Question

What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if Δ=2^-b?

(a) (0,Δ)

(b) (-Δ,0)

(c) (-Δ/2,Δ/2)

(d) None of the mentioned

I had been asked this question in exam.

I'd like to ask this question from Quantization Effects in the Computation of DFT in chapter DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

Answer 1

The correct choice is (c) (-Δ/2,Δ/2)

To explain: The Quantization errors due to rounding off are uniformly distributed random variables in the range (-Δ/2,Δ/2) if Δ=2^-b. This is one of the assumption that is made about the statistical properties of the quantization error.