Most of the controllers designed for systems with timedelays involve finite impulse response (FIR) filters in their structure, in particular prediction based controllers for systems with input/output delays. We present theory, algorithms and software to evaluate the frequency response, to approximate the filters by stable linear timeinvariant systems and to compute their induced L-2 gain. The approach is based on the theory of functions of matrices. In the approach pole zero cancelations in frequency domain representations are explicitly taken into account.