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A discrete integrator for switched-capacitor (SC) filter applications is developed. The proposed integrator is generated from an optimal linear combination of the lossless discrete integrator (LDI) and the bilinear discrete integrator, and therefore it is called the composite discrete integrator (CDI). This integrator is ideal for high-frequency applications because it doubles the normal folding frequency and minimises high-frequency discrete integrator errors. Several SC realisations of the CDI are given. SC circuits for emulating general first- and second-order analogue filter sections based on the CDI are also given.