Question

If the quantization error is uniformly distributed in the range (-Δ/2, Δ/2), the mean value of the error is zero then the variance Pn is?

(a) \(P_n=\sigma_e^2=\Delta^2/12\)

(b) \(P_n=\sigma_e^2=\Delta^2/6\)

(c) \(P_n=\sigma_e^2=\Delta^2/4\)

(d) \(P_n=\sigma_e^2=\Delta^2/2\)

The question was asked by my college director while I was bunking the class.

My question comes from Analysis of Quantization Errors in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct option is (a) \(P_n=\sigma_e^2=\Delta^2/12\)

The explanation is: \(P_n=\sigma_e^2=\int_{-\Delta/2}^{\Delta/2} e^2 p(e)de=1/\Delta \int_{\frac{-\Delta}{2}}^{\frac{\Delta}{2}} e^2 de = \frac{\Delta^2}{12}\).