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For example
Are sin(2Πfct) and sin(2Πfct) orthogonal for one period?
Is this possible?
Does that have mathematical expression?
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My understanding about orthogonal is as: If the dot product of two vectors (or signals) is equal to zero, then they are orthogonal. This is very fundamental check on orthogonality. In your example, I dont think that these two signals (provided that they are equal in all respects) can be orthogonal. You can get orthogonal projection of one signal on anohter by using Gram-Schmidt transformation, Householder Transformation, or Givens Transofrmations.
In some sense orthogonality is realted to Correlation as well. So if two signals are orthogonal, then they will be somehow un-correlated, but this is very loose check, because Correlation has some other meanings as well. But for your example as signals are correlated so they eventually cant be orthogonal.
sin(2Πfct) is not orthogonal to itself as long as -infinity<t<infinity.
If you divite t into intervals t1 and t2 which has the property you propose then you will get 2 orthogonal signals, but they are not sine functions, they are truncated sines. Assuming that you want only one sine period per signal, the mathematical expressions may be
no they are not orthogonal,
one guy has talked about correlation, when 2 signals are transmitted, u can get them individually at receiver by the method of correlation.
in this example, if both signals are same, then u cannot be sure about the fact u got which one signal. so, its sure that same signals are not orthogonal.
--------------------------------------------------------------------------------- Two sin functions are only orthogonal if their frequency's differ
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Concerning sinus or cosinus it's true. But other signals may not satisfy this private criterion.
Of cource, if too signals don't overlap either in time or in frequency domain they are orthogonal. But also exist special functions which occupy the same frequency band, but at the same time are orthogonal. This is also applied to time domain.
For example, Walsh, Haar and Rademaher functions overlap in time and frequency domains, but they are orthogonal and due to it are widely used, for example, in CDMA.
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