Towards unified code generation for libms and filters . " May

A digital filter, or a general digital signal processing system, operates on a discrete input data to produce a discrete output by means of a computational algorithm. We are interested in such algorithms that are implemented for control and signal processing application in embedded systems. Regardless of the type of embedded system, the data processed by the digital system is ultimately stored in memory registers with finite capacity. Therefore, all the computations are performed in finite-precision arithmetic and thus result in an inherent limitation on the accuracy of the result. In this thesis we investigate the effects of finite-precision implementation of digital filters. We apply a rigorous computer arithmetic approach to evaluate the errors due to those effects in order to provide a reliable implementation. We consider implementation of discrete Linear Time-Invariant (LTI) systems [1] and more specifically infinite impulse response filters, which means that in response to a brief initial input the filter output does not become exactly zero past a certain point but continues indefinitely. A discrete-time digital filter is usually characterized by its transfer function. A transfer function is a representation in frequency domain of the relation between the input and output of a LTI system with zero initial conditions. It can be expressed as the Z-transform of the inputs and outputs of the filter [2] and it