Embodiments include integrator systems, switched-capacitor circuits, and methods of their operation. An integrator system comprises a differential amplifier and first and second sampling modules. The first sampling module includes a first capacitor and a first set of switches. The first set of switches changes a connection status between the first capacitor and first and second amplifier input terminals when a change in a polarity of a differential input signal does not occur between consecutive switching cycles, and refrains from changing the connection status when the change in the polarity does occur. The second sampling module includes a second capacitor and a second set of switches. The second set of switches changes a connection status between the second capacitor and the first and second amplifier input terminals when the change in the polarity does occur, and refrains from changing the connection status when the change in the polarity does not occur.