An example apparatus includes an input circuit including a first adder and a first multiplier, the first adder configured to level-shift an input signal by an amount and the first multiplier configured to multiply output of the adder by a factor. The apparatus further includes a multi-stage noise shaping (MASH) circuit having an input coupled to the first multiplier. The apparatus further includes an output circuit including a second multiplier and a second adder, the second multiplier configured to multiply output of the MASH circuit by a reciprocal of the factor and the second adder configured to level-shift output of the second multiplier by an inverse of the amount.