Estimating algorithmic error of digital recursive filters

The algorithmic error in the output signal of a digital recursive filter synthesized on the basis of an analog prototype filter is estimated, considering that this error is caused by time discretization only and assuming that the discretization interval is known. The filter is treated as a linear system operating in the pulse mode and the effect of level quantization on the algorithm is disregarded. Analysis and calculations on this basis yield the maximum difference between the steady-state values of the output signal of such a filter and the discrete values of the output signal of an ideal analog filter, this difference being obtained from the particular solution to the differential equation of the filter. For a typical filter with the transfer function (H(z) = KT 1 (e to the -I/IL sub z-1-1 and an input signal u (tau) = sin (omega tau) this error is 0.0516 when Il-2s, K=2, T=0.1s, omega=1 rad/s, max u' (tau) = 1.