend them. It is only when the sine wave components of the signal are bent that the distortion is nonlinear.

To be honest, I think this is confusing. We can discuss frequency response and phase problems all day without describing them as distortion. So in my book, distortion only ever means changing the shape of the individual sine wave components of the signal, and it is always nonlinear.

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By David Mellor Monday August 28, 2006
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