This paper is concerned with the design of nearly linear phase IIR two-channel filter banks. Exactly linear phase IIR filters are employed in analysis filter banks, and nearly linear phase IIR synthesis filter banks are designed such that the overall filter banks are approximately linear phase. The filter bank design problem is formulated as a H/sub /spl infin// norm minimization of the difference between pure delay and products of some polyphase components. The H/sub /spl infin// norm optimizing problem is converted to a series of LMIs and solved by semidefinite programming. The magnitude, phase and aliasing distortions are all incorporated in the design procedure. The designed filter banks found application in image coding.