Design of FIR digital filters with discrete coefficients via convex relaxation

Digital filters with discrete coefficients that can be expressed as sums of power of two (SP2) are of practical use because they admit fast implementations that do not require multiplications. In this paper, a new method for the design of finite-impulse-response (FIR) digital filters with SP2 coefficients by convex relaxation is proposed. The major difference of the proposed method from the semidefinite programming relaxation (SDPR) method proposed in the literature is that a sequential convex quadratic programming relaxation (QPR) in conjunction with a low-bit descent search technique replaces SDPR, yielding much reduced algorithmic complexity. Design examples are presented to illustrate the proposed algorithm and to demonstrate its near optimal performance against a weight least squares error measure.