Optimal design of multichannel transmultiplexers with stopband energy and passband magnitude constraints

Optimal design incorporating filter stopband energy and passband magnitude constraints is studied for multichannel, uniform, and nonuniform transmultiplexers. Central to the development is a reformulation of the design problem as a quadratic programming problem with quadratic constraints and semi-infinite constraints while the composite distortion measure for reconstruction is minimized. An iterative optimal design procedure for finite-impulse-response synthesis and analysis filters is developed and applied to two design examples, one for the uniform case and another for the nonuniform case based on general building blocks.