An apparatus may include a delta sigma modulator. A first portion of the delta sigma modulator may form a digital predictor while a second portion of the delta sigma modulator may form an analog approximator. An output of the analog approximator may be coupled with a quantizer. The digital predictor, the analog approximator, and the quantizer may form a digitizing loop configured to convert an analog input into a digital output. The digital predictor may be configured to generate, based on a polarity of one or more digital outputs from the quantizer, a digital prediction of an expected amplitude of the analog input. The quantizer may be configured to respond to the digital prediction by adjusting a dynamic range of the digitizing loop including by changing a quantization step size used by the quantizer to quantize the analog input. Related methods are also provided.