 the necessary HTM inversions by means of (3.80), we introduce a dummy 4.3.5 Computational flow of the SymbolicHTM algorithm variable in the expansion, writing s)1-((( (4.82) Here, for example, H(s) =I+G11 The dummy variable is carried along during all subsequent inversion and substitution processes. As a heuristic for obtaining only the relevant terms, it is assumed that all contributions which are (MR) are unimportant and can hence be neglected. Choosing suitable values for both K and R can be done automatically, based on error control, when numerical data are available. If not so, they need to be chosen manually. This may require some educated guessing. The validity of the results that are obtained for the chosen values of K and R then, of course, needs to be verified further on in the design process, when numerical data becomes available. 4.3.5.3 Symbolic simplification In a final step, the expressions for the input/output HTM elements can be simplified by eliminating all terms with negligible energy, as is done in traditional linear symbolic analysis [Fern98, Gie91, Gie94, Wamb98b]. Given the HTM element (4.83) the most straightforward approach is to eliminate all terms Hm,n,k(s) for which (4.84) Practically, this elimination is done by ranking the terms in equation (4.83) in order of decreasing magnitude Hm,n;k(s) Terms are then eliminated, starting with the smallest ones, until the error being introduced exceeds some specified threshold. For the norm m,n;k(s) one can for example use (4.85) Here, the set of frequencies {fi} is chosen to cover the frequency range of interest. The weight coefficients WI allow us to (de-)emphasize frequency bands with respect to each other. Note that this simplification procedure is only possible if numerical data are available to estimate and control the simplification error. 4.3.5.4 Computational complexity The complexity of the Symbolic HTM algorithm is roughly proportional to the total number of all terms generated during the second (elimination) step. This number is (in w