Design of Linear-phase Fir Filters with Minimum Hamming Distance

In this paper a new approach for the design of linear phase FIR filters with discrete coefficients is proposed. A mixed integer linear programming (MILP) problem is formulated that minimizes the total Hamming distance between the adjacent coefficients, i.e., the number of bit switches of the coefficients. The Hamming distance between the coefficients is a good measure of the power consumption, when the FIR filters is implemented on a programmable architecture. The method is applicable both for filters with a specified passband gain and filters where the normalized peak ripple magnitude is of interest. In both cases the globally minimal solution is found subject to the filter specification, filter order, and number of coefficient bits. A preprocessing method that removes a significant part of the variables is also proposed and it is shown by an example that this method speeds up the optimization process significantly. Both two’s complement and signed magnitude representation of the coefficients are considered.