Filter bank design using nilpotent matrices

We present a design method for filter banks with unequal length of the impulse responses for the analysis and synthesis part. This is useful e.g. for audio coding applications. A further advantage of the design method is the possibility to explicitly control the overall system delay of the filter bank, when causal filters are desired. The design method is based on a factorization of the polyphase matrices into factors with nilpotent matrices. These factors guarantee mathematical perfect reconstruction of the filter bank, and lead to FIR filters for analysis and synthesis. Using matrices with nilpotency of higher order than 2 leads to FIR filter banks with unequal filter length for analysis and synthesis.