What is the variance of the difference between two successive signal

1.	What is the variance of the difference between two successive signal samples, d(n) = x(n)–ax(n-1)?
A.	$σ_d^2=2σ_x^2 [1-a^2]$
B.	$σ_d^2=σ_x^2 [1+a^2]$
C.	$σ_d^2=σ_x^2 [1-a^2]$
D.	$σ_d^2=2σ_x^2 [1+a^2]$
Answer» D. $σ_d^2=2σ_x^2 [1+a^2]$

Discussion

1.	What is the variance of the difference between two successive signal samples, d(n) = x(n)–ax(n-1)?
A.	\(σ_d^2=2σ_x^2 [1-a^2]\)
B.	\(σ_d^2=σ_x^2 [1+a^2]\)
C.	\(σ_d^2=σ_x^2 [1-a^2]\)
D.	\(σ_d^2=2σ_x^2 [1+a^2]\)
Answer» D. \(σ_d^2=2σ_x^2 [1+a^2]\)