Non-causal complementary filters (Q1196235)

Introducing the idea of non-causal filtering into the design of complementary filter pairs, an extension of this filter is obtained. It is also shown that the magnitude of any non-causal complementary filter is the cosine of its phase. Using a lemma about non-causal polynomials for a given filter order, the number of poles outside the unit circle can be selected. Possibilities like maximum-ripple filters and filters with fixed passband or stopband edge frequency are examined. The methods seems to be also interesting in cases where either downsampling cannot be applied, like wide-band design, or where downsampling factors are small.