Algorithm of variable transition bandwidth FIR filters with weighted-least-square method

This paper deals with the design of variable bandwidth linear-phase FIR digital filters by weighted least square method. This proposed algorithm is constructed by a linear combination of fixed-coefficient linear-phase filters, of which the variable bandwidth characteristics are provided by an embedded tuning parameter. Using the weighted least square objective function, the optimal solution is obtained by solving a set of linear equation, which is an error function reflecting the difference between the desired variable bandwidth filter and the practical filter. The proposed algorithm can implement the variable digital filter efficiently by the familiar Farrow structure with only one variable spectral parameter that determines the bandwidth. Mathematics deduction and simulations show this algorithm is simple and effective in designing FIR variable digital filter with better performance than previous ones.