A noise shaping module includes a first addition module that receives an N-bit digital input signal, where N is an integer greater than one. A first filter module generates a first filtered output signal based on an output signal of the first addition module. A truncation module generates an M-bit truncated output signal based on the first filtered output signal, where M is an integer less than N. A second filter module generates a second filtered output signal based on the M-bit truncated output signal. The second filtered output signal is an input to the first addition module.