Optimal quantization levels Minimize distortion D 对)f(x Optimal value affects distortion only within its region 220-8(8=0 xf(x a-1sx sa, )dx =EXa sosaI Quantization values should be the" centroid of their regions The conditional expected value of that region Approach can be used to find optimal quantization values for the uniform quantizer as well Slide 10Optimal quantization levels ai • Minimize distortion, D DR = ∫ ( x − x√ i) fx ( x ) dx ai−1 – Optimal value affects distortion only within its region − dDR = ∫ ai 2 (x x√ i)2 fx ( x ) dx = 0 dx√ ai−1 i ai x√ i = ∫ xfx (| ai−1 ≤ x ≤ ai x ) dx ai−1 [| ai−1 ≤ x ≤ ai – x√ ] i = E X • Quantization values should be the “centroid ” of their regions – The conditional expected value of that region • Approach can be used to find optimal quantization values for the uniform quantizer as well Eytan Modiano Slide 10