A noise-shaping module including a first addition module configured to receive a digital input signal and a filtered output signal. A truncation module is configured to remove selected bits from the digital input signal and output a truncated output signal. The truncated output signal corresponds to the digital input signal with the selected bits removed. A second addition module is configured to output a difference signal. The difference signal is based on a difference between the digital input signal and the truncated output signal. A filter module is configured to generate the filtered output signal based on the difference signal and provide the filtered output signal to the first addition module.