A higher order generalization of magnitude and power complementary filters is proposed. The proposed scheme is shown to have superior frequency characteristics compared to the ordinary complementary filters. Applications of these generalized complementary filters include subband coding for audio and video and sharpening of magnitude characteristics of digital filters. This new design procedure can be used to generate ordinary multichannel magnitude and power complementary filters with sharper passband responses. A new method is outlined to obtain the class of filters that satisfies the higher order complementary condition for an arbitrary number of channels. >