Design of variable lowpass FIR filters with flat magnitude and group delay constraints

This paper describes the design of variable FIR filters which have magnitude and group delay flatness at ω = 0, and have zeros at ω = π. The filter coefficients are given by multidimensional polynomials of variable parameters to specify variable frequency characteristics, and optimal polynomial coefficients are obtained by minimizing squared error function subject to flat magnitude and group delay constraints. The flatness conditions are transformed so as to be satisfied irrespective of variable parameters. Because the derived conditions are given as simple equality constraints, the optimal polynomial coefficients can be easily obtained. A numerical example is given to show the validity of the proposed technique.