A figure of merit for digital filters

The combined effects of amplitude quantization are brought together in such a way that the designer can readily choose cost effective word lengths for his A-D converter and digital filter. A degradation factor is suggested which relates the performance of the digital circuit to its analog counterpart in terms of the filter´s frequency transfer characteristic, sampling rate, input noise, dynamic range and word length. Only low-pass filters using fixed-point arithmetic and rounding are considered. A practical design illustration is presented using the degradation factor and a Fortran IV computer program to define word lengths and to choose the best realization from among the parallel or cascade digital filter realizations with first and second-order sections.