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Mode splitting induced by coherent optical mode interference in coupled resonant cavities is a key phenomenon in photonic resonators that can lead to powerful and versatile filtering functions, in close analogy to electromagnetically-induced-transparency, Autler-Townes splitting, Fano resonances, and dark states. It can not only break the dependence between quality factor, free spectral range, and physical cavity length, but can also lead to group delay response and mode interactions that are useful for enhancing light-material interaction and dispersion engineering in nonlinear optics. In this work, we investigate mode splitting in standing-wave (SW) resonators implemented by cascaded Sagnac loop reflectors (CSLRs) and demonstrate its use for engineering the spectral profile of integrated photonic filters. By changing the reflectivity of the Sagnac loop reflectors (SLRs) and the phase shifts along the connecting waveguides, we tailor mode splitting in the CSLR resonators to achieve a wide range of filter shapes for diverse applications including enhanced light trapping, flat-top filtering, Q factor enhancement, and signal reshaping. We present the theoretical designs and compare the performance of CSLR resonators with three, four, and eight SLRs fabricated in silicon-on-insulator nanowires. We achieve high performance and versatile filter shapes via diverse mode splitting that agree well with theory. The experimental results confirm the effectiveness of our approach towards realizing integrated multi-functional SW filters for flexible spectral engineering.