This paper reports a novel application of 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. An FPGA (Field Programmable Gate Array) implementation of the finite horizon constrained optimization technique to construct the modulator is presented. Experimental results are shown by driving the loudspeaker load.