One correction to my own email.... I said:

"All linear systems pass sine waves undistorted"

I should have said "All linear TIME-INDEPENDENT systems pass sine waves undistorted."

There are linear time-dependent systems which alter frequency, such as some mixers. A true multiplying mixer fed by an oscillator and then considered as a single input, single output system is linear, but will generate multiple output frequencies.

The criterion for linearity is the following:   

If F(q(t)) is the output of the system when operating on input q(t), then the system is linear if and only if F(a*X(t)+b*Y(t))=a*F(X(t))+b*F(Y(t)). Said in words, this means that scaling the input just scales the output by the same amount and that feeding a sum into the input is the same as operating on the two components separately in two idtentical linear systems and adding the outputs.

Sean



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