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Linear theory, i.e., the study of linear systems concerns operators (functions) that satisfy the property of superposition, i.e., if function F is such that A = F(x) and B = F(y), then A + B = F(x+y). Such a system has nice properties when the Fourier transform is applied: the sum of sine waves according to the transform's output matches the input. Linear theory is used in signal processing and analysis of time-variant functions.