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The need for digital simulation or modeling of linear modulated communication and control systems frequently arises. This paper presents a method for accomplishing this task which has outstanding computational efficiency. It applies to those situations in which the input to the modulator or detector can be presented as a sum of sinusoids of arbitrary amplitudes, phases, and frequencies. Post modulator or post detector filtering is assumed to be accomplished by a linear stationary differential system. The method is considerably more efficient than conventional methods because the action of the modulator or detector is accounted for analytically and because an alternate expression for the transition matrix is employed which eliminates derivatives of the input signal from the integrand of the convolution of the transition matrix. The advantages accruing to these measures are demonstrated by two examples, one of which is frequently encountered in discrete phaselock loops and in identification of system parameters by sinusoidal response methods.