A circuit in an analog-to-digital converter (ADC) includes an amplifier configured to receive an output of a backend DAC; a harmonic distortion correction circuit (HDC) coupled to the amplifier and configured to correct distortion components due to the residue amplifier present in a digital signal from the backend ADC, the HDC circuit providing an output to an adder, the adder receiving a coarse digital output from a coarse ADC; and a DAC noise cancellation circuit (DNC) configured to provide an output to the adder, wherein the DNC circuit is configured to correct distortion components due to the DAC present in the digital signal from the backend ADC; wherein the output of the adder is an ADC digital output and wherein the ADC digital output forms an input to the HDC and the DNC.