I've never heard it called that either but perhaps a fourier analysis of a step function, or click (very narrow step function), identifies all the sundry frequency components generated.I have never heard this before. Why is it called Fourier click?
Interrupting audio signals at other than zero crossings is a somewhat different problem from DC offset clicks. If you visualize a sine wave started or stopped away from a zero crossing, that introduces a DC component. Complex audio is more complex.
A great deal of work has gone into splicing unrelated audio samples together. With pitch shifters reassembling the processed samples after they have been streched out or squeezed together requires some finesse.
Synchronizing wiper changes in digital pots to be correlated to signal zero crossings reduces the energy from those switching perturbations.
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IMO switch clicks are pretty low on the list of summing bus design problems.
JR