The round-trip error bound

ProofFoundation⏱ 15 minQuantizationroundingbound

Theory: Uniform Quantization and Its Error →

Problem

Prove that an affine quantizer with step $\Delta$ satisfies $|\widehat x - x| \le \Delta/2$ for every unclipped $x$ , and show the bound is attained. Then show that the bound fails, and by how much, when $x$ lies outside the clipping range.

Write a complete argument. Every inequality you use should be one you could state precisely.

Solution

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

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