Question

What is the relation defined by the operation of quantizer?

(a) xq(n) ≡ Q[x(n)] = \(\hat{x}_k\)

(b) xq(n) = Q[x(n)] = \(\hat{x}_k\), if x(n) ∈ Ik

(c) xq(k) ≡ Q[x(k)] = \(\hat{x}_k\)

(d) none of the mentioned

The question was posed to me by my school principal while I was bunking the class.

My doubt is from Quantization and Coding in division Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

The correct option is (b) xq(n) = Q[x(n)] = \(\hat{x}_k\), if x(n) ∈ Ik

To explain: The possible outputs of the quantizer (i.e., the quantization levels) are denoted as \(\hat{x}_1, \hat{x}_2,…\hat{x}_L\). The operation of the quantizer is defined by the relation, xq(n) ≡ Q[x(n)]= \(\hat{x}_k\), if x(n) ∈ Ik.