An analysis of a recent modified frequency-domain procedure for computing the response of linear systems using the fast Fourier transform (FFT) algorithm is described. This modified procedure eliminates the appended free-vibration interval that is used in the standard approach. The duration of the period of computation still needs to be longer than that of the response interval of interest, but only slightly. Reducing the period of computation lowers the number of frequencies at which the transfer function needs to be defined. The major drawback of the method is a high sensitivity to errors in the computed values of the transfer function, which reduces the role of interpolation in the transfer function definition. The modified method is related to the discrete Laplace transform.