This paper reports a novel application of receding finite horizon constrained optimization techniques to design an audio-band full digital amplifier. The digital amplifier using power MOSFET requires a modulator to modulate the reference signal into binary sequences. The modulator can be viewed as an over-sampled quantizer with noise-shaping requirement. One of the main issues in designing the modulator is to maintain stability while maximizing the range of the reference input signal. The quantization scheme resulting from the optimization is derived in detail to arrive at the stability condition under zero initial conditions. It shows the stability condition becomes more stringent when the relative degree of the shaping filter is high. Simulations results are given to illustrate the effectiveness of the design methodology.