Optimal uniform quantizer Given the number of regions N Find the optimal value of a Find the optimal quantization values within each region Optimization over N+2 variables Simplification Let quantization levels be the midpoint of the quantization regions(except first and last regions, when input not finite valued) Solve for a to minimize distortion Solution depends on input pdf and can be done numerically for commonly used pdfs(e.g, Gaussian pdf, table 6. 2, p. 296 of text) Eytan Modiano∆ ∆ Optimal uniform quantizer • Given the number of regions, N – Find the optimal value of ∆ – Find the optimal quantization values within each region – Optimization over N+2 variables • Simplification: Let quantization levels be the midpoint of the quantization regions (except first and last regions, when input not finite valued) • Solve for ∆ to minimize distortion – Solution depends on input pdf and can be done numerically for commonly used pdfs (e.g., Gaussian pdf, table 6.2, p. 296 of text) Eytan Modiano Slide 7