Abstract
AbstractThis paper considers digital filters with hyper‐complex coefficients. Filters of this type can reduce the order of filters to one‐fourth the one with real coefficients. It is reported that the first‐order digital filter with hypercomplex coefficients can realize the fourth‐order digital filter with real coefficients which can be expressed by a second‐order all‐pass filter with complex coefficients.This paper considers also generalization including the foregoing special case and shows that the first‐order digital filter with hypercomplex coefficients can realize an arbitrary‐order digital filter with real coefficients less than 4.Arbitrary higher‐order digital filter with real coefficients can be realized by parallel connection or cascade connection of first‐order digital filters with hypercomplex coefficients. This paper considers the following three different realizations: (a) realization by parallel connection; (b) realization by cascade connection of real part; and (c) realization by cascade connection. We find that case (b) is the most low sensitive. Finally, stability criteria of hypercomplex digital filters of first‐order are suggested.
Published Version
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