Causes and effects of algorithmic error in digital filters

Abstract Various methods are described in text books and research papers for generating a digital filter which will emulate the performance of a given analogue filter, normally without comment on the effectiveness of the methods. This paper investigates among other things the problem of comparing methods of emulation. Two distinct types of error are inherent in digital filters: quantisation error and algorithmic error. This paper concerns itself with algorithmic error and highlights techniques which can be used to evaluate this type of error given a digital transfer function and the analogue counterpart from which it was derived. It shows how the observed algorithmic error is dependent upon the emulation technique used and the sampling interval of the digital filter. Algorithmic error analysis is shown to be a useful tool for determining a lower bound on the sampling frequency of the filter. Considerations of local error and step error show how the global algorithmic error is generated.