In some applications we want to synthesize a discrete signal from another discrete signal by designing a system that maps the signal we have to the desired one. The problem of obtaining a specific output g corresponding to a specific input f is not an interesting problem if all entries of f are nonzero, because we may recover g from f by using only a single multiplicative filter h. However, in the event that some of the entries of f are zero, the problem is no longer trivial and a number of iterative algorithms have been proposed. A distinct problem arises when, rather than specifying a specific output for a specific input, an input-output relation is specified. This is the system synthesis problem, as opposed to the signal synthesis problem.
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