Synthesis of Wideband Linear-Phase FIR Filters with a Piecewise-Polynomial-Sinusoidal Impulse Response

A method is presented to synthesize wideband linear-phase FIR filters with a piecewise-polynomial-sinusoidal impulse response. The proposed method is based on merging the earlier synthesis scheme proposed by the authors with the method proposed by Chu and Burrus and by modifying it by using an arbitrary number of separately generated center coefficients instead of only one used in the method by Chu-Burrus. The desired impulse response is created by using a parallel connection of several filter branches and by adding an arbitrary number of center coefficients to form it. The arithmetic complexity of these filters is proportional to the number of branches, the common polynomial order for each branch, the number of separate center coefficients, and the number of complex multipliers. The filter coefficients are optimized by using linear programming. An example shows the benefits of these filters with regard to reducing the number of coefficients as well as the arithmetic complexity.