Filter Bank Design using Nilpotent Matrices

We present a simple design method for FIR N-band filter banks based on nilpotent matrices. Our design allows for diffferent filter lengths for the analysis and synthesis and can be used to build causal filter banks with explicit control over the system delay. This method can be used e.g to design filterbanks for audio coding with reduced pre-echoes. Longer filters could be used for the encoder to obtain good redundancy reduction by better frequency selectivity, and shorter filters in the decoder to limit the time domain spreading of the quantization noise.