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.