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A computationally oriented transform technique for the analysis of time-varying linear systems involving both discrete-time (i.e., sampled-data) variables and continuous-time variables is presented in this paper. Finite-dimensional representations are described for the various linear operators involved, and methods for obtaining singular-value decompositions of these operators are given. The three parts of the singular-value decomposition are analogous to the direct transform, transfer function, and inverse transform of Laplace and Fourier transforms, and offer analogous insights into analysis and synthesis problems. An example is included to illustrate the analysis procedures.