Finding the optimal quantizer Start with arbitrary regions(e.g, uniform 4) A)Find optimal quantization values("centroids") B )Use quantization values to get new regions ("midpoints") Repeat a &B until convergence is achieved Can be done numerically for known distributions Table 6.3(p. 299)gives optimal quantizer for Gaussian source E.g., NE4, D=0.1175,H(Xx)=1911 Recall: uniform quantizer, D=0. 1188, H(x)=1.904(slight improvement -09816 04528 0.4528 09816 Slide 12 1.51∆ Finding the optimal quantizer • Start with arbitrary regions (e.g., uniform ) A) Find optimal quantization values (“centroids”) B) Use quantization values to get new regions (“midpoints”) – Repeat A & B until convergence is achieved • Can be done numerically for known distributions – Table 6.3 (p. 299) gives optimal quantizer for Gaussian source • E.g., N=4, – D = 0.1175, H(x) = 1.911 – Recall: uniform quantizer, D= 0.1188, H(x) = 1.904 (slight improvement) 0.9816 1.51 0.4528 -0.9816 -0.4528 Eytan Modiano Slide 12 - 1.51