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

If the quantization error is uniformly distributed in the range (-Δ/2

1.	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» CORRECT option is (a) \(P_n=\sigma_e^2=\Delta^2/12\) The explanation is: \(P_n=\sigma_e^2=\int_{-\Delta/2}^{\Delta/2} e^2 P(e)DE=1/\Delta \int_{\frac{-\Delta}{2}}^{\frac{\Delta}{2}} e^2 de = \frac{\Delta^2}{12}\).

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