Design of approximately linear phase lattice digital allpass filters via lattice parameters

The design of lattice allpass subfilters approximating linear phase in passband and stopband is studied. The problem is reduced to a nonlinear optimization inside a hypercube in the lattice parameters space and solved using Fletcher-Powell algorithm. Using the recursive expressions for the phase response of lattice allpass filters, the authors also illustrate a simple method for fast design. This method uses one-variable optimization techniques and enables one to acquire initial values of lattice parameters for the optimization algorithm. It is shown that the method results in filters that are close to the optimum solution, from various design examples