Design of multirate FIR digital filters with arbitrary passband

This paper proposes a new method of con structing the multirate FIR digital filter with arbitrary passband, using real-coefficient filters for the decimator and interpolator composing the multirate filter. It is already known that the bandpass filter can easily be realized using the complex-coefficient filter. In such a construction, however, the processing of the analytic signal is required using Hubert transform, which makes the whole system somewhat complex. From such a viewpoint, this paper pre sents a method of constructing the multirate bandpass digital filter using the real-coefficient filter. Another method is also presented, where the muitirate lowpass filter with arbitrary passband can be constructed by combining the complementary response and a lowpass filter. the multirate method is effective in realizing a narrowband response, but may not be useful in realizing a relatively wideband response. By the proposed method, the latter can easily be realized, drastically reducing the number of multiplications. Similar methods can be applied to highpass and bandstop filters.