On Two-channel orthogonal cyclic filter banks with half-sample symmetric filters

This paper describes a design method of twochannel orthogonal cyclic filter banks with a linear phase for image coding. In the cyclic filter bank, all arguments are interpreted modulo some integer due to the periodicity of signals. This provides more degrees of freedom in design problems. In this paper, we present a systematic method to design two-channel linear phase orthogonal cyclic filter banks with real-valued coefficients. With the aim of employing half-sample symmetric cyclic filters, we derive a condition of the magnitude response for a cyclic filter bank to satisfy the orthogonality. The orthogonal cyclic filter bank with half-sample symmetric filters, which have a nearly ideal magnitude response at discrete values of the frequency, can be designed via the proposed scheme. As one design example, we show such a linear phase orthogonal cyclic filter bank with the period L = 32. Finally, several simulations that compare the performance of our designed cyclic filter bank, the conventional cyclic filter bank and the noncyclic Daubechies 9/7-tap filter bank in image compression are illustrated to evaluate the performance of the proposed approach for images with highly detailed content.