Discrete Time Signal Correlation

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Correlation of Discrete Time Signals”.

1. 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

2. The cross correlation of two real finite energy sequences x(n) and y(n) is given as __________
a) rxy(l)=∑∞n=−∞x(n)y(n−l) where l=0,±1,±2,…
b) rxy(l)=∑∞n=0x(n)y(n−l) where l=0,±1,±2,…
c) rxy(l)=∑∞n=−∞x(n)y(n−l) where -∞<l<∞
d) none of the mentioned

3. Which of the following relation is true?
a) rxy(l)= rxy(-l)
b) rxy(l)= ryx(l)
c) rxy(l)= ryx(-l)
d) none of the mentioned
.

4. 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}

5. Which of the following is the auto correlation of x(n)?
a) rxy(l)=x(l)*x(-l)
b) rxy(l)=x(l)*x(l)
c) rxy(l)=x(l)+x(-l)
d) None of the mentioned

6. 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)+2abrxy(0)
b) a2rxx(0)+b2ryy(0)-2abrxy(0)
c) a2rxx(0)+b2ryy(0)+2abrxy(1)
d) a2rxx(0)+b2ryy(0)-2abrxy(1)

7. What is the relation between cross correlation and auto correlation?
a) |rxy(l)|=rxx(0).ryy(0)−−−−−−−−−−√
b) |rxy(l)|≥rxx(0).ryy(0)−−−−−−−−−−√
c) |rxy(l)|≠rxx(0).ryy(0)−−−−−−−−−−√
d) |rxy(l)|≤rxx(0).ryy(0)−−−−−−−−−−√
≤rxx(0).ryy(0)−−−−−−−−−−√.

8. 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

9. Auto correlation sequence is an even function.
a) True
b) False

10. What is the auto correlation of the sequence x(n)=anu(n), 0<a<l?
a) 11−a2 al (l≥0)
b) 11−a2 a-l (l<0)
c) 11−a2 a|l|(-∞<l<∞)
d) All of the mentioned

11. Which of the following relation is true?
a) ryx(l)=h(l)*ryy(l)
b) rxy(l)=h(l)*rxx(l)
c) ryx(l)=h(l)*rxx(l)
d) none of the mentioned

12. If x(n) is the input signal of a system with impulse response h(n) and y(n) is the output signal, then the auto correlation of the signal y(n) is?
a) rxx(l)*rhh(l)
b) rhh(l)*rxx(l)
c) rxy(l)*rhh(l)
d) ryx(l)*rhh(l)

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