Question

The in-band quantization noise variance is given as?

(a) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^3 S_e (F)dF\)

(b) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^2 S_e (F)dF\)

(c) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^1 S_e (F)dF\)

(d) None

The question was asked in an online quiz.

The query is from Discrete-Time Processing of Continuous Time Signals in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct answer is (b) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^2 S_e (F)dF\)

The best I can explain: The in-band quantization noise variance is given as: \(\sigma_n^2=\int_{-B}^B |H_n (F)|^2 S_e (F)dF\) where \(S_e (F)=\frac{\sigma_e^2}{F_(s)}\) is the power spectral density of the quantization noise.