Design of Multi-Band Digital Filters and Full-Band Digital Differentiators Without Frequency Sampling and Iterative Optimization

Most design problems of digital filters (or differentiators) are formulated with a set of grid point in the frequency region (frequency sampling). These problems are usually difficult to solve, and often require iterative optimization. The objective of this paper is to provide an efficient and simplified design approach to multi-band filters (including low-pass filters or high-pass filters) as well as full-band differentiators. The proposed method does not require frequency sampling and iterative optimization to compute the coefficients of the filters or that of the differentiators. The magnitude and phase specifications are simultaneously approximated, and the errors in the specified frequency bands are controlled by using frequency-weighting factors. In addition, a maximum pole radius, which corresponds to a stability margin, can be specified to robustly ensure the stability of the filters or the differentiators. To evaluate the efficiency of proposed method, we compare the proposed method with several established methods. Simulation results show that, although the propose method does not utilize frequency sampling and iterative optimization, the designed filters and differentiators have sufficient performance.