Questions: Answer the following multiple choice questions.

Q.1 The cross correlation of two real finite energy sequences x(n) and y(n) is given as:

a) r_xy(1) = Σ^∞_n=-∞ x(n)y(n-1) where 1 = 0, ±1, ±2, ...
b) r_xy(1) = Σ^∞_n=0 x(n)y(n-1) where 1 = 0, ±1, ±2, ...
c) r_xy(1) = Σ^∞_n=-∞ x(n)y(n-1) where 1 = -∞ < 1 < ∞
d) None of the mentioned

Q.2 What is the cross correlation sequence of the following sequences?
x(n)={....0,0,2,-1,3,7,1,2,-3,0,0....}
y(n)={....0,0,1,-1,2,-2,4,1,-2,5,0,0....}
a) {10,9,19,36,-14,33,0,7,13,-18,16,7,5,-3}
b) {10,-9,19,36,-14,33,0,7,13,-18,16,-7,5,-3}
c) {10,9,19,36,14,33,0,-7,13,-18,16,-7,5,-3}
d) {10,-9,19,36,-14,33,0,-7,13,18,16,7,5,-3}

Q.3 What is the energy sequence of the signal ax(n)+by(n-l) in terms of cross correlation and auto correlation sequences?
a) a²rxx(0)+b²ryy(0)+2abr_xy(0)
b) a²rxx(0)+b²ryy(0)-2abr_xy(0)
c) a²rxx(0)+b²ryy(0)+2abr_xy(1)
d) a²rxx(0)+b²ryy(0)-2abr_xy(1)

Q.4 The normalized auto correlation ρxx(l) is defined as:

a) (rxx (l))/(rxx (0))
b) -(rxx (l))/(rxx (0))
c) (rxx (l))/(rxy (0))
d) None of the mentioned

Q.5 What is the auto correlation of the sequence x(n)=aⁿu(n), 0

a) 1/(1-a² )a¹ (1≥0)

b) 1/(1-a² )a^-1 (1<0)
c) 1/(1-a² )a^|1|(-∞<1<∞)

d) All of the mentioned

Q.6 Which of the following parameters are required to calculate the correlation between the signals x(n) and y(n)?
a) Time delay b) Attenuation factor c) Noise signal d) All of the mentioned

Q.7 Which of the following relation is true?

a) r_xy(l)= r_xy(-l)
b) r_xy(l)= r_yx(l)
c) r_xy(l)= r_yx(-l)

d) None of the mentioned

Q.8 Which of the following is the auto correlation of x(n)?

a) r_xy(l)=x(l)*x(-l)
b) r_xy(l)=x(l)*x(l)
c) r_xy(l)=x(l)+x(-l)

d) None of the mentioned

Q.9 What is the relation between cross correlation and auto correlation?

a) |r_xy(l)|=√(r_xx(0).r_yy(0))
b) |r_xy(l)|≥√(r_xx(0).r_yy(0))
c) |r_xy(l)|≠√(r_xx(0).r_yy(0))
d) |r_xy(l)|≤√(r_xx(0).r_yy(0))

Q.10 Auto correlation sequence is an even function.

a) True
b) False