Constrained eigenfilter allpass design for photonic systems

We present a least squares based allpass filter design with a prescribed maximum pole magnitude constraint suitable for photonic systems. The constraint comes from the physical limitations of realizing digital filters using photonic components, and must be addressed in the designing phase. We develop our design algorithm following the eigenfilter approach for allpass filters. The constraint is formulated using the Argument Principle and modified to match the eigenfilter objective function. An iterative approach is then employed to obtain the filter coefficients that best satisfy both the objective function and the constraint. Our algorithm will be ideal for yielding allpass filters suitable for narrowband designs that are common to the optical domain. Examples relevant to filtering in the optical frequency range are subsequently demonstrated. Physical origins of the pole magnitude constraints are also briefly explained.