Narrowband filtering with frequency sampling filters

A reduction on the number of multiplies per point is achieved for narrowband filtering when frequency sampling filters are used. Agarwal and Cooley [4] tabulated some optimal block size segments of long sequences when convolving them with a short sequence by FFT methods. In this paper we describe how, by using block lengths of twice the filter´s length (which is not the optimum size for filters of order > 4), and by utilizing frequency sampling filters, the number of multiplies per point is reduced over that obtained with other filters using the optimum block length. We also show that by doing a decimation (i.e. reducing the sampling frequency) in the frequency domain, we then only have to compute a short IDFT, as compared with decimating in the time domain after the long block sized IDFT has been computed.