| This report describes the stages of realization of various structures of digital filters. A detailed theoretical study of their stability thus a comparison of the characteristics. Finite-word-length effects are an important factor in implementation of digital signal processing systems. In this document we described the effects of a finite word length in digital filtering.; Specifically, we considered several parameters like quantiaztion and round-off noise in multiplication.; These effects are internal to the filter and influence the method by which the system will be implemented. More specifically, we demonstrated high-order systems, especially IIR systems, should be realized by using second-order sections as building blocks. We advocated the use of the direct form II realization.; The state-space formulation provides an internal description of a system and, as a consequence, we obtained additional system realisation called state-space realizations. These realizations represent additional possible structures that provide good alternative candidate realization for the system.; As an alternative to use of direct form II second-order filters as building blocks for high-order filters, we can use second-order state-variable forms. Such sate-variable forms can be optimized with respect to the state transition matrix to minimize round-off errors. The optimization leads to minimum-round-off-noise second-order sate-variable filters that are highly robust for implementing narrowband filters present in the case we consider. |
