Two-Channel, Separable, Complex, Biorthogonal, Perfect Reconstruction Filter Banks

This paper demonstrates the design of two-channel, separable, complex, biorthogonal perfect reconstruction filters (BPRFs), which are filters which form perfect reconstruction filter banks. Separable complex perfect reconstruction filters (PRFs) are PRFs in which the real or imaginary part is also a valid real PRF pair. Separable complex filters are designed in a two step process of first designing a real PRF pair then finding a "complex complementary" filter pair that results in an overall complex PRF. Previous research parameterized separable PRFs for the orthogonal case. The limited design flexibility and limited practical applications in the orthogonal case motivated this investigation of separable complex filters for the biorthogonal case. The analysis and results in this paper are limited only to biorthogonal filters which are symmetric.