Interpolation, extrapolation, and reduction of computation speed in digital filters

Abstract

Any digital filter can be decomposed into two basic subsets, an extrapolator the output of which is sampled at a frequency depending only on the filter bandwidth and an interpolator delivering the filtered signal at the imposed output sampling rate. Redundancy in extrapolator and interpolator is removed by introducing half-band nonrecursive filtering elements for which definition, performance figures and efficient implementation are supplied. They reduce significantly the necessary computation and storage at the cost of a slight group delay increase. A formula is given for the amount of multiplications to be carried out every second in a filter; it depends on the filter bandwidth, signal to distortion ratio, and input-output sampling rate. The method is extended to recursive filters and a comparison is made with existing techniques of implementing digital filters for the needs in computation and storage hardware: a specific example of design underlines the reduction in computation speed achieved in practice through this method, which brings digital filters in a most favorable position for their competition against analog filters in many application fields.