Example x is uniformly distributed between-A and a f(x=1/2A,A<EX<=A and o otherwise · Uniform quantizer with n levels=>Δ=2AN Q(x]=quantization level midpoint of quantization region in which x lies D= E[e(x) 2] is the same for quantization regions D=Ee(x)2|x∈ R=2x2(x)s4 12 EIX=I xdx A2/3A2/3 SON N2,(△=2A/N) △2/12(2N2/12 Eytan Modiano∆ E X Example • X is uniformly distributed between -A and A – f(x) = 1/2A, -A<=x<=A and 0 otherwise • Uniform quantizer with N levels => ∆ = 2A/N – Q(x) = quantization level = midpoint of quantization region in which x lies • D = E[e(x)2] is the same for quantization regions D E e x 2 ∈ ∆ / 2 1 ∆ / 2 ∆2 = [( ) | x Ri] = ∫−∆ / 2 x2 f(x)dx = ∆ ∫−∆ / 2 x2 dx = 12 1 A 2 A2 [] = 2 A ∫− Ax dx = 3 A2 / 3 A2 / 3 SQNR= ∆2 /12 = (2 A N)2 /12 = N2 , (∆ = 2 A/ N) / Eytan Modiano Slide 5