definition of orthogonal?

[david753]

orthogonal variables definition

As everyone knows, the signal of sin(wt) and cos(wt) are orthogonal with each other due to the 90 degrees difference of phase.

But, beside that, sin(wt), sin(2*wt), sin(3*wt)...etc, are they orthogonal with each other? Such as OFDM system.

Does anyone can tell me what the clear and precise definitoin of orthogonal is expect 90 degrees difference of phase in the same frequency?

 

[Belsugului]

definition for orthogonal signal

By orthogonal in general is meant that the angle between two vector / plan is 90 degree. In case of sin(wt) and cos(wt) we have the 90 degree angkle between the two phasors (vectors with unity amplitude and roting anticlockwise with w frequency). Because the phase differnce between sin and cos is 90 degree so is between the phasors of them all the time.
sin(wt), sin(2wt) might be some momentums when there phasers are orthogonal but in most of the time they are not. In fact one phasor rotes with one frequency the other with the double of it.

Belsugului

 

[flatulent]

cosine definition of orthogonal signal

Mathematically, the general definition is that two functions are orthogonal if their product integrated over a certain set of limits comes out to the value of zero. They are said to be orthogonal over that interval between the integration limits.

In OFDM the time duration of a data symbol is an integer number of cycles for all of the subcarriers. If you multiply the whole set of subcarriers by a sine wave at the frequency of one of them and integrate over the symbol period you get the modulation of just one subcarrier.

OFDM was invented around 1948 and used in secret military systems. Around 1955 it was declassified and several journal articles appeared about it. In 1958 there were commercial products available. Then it went out of popularity. About 25 years ago it was mentioned in communication theory books.

More recently the US patent office issued a patent on it. In 1945 frequency hopping spread spectrum was pathented. It had been described in an engineering text book in 1917. So much for the usefulness of the patent system.

 

[suvendu]

orthogonal signal definition in wikipedia

the orthogonal of two functions means their inner product is zero.this is applicable for all cases u said.

 

[anto2]

orthogonal signal processing definition

if two functions, variables are orthogonal that means that there is no relationship between them. Take for example if you were to convert some variable function etc into another form i.e. fourier transform etc it doesn't , then it is orthogonal if one function , variable maps uniquely to another variable function etc in another domain.
The mathematical definition itself changes depending on what you are talking about . there are different fomulas for orthogonal vectors, orthogonal matrices and orthogonal polynomials. these are pretty easy to find on the web. have fun .

 

[freeinthewind]

definition of orthogonal signaling

u can describe it as follows : there are 2 vectors a and b, if <a * b> is equal to zero , a is orthogonal to b.

 

[joinfaisal]

kartizian product

Yes two signals are orthogonal if their vector product is zero.This is the most complete and general defination.

 

[wcz]

Please take a brief read on the following link,
https://en.wikipedia.org/wiki/Orthogonal

 

[zhaoyimiao]

Two signal are orthogonal also means that when you sample one signal the other one's interference is zero.

 

[ali]

Dear All,
i think the most general answer is flatulent's one but to find more general definition of ortogonality:
If we have a "dot-product space" then two vector are ortogonal if and only if their dot-product(Inner product) is equal to zero ,you are familier with dot-product in kartizian sapace , continous function space , descret and continous random fields (it is corelletion at the orgin) , .....