Digital Signal Processing

Correlation of Discrete Time Signals

Question 1
Marks : +2 | -2
Pass Ratio : 100%
What is the energy sequence of the signal ax(n)+by(n-l) in terms of cross correlation and auto correlation sequences?
a2rxx(0)+b2ryy(0)+2abrxy(0)
a2rxx(0)+b2ryy(0)-2abrxy(0)
a2rxx(0)+b2ryy(0)+2abrxy(1)
a2rxx(0)+b2ryy(0)-2abrxy(1)
Explanation:
The energy signal of the signal ax(n)+by(n-l) is
Question 2
Marks : +2 | -2
Pass Ratio : 100%
The normalized auto correlation ρxx(l) is defined as _____________
\\(\\frac{r_{xx}(l)}{r_{xx}(0)}\\)
–\\(\\frac{r_{xx}(l)}{r_{xx}(0)}\\)
\\(\\frac{r_{xx}(l)}{r_{xy}(0)}\\)
None of the mentioned
Explanation:
If the signal involved in auto correlation is scaled, the shape of auto correlation does not change, only the amplitudes of auto correlation sequence are scaled accordingly. Since scaling is unimportant, it is often desirable, in practice, to normalize the auto correlation sequence to the range from -1 to 1. In the case of auto correlation sequence, we can simply divide by rxx (0). Thus the normalized auto correlation sequence is defined as ρxx(l)=\\(\\frac{r_{xx}(l)}{r_{xx}(0)}\\).
Question 3
Marks : +2 | -2
Pass Ratio : 100%
What is the cross correlation sequence of the following sequences?
{10,9,19,36,-14,33,0,7,13,-18,16,7,5,-3}
{10,-9,19,36,-14,33,0,7,13,-18,16,-7,5,-3}
{10,9,19,36,14,33,0,-7,13,-18,16,-7,5,-3}
{10,-9,19,36,-14,33,0,-7,13,18,16,7,5,-3}
Explanation:
We know that rxy(l)=\\(\\sum_{n=-\\infty}^{\\infty} x(n)y(n-l)\\) where l=0,±1,±2,…
Question 4
Marks : +2 | -2
Pass Ratio : 100%
What is the auto correlation of the sequence x(n)=anu(n), 0<a<l?
\\(\\frac{1}{1-a^2}\\) al (l≥0)
\\(\\frac{1}{1-a^2}\\) a-l (l<0)
\\(\\frac{1}{1-a^2}\\) a|l|(-∞<l<∞)
All of the mentioned
Explanation:
Question 5
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the auto correlation of x(n)?
rxy(l)=x(l)*x(-l)
rxy(l)=x(l)*x(l)
rxy(l)=x(l)+x(-l)
None of the mentioned
Explanation:
We know that, the correlation of two signals x(n) and y(n) is rxy(l)=\\(\\sum_{n=-\\infty}^{\\infty} x(n)y(n-1)\\)
Question 6
Marks : +2 | -2
Pass Ratio : 100%
What is the relation between cross correlation and auto correlation?
|rxy(l)|=\\(\\sqrt{r_{xx}(0).r_{yy}(0)}\\)
|rxy(l)|≥\\(\\sqrt{r_{xx}(0).r_{yy}(0)}\\)
|rxy(l)|≠\\(\\sqrt{r_{xx}(0).r_{yy}(0)}\\)
|rxy(l)|≤\\(\\sqrt{r_{xx}(0).r_{yy}(0)}\\)
Explanation:
We know that, a2rxx(0)+b2ryy(0)+2abrxy(l) ≥0
Question 7
Marks : +2 | -2
Pass Ratio : 100%
Auto correlation sequence is an even function.
True
False
Explanation:
Let us consider a signal x(n) whose auto correlation is defined as rxx (l).
Question 8
Marks : +2 | -2
Pass Ratio : 100%
Which of the following relation is true?
rxy(l)= rxy(-l)
rxy(l)= ryx(l)
rxy(l)= ryx(-l)
none of the mentioned
Explanation:
we know that, the correlation of two signals x(n) and y(n) is
Question 9
Marks : +2 | -2
Pass Ratio : 100%
Which of the following parameters are required to calculate the correlation between the signals x(n) and y(n)?
Time delay
Attenuation factor
Noise signal
All of the mentioned
Explanation:
Let us consider x(n) be the input reference signal and y(n) be the reflected signal.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
The cross correlation of two real finite energy sequences x(n) and y(n) is given as __________
\\(r_{xy}(l)=\\sum_{n=-\\infty}^{\\infty}x(n)y(n-l)\\) where l=0,±1,±2,…
\\(r_{xy}(l)=\\sum_{n=0}^{\\infty}x(n)y(n-l)\\) where l=0,±1,±2,…
\\(r_{xy}(l)=\\sum_{n=-\\infty}^{\\infty}x(n)y(n-l)\\) where -∞<l<∞
none of the mentioned
Explanation:
If any two signals x(n) and y(n) are real and finite energy signals, then the correlation between the two signals is known as cross correlation and its equation is given as