Optimal design of transform-based block digital filters using a quadratic criterion

Block digital filtering is a powerful tool to reduce the computational complexity of digital filtering systems. However, due to their block structure, block digital filters (BDFs) are time-varying linear systems, hence, their design is not easy. The most widely spread approaches to BDF design consist of constraining the BDF to be time-invariant (by restricting the design process to a specific subset of possible solutions) and then using conventional filter synthesis techniques. In this paper, we do not restrict the design process, and we propose a simple and optimal matrix-oriented approach to optimize the BDF coefficients. Furthermore, the proposed approach takes profit of the structure of transform-based BDFs to considerably reduce the computational complexity and memory requirements of the design process. Experimental results confirm that as expected, the obtained global distortion is lower than the distortion obtained with a traditional technique such as overlap-save.