Unitary and nonunitary filter banks with uniform frequency separation have been extensively studied in the past. Improvement in coding gain has been achieved when allowing for nonunitary filter banks in image coders. Subjective improvements can be achieved by employing nonuniform filter banks.
The paper presents a method to construct nonuniform nonunitary perfect reconstruction filter banks. A polyphase matrix representation of nonuniform parallel filter banks is given for octave band splitting. In this case, results show that the parallel filter banks tend to become the tree-structured filter banks. It is further shown that the perfect reconstruction property can be met only by examining each stage of the tree-structured system in a polyphase matrix representation. Finally, frequency responses are presented when the filter banks are optimized for coding gain.