  A new optimization method for the design of nearly linear-phase IIR digital
filters that satisfy prescribed specifications is proposed. The group-delay
deviation is minimized under the constraint that the passband ripple and
stopband attenuation are within the prescribed specifications and either a
prescribed or an optimized group delay can be achieved. By representing the
filter in terms of a cascade of second-order sections, a non-restrictive
stability constraint characterized by a set of linear inequality constraints
can be incorporated in the optimization algorithm. An additional feature of the
method, which is very useful in certain applications, is that it provides the
capability of constraining the maximum gain in transition bands to be below a
prescribed level. Experimental results show that filters designed using the
proposed method have much lower group-delay deviation for the same passband
ripple and stopband attenuation when compared with corresponding filters
designed with several state-of-the-art competing methods.
