This thesis aims to develop an improved and high-robust infinite impulse response (IIR) digital filter using software implementations. For an nth order filter, at most 4n+1 multiplications are needed per output sample. Moreover, the developed structure of the filter is suitable for parallel processing, and thus can be efficiently performed in the computer system of which with multiple cores or processors, such as smart phones, or backend or cloud servers. The key techniques in this thesis are based on a sparse normal-matrix as well as the trace inequality of John von Neumann such that the optimal filter realization in the sense of pole-zero sensitivity can be synthesized analytically. The developed filter structure in this the-sis can be simultaneously with good computational performance, low computational complexity, and high robustness (low quantization errors and limit-cycle free property).
