Hybrid method for designing digital Butterworth filters

A procedure for designing digital Butterworth filters is proposed. The procedure determines the denominator and the numerator of the filter transfer function based on the positions of the poles in the s-plane and zeros in the z-plane, respectively, and calculates the gain factor using a maximum point normalization method. In contrast to some conventional algorithms, the presented procedure is much simpler by directly obtaining the filter with 3-dB frequencies. This makes the presented algorithm a useful tool for determining the boundaries in electronic or communication systems' frequency responses. Moreover, the proposed algorithm is compatible with high-order transformations which are the limitations of general pole-zero placement techniques. The proposed method is illustrated by the examples of designing the low-pass, high-pass, band-pass, and band-stop filter.