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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))
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the relation between cross correlation and auto correlation?a)...
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)).
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)).
Most Upvoted Answer
What is the relation between cross correlation and auto correlation?a)...
The relation between cross correlation and auto correlation is as follows:
Cross correlation measures the similarity between two signals or sequences at different time lags. It is used to determine if there is a relationship or similarity between two signals, such as comparing a reference signal with a received signal to detect a specific pattern or signal.
Auto correlation, on the other hand, measures the similarity between different points in the same signal or sequence at different time lags. It is used to determine the presence of periodicity or repeating patterns within a signal.
The mathematical formula for cross correlation is:
rxy(l) = E[x(n) * y(n+l)]
where rxy(l) is the cross correlation between signals x and y at lag l, and E[] denotes the expected value.
The mathematical formula for auto correlation is:
rxx(l) = E[x(n) * x(n+l)]
where rxx(l) is the auto correlation of signal x at lag l.
In summary, cross correlation measures the similarity between two different signals at different time lags, while auto correlation measures the similarity between different points in the same signal at different time lags.
Cross correlation measures the similarity between two signals or sequences at different time lags. It is used to determine if there is a relationship or similarity between two signals, such as comparing a reference signal with a received signal to detect a specific pattern or signal.
Auto correlation, on the other hand, measures the similarity between different points in the same signal or sequence at different time lags. It is used to determine the presence of periodicity or repeating patterns within a signal.
The mathematical formula for cross correlation is:
rxy(l) = E[x(n) * y(n+l)]
where rxy(l) is the cross correlation between signals x and y at lag l, and E[] denotes the expected value.
The mathematical formula for auto correlation is:
rxx(l) = E[x(n) * x(n+l)]
where rxx(l) is the auto correlation of signal x at lag l.
In summary, cross correlation measures the similarity between two different signals at different time lags, while auto correlation measures the similarity between different points in the same signal at different time lags.
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