# Why is the term deconvolution used more for signals and not so much (or at all) for systems?

Wikipedia defines mathematical deconvolution here, and with the examples given and my experience, what I've read over the years is that deconvolution is used to determine an input signal provided a measurement of a system's output signal, and the known frequency response or transfer function of the system.

But in the case where you know the input and output signals of a system, and rather chose to determine the frequency response or transfer function of the system, I don't think I've ever seen that called deconvolution - but it is deconvolution nevertheless, right? Even though most call it "System Identification"

The examples given in wikipedia seem to suggest deconvolution is strictly involving derivation of a signal, but given the equivalence of signals and systems in a mathematical sense, is it wrong to call system identification deconvolution?

• Eventhough you are basicly right as the convolution operation is commutative it's a matter of nomenclature with some reason behind, as there is a conceptual asymmetry between a signal $x[n]$ and an impulse response $h[n]$. The former generally is produced indefinetely (as long as there is data) by a deconvolution operation (or equivalently an inverse filtering if possible) while the latter is produced by a possibly finite procedure whose convergence is seeked. The procedures are aiming quite different things. But mathematics is bound only by imagination isn't it? – Fat32 Jun 26 '16 at 17:02
• @Fat32 Yes I agree with your last statement. And thanks for pointing out the conceptual asymmetry. I agree there as well. And in the case of the impulse response you are also trying to wash out signal (input or output) noise that corrupts the measurement. For signal deconvolution you have to somehow deal with un-modeled dynamics. – docscience Jun 26 '16 at 17:12
• by the way, the answer to your question "Is it wrong to call System Identification deconvolution" is yes imho. Because system identification is a broad (huge) topic with a multitude of approaches and techniques, of which may be only one of them can be considered similar to a deconvolution operation. therefore wouldn't it be wrong to call a superset by the name of one of its subsets ? – Fat32 Jun 26 '16 at 18:55