Optimal design of multi-channel transmultiplexers with stopband energy constraints

Optimal design incorporating filters' stopband energy constraints for multi-channel, uniform and non-uniform transmultiplexers is studied. Central to the development is a reformulation of the design problem as a quadratically constrained quadratic programming problem where the stopband energy requirements are met by imposing a systems of quadratic constraints while the composite distortion measure proposed for reconstruction is minimized. An iterative optimal design procedure for FIR, synthesis filters and analysis filters is developed and applied to two design examples, one for the uniform case and the other for the nonuniform case.