Designing One-Dimensional FIR Filters with Arbitrary Frequency Response Using Second-Order Cone Programming Theory

In this paper, we employ second-order cone programming (SOCP) theory to design one-dimensional FIR filters with arbitrary frequency responses. This methodology enables flexible control over filter frequency characteristics to meet diverse application requirements. SOCP serves as a powerful optimization framework that enhances filter design efficiency and performance through convex optimization techniques. The implementation typically involves formulating filter design constraints as second-order cone constraints and solving them using optimization solvers like MATLAB's fmincon or CVX toolbox. Key steps include defining frequency response specifications, constructing the SOCP problem with magnitude/phase constraints, and implementing the optimization algorithm to obtain optimal filter coefficients. Through meticulous design incorporating SOCP principles, we achieve superior signal processing accuracy and filtering performance. This study explores methodological approaches and technical nuances of applying SOCP theory to one-dimensional FIR filter design, demonstrating practical implementation strategies for obtaining optimized results in digital signal processing applications.