Modulated filter bank design with nilpotent matrices

Gerald Schuller; Wim Sweldens

doi:10.1117/12.366788

26 October 1999 Modulated filter bank design with nilpotent matrices

Gerald Schuller, Wim Sweldens

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366788
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

We present a technique based on nilpotent matrices for building filter banks with FIR filters and perfect reconstruction. The general design method can be used to design bi-orthogonal filters with unequal filter lengths between analysis and synthesis. This is useful for audio or image coding applications. We can also explicitly control the overall system delay of causal filter banks. 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. The general theory is then applied to the design of cosine modulated filter banks. This leads to an efficient implementation, and it is shown that in this case the filters have to have the same length for analysis and synthesis.

Citation Download Citation

Gerald Schuller and Wim Sweldens "Modulated filter bank design with nilpotent matrices", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366788

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