Design of multirate bandpass digital filters with complex coefficients

The multirate digital filter is useful in realizing narrowband characteristics because multiplication can be reduced by using different sampling frequencies, at the same time reducing the order of the filter to be realized. This paper introduces the complex coefficient into the traditional design of the low‐pass multirate filter. The construction method is proposed for the multirate bandpass digital filter with complex coefficients. By applying the complex coefficient filters to the decimeter and interpolator composing the multirate filter, bandpass characteristics can easily be obtained. By employing the multistage cascade structure, the number of multiplications and the memory capacity for coefficients can be reduced greatly. Then a new design method for the complex‐coefficient filter is proposed based on the properties of the analytic signal. The discussion in this paper applies to both FIR and IIR filters.