Filter Design (MATLAB and Mathematica-Based Design Methods)

Filter design represents a critical domain in signal processing. This article presents original MATLAB and Mathematica-based design methodologies for implementing multiplier-free elliptic IIR filters, emphasizing computationally efficient implementations through coefficient quantization and shift-and-add operations. The developed algorithms demonstrate significant potential in practical filter design applications by eliminating hardware multipliers while maintaining frequency response specifications. The provided code frameworks facilitate streamlined filter design workflows, supporting diverse signal processing requirements through customizable passband/stopband parameters and ripple controls. As a fundamental signal processing technique, proficient filter design enables effective noise suppression, signal enhancement, and improved output reliability - making mastery of these methods particularly valuable for professionals working with digital signal processing systems. The implementation includes key functions for elliptic approximation calculations, coefficient conversion to power-of-two representations, and structural optimization for multiplier-free architectures.