Polyphase FIR Networks Based on Frequency Sampling for Multirate DSP Applications

It is well known that the frequency sampling approach to the design of Finite Impulse Response digital filters allows recursive implementations which are computationally efficient when most of the frequency samples are integers, powers of 2 or null. The design and implementation of decimation (or interpolation) filters using this approach is studied herein. Firstly, a procedure is described which optimizes the tradeoff between the stopband energy and the deviation of the passband from the ideal filter. The search space is limited to a small number of samples (in the transition band), imposing the condition that the resulting filter have a large number of zeros in the stopband. Secondly, three different structures to implement the decimation (or interpolation) filter are proposed. The implementation complexity, i.e., the number of multiplications and additions per input sample, are derived for each structure. The results show that, without taking into account finite word-length effects, the most efficient implementation depends on the filter length to decimation (or interpolation) ratio.