Fixed-point protoype design for biorthogonal modulated filter banks

In this paper, we consider optimizing the prototype filter of biorthogonal cosine-modulated filter banks in order to reduce overflow occurrence in a fixed-point implementation. We assume that the wordlength of the fixed-point implementation is constant throughout the implementation. We implement the polyphase filters in a form which is inherent to perfect reconstruction. However, the frequency response is subject to fixed-point error, most dominantly overflow. We demonstrate that the floating-point prototype filter with the lowest stopband energy does not result in the fixed-point implementation with the best performance. Based on this result, we show how the fixed-point performance can be improved by preventing amplification by large filter coefficients and by modifying the cost function of the optimization in such a way that all filters have a similar gain. Since the filter bank allows an integer-to-integer mapping with no increase in wordlength, it is well suited for lossless compression algorithms as well as a fast and inexpensive implementation on a hardware platform with fixed-point number format.