Optimal quantization regions Take derivative of d with respect to a Take derivative with respect to integral boundaries dD d=1()(-8)2(-2.)1=0 x+1 2 Boundaries of the quantization regions are the midpoint of the quantization values Optimality conditions 1. Quantization values are thecentroid"of their region 2. Boundaries of the quantization regions are the midpoint of the qui quantization values 3. Clearly 1 depends on 2 and visa-versa. The two can be solved iteratively to obtain optimal quantizerOptimal quantization regions • Take derivative of D with respect to ai – Take derivative with respect to integral boundaries dD 2 = f ai)[( ai − x√ i)2 − ( ai − x√ i+1 x ( )] = 0 dai x√ √x i + i+1 ai = 2 – Boundaries of the quantization regions are the midpoint of the quantization values • Optimality conditions: 1. Quantization values are the “centroid ” of their region 2. Boundaries of the quantization regions are the midpoint of the quantization values 3. Clearly 1 depends on 2 and visa-versa. The two can be solved iteratively to obtain optimal quantizer Eytan Modiano Slide 11