Optimal design and verification of temporal and spatial filters using second-order cone programming approach

Temporal filters and spatial filters are widely used in many areas of processing. A number of optimal design criteria to these problems are available in literature. Various computational techniques are also presented to optimize these chosen. There are many drawbacks in these methods. In this paper, we introduce a framework for optimal design of temporal and spatial filters. Most of the optimal problems of FIR filters and beamformers are included in the framework. It is shown that the design problems can be reformulated as convex optimization form as the cone programming (SOCP) and solved efficiently via the well-established interior methods. The main advantage of our SOCP approach as compared with earlier approaches is that it can include most of the existing methods as its special cases, leads to more flexible designs. Furthermore, the SOCP approach can optimize required performance measures, which is the drawback of earlier approaches. The approach is also developed to optimally design temporal and spatial two-dimensional and spatial matrix filter. Numerical results demonstrate the effectiveness of the approach.