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Test: Discrete Time Signal Correlation


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10 Questions MCQ Test Digital Signal Processing | Test: Discrete Time Signal Correlation

Test: Discrete Time Signal Correlation for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The Test: Discrete Time Signal Correlation questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Discrete Time Signal Correlation MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Discrete Time Signal Correlation below.
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Test: Discrete Time Signal Correlation - Question 1

Which of the following parameters are required to calculate the correlation between the signals x(n) and y(n)?

Detailed Solution for Test: Discrete Time Signal Correlation - Question 1

Explanation: Let us consider x(n) be the input reference signal and y(n) be the reflected signal.
Now, the relation between the two signals is given as y(n)=αx(n-D)+w(n)
Where α-attenuation factor representing the signal loss in the round-trip transmission of the signal x(n)
D-time delay between the time of projection of signal and the reflected back signal
w(n)-noise signal generated in the electronic parts in the front end of the receiver.

Test: Discrete Time Signal Correlation - Question 2

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

Detailed Solution for Test: Discrete Time Signal Correlation - Question 2

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

Test: Discrete Time Signal Correlation - Question 3

Which of the following relation is true? 

Detailed Solution for Test: Discrete Time Signal Correlation - Question 3

Explanation: we know that, the correlation of two signals x(n) and y(n) is

Test: Discrete Time Signal Correlation - Question 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….}

Detailed Solution for Test: Discrete Time Signal Correlation - Question 4

Explanation:

Test: Discrete Time Signal Correlation - Question 5

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

Detailed Solution for Test: Discrete Time Signal Correlation - Question 5

Explanation: We know that, the correlation of two signals x(n) and y(n) is

Test: Discrete Time Signal Correlation - Question 6

What is the relation between cross correlation and auto correlation? 

Detailed Solution for Test: Discrete Time Signal Correlation - Question 6

Explanation:
We know that, a2rxx(0)+b2ryy(0)+2abrxy(l) ≥0
=> (a/b)2rxx(0)+ryy(0)+2(a/b)rxy(l) ≥0
Since the quadratic is nonnegative, it follows that the discriminate of this quadratic must be non positive, that is 4[r2xy(l)- rxx(0) ryy(0)] ≤0 =>|rxy(l)|≤√(rxx(0).ryy(0)).

Test: Discrete Time Signal Correlation - Question 7

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

Detailed Solution for Test: Discrete Time Signal Correlation - Question 7

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)= (rxx (l))/(rxx (0)).

Test: Discrete Time Signal Correlation - Question 8

Auto correlation sequence is an even function. 

Detailed Solution for Test: Discrete Time Signal Correlation - Question 8

Explanation: Let us consider a signal x(n) whose auto correlation is defined as rxx (l).
We know that, for auto correlation sequence rxx (l)=rxx (-l).
So, auto correlation sequence is an even sequence.

Test: Discrete Time Signal Correlation - Question 9

What is the auto correlation of the sequence x(n)=anu(n), 0<a<l? 

Detailed Solution for Test: Discrete Time Signal Correlation - Question 9

Explanation:

Test: Discrete Time Signal Correlation - Question 10

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: 

Detailed Solution for Test: Discrete Time Signal Correlation - Question 10

Explanation: ryy(l)=y(l)*y(-l)
=[h(l)*x(l)]*[h(-l)*x(-l)] =[h(l)*h(-l)]*[x(l)*x(-l)] =rhh(l)*rxx(l).

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