Variable digital filter design with least square criterion subject to peak gain constraints

Variable digital filters (VDFs) are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this paper, we present a formulation that allows the trade-off between the integral squared error and the maximum deviation from the desired response in the passband and stopband. With this formulation, the maximum deviation can be reduced below the least square solution with a slight change in the performance of the integral squared error. Similarly, the total square error can be reduced below the minmax solution with a minor change in the maximum deviation from the minmax solution. Numerical schemes with adaptive grid size are presented for solving the optimization problems.