What is the variance of the difference between two successive signal samples, d(n) = x(n) – x(n-1)?(a) \(σ_d^2=2σ_x^2 [1+γ_{xx} (1)]\)(b) \(σ_d^2=2σ_x^2 [1-γ_{xx} (1)]\)(c) \(σ_d^2=4σ_x^2 [1-γ_{xx} (1)]\)(d) \(σ_d^2=3σ_x^2 [1-γ_{xx} (1)]\)This question was posed to me in an interview for internship.This is a very interesting question from Oversampling A/D Converters in section Sampling and Reconstruction of Signals of Digital Signal Processing

What is the variance of the difference between two successive signal s

1.	What is the variance of the difference between two successive signal samples, d(n) = x(n) – x(n-1)?(a) \(σ_d^2=2σ_x^2 [1+γ_{xx} (1)]\)(b) \(σ_d^2=2σ_x^2 [1-γ_{xx} (1)]\)(c) \(σ_d^2=4σ_x^2 [1-γ_{xx} (1)]\)(d) \(σ_d^2=3σ_x^2 [1-γ_{xx} (1)]\)This question was posed to me in an interview for internship.This is a very interesting question from Oversampling A/D Converters in section Sampling and Reconstruction of Signals of Digital Signal Processing
Answer» The correct answer is (b) \(σ_d^2=2σ_x^2 [1-γ_{XX} (1)]\) Explanation: \(σ_d^2=E[d^2 (n)] = E{[X(n)- x(n-1)]^2}\) = \(E [x^2 (n)]-2E{x(n)x(n-1)}+E[x^2 (n-1)]\) = \(2σ_x^2 [1+γ_{xx} (1)]\).

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