Design of FIR filter over a discrete coefficient space with applications to HDTV signal processing

A new algorithm for the optimal design of finite impulse response (FIR) filters over a discrete coefficient space is presented. The algorithm is based on the branch and bound algorithm, where each of the subproblems are solved with a reduced number of constraints by exploiting the dependencies between the subproblems. As a result, the computation time is significantly reduced as compared to the conventional branch and bound algorithm. Some technical aspects in applying the filter with CSD (canonic signed digit) coefficient for image interpolation are presented. It is shown that minimizing the error at the critical frequencies is more important than minimizing the maximum ripple in the case of image interpolation. The filter designed by rounding one of the continuous coefficients to the nearest CSD value provides better results than the filter designed by the optimal algorithm