Other than preferences to use one or the other words in different domains, do they refer to essentially the same process? And likewise for the opposite operations, demultiplexing and deconvolution?
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3$\begingroup$ No. Convolution en.wikipedia.org/wiki/Convolution; Multiplexing en.wikipedia.org/wiki/Multiplexing $\endgroup$– AlexTPCommented Nov 3, 2017 at 16:46
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$\begingroup$ What does multiplexing's definition look like in the domain of signal processing, rather than the domain of electronics/networking? $\endgroup$– Matt ChambersCommented Nov 3, 2017 at 17:04
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Multiplexing is the name given to the process of stuffing/switching/packing multiple signals, channel, bits, etc into a single stream/medium/band, whereas the opposite act of separating each individual packed signal, bit etc, back is named as de-multiplexing. In multiplexing each signal (or bits) remains completely intact and have no kind of intersignal interaction other than errors and ditortions whatsoever.
Convolution, on the other hand, operates on two signals and produces a new third signal which is somewhat like the child of the two parents. It's properties are related to its parents by the mathematics of the convolution process. Usually a convolution will be used to produce the output signal of LTI systems where the input signal is convolved with the system impulse response. Rarely a convolution between two arbitrary signals also considered (especially in frequency domain, which is more of a theoretical guide rather than a computational one, circular DFT convolution being an exception). The opposite operation of convolution is named as deconvolution and seeks for finding the driving input from a given output under different constraints.
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$\begingroup$ So multiplexing is a kind of losslessly reversible convolution? $\endgroup$ Commented Nov 3, 2017 at 18:29
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$\begingroup$ I don't know what to say... The literature and the established practices tend to clearly separate their definitions. I've never tried to reduce the implementation of a multiplexer into a convolution framework. Perhaps because I could see no benefit of doing so? May I ask what would be your benfit of considering so? $\endgroup$– Fat32Commented Nov 3, 2017 at 19:43
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$\begingroup$ The signals I'm thinking about are from mass spectrometers. There are methods to deconvolve and methods to demultiplex, depending on the phenomenon that caused the combination of signals that a user wants to separate. Sometimes the phenomenon is natural (like the same protein showing up at multiple charge states), sometimes it's part of the method (like multiplex isolating several m/z windows at once and scanning it in one spectrum). It would be more work than I want to do to properly describe the situation for further discussion, but thanks for input regardless. :) $\endgroup$ Commented Nov 3, 2017 at 22:32