Determining whether two signals are othogonal?

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silent7

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Hi there How do I determine whether two signals are orthogonal to one another?, given the following


Ive used this integral but I'm not sure if it is correct.

(edit:integral here should be without w(x) )

integral from 0 to 1 of f(t) multiplied with integral of g(t) for the same time period
where f(t) = t, and g(t) = -t+1
gives me 0, for that time period.
so..

0<t<1 integral was 0
1<t<2 integral was 7/3
2<t<3 integral was -19/3
3<t<4 integral was 37/3

I summed all the above and got 25/3. (25/3 > 0 )
is this correct and does this indicate that this is not in fact orthogonal?
 
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I don't have mat lab, I'm just wondering if the working and method is correct
 

you are using the right formula. if the intg ans is 0 signals are orthogonal.
 

malik_zohaib said:
you are using the right formula. if the intg ans is 0 signals are orthogonal.
Click to expand...

oh thanks. Is summing the intg through the given time domain also correct in my case?. [ie 0 + (7/3) + (-19/3) + (37/3)]
 

during 0<t<1 g(t) is -t+1 and f(t) is t
intg (0 to 1) giver>> intg(-t^2 + t) >> -t^3/3 + t^2/2 after applying limits -1/3 + 1/2 is not zero, am i right??
then how can you say "0<t<1 integral was 0"
check again all your intg and sum up if 0 then signals are orthogonal
 

I summed all the above and got 25/3. (25/3 > 0 )
is this correct and does this indicate that this is not in fact orthogonal?
Click to expand...
integral from 0 to 1 of f(t) multiplied with integral of g(t)
Click to expand...
1. Your method to calculate integral of a product is wrong.
2. The results are wrong anyway, either for your or the correct method.
integral here should be without w(x)
Click to expand...
3. You didn't understand the purpose of the weight function w(x). Although f(t) and g(t) are actually orthogonal on the interval [0,4] with w(t) equals unity (with convenient selection of f(t) and g(t)), this is not the general case of orthogonality.
 

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