Abstract: 
	This paper presents novel results on the optimal
	design of Noise-Shaping Differential Pulse-Coded Modulation
	coders. The main contribution resides in the derivation of explicit
	analytic formulas for the optimal filters and the minimum
	achievable frequency weighted reconstruction error. A novel
	aspect in the analysis is the fact that we account for fed-back
	quantization noise and that we make no restrictions on the order
	of the filters deployed.