what is the difference between orthogonal in time and freq ?

Orth in time and freq

hi every body i have a question
what is the difference between orthogonal in time and orthogonal in frequency
i know that in time is int(GxG*)=0
can any body help

Re: Orth in time and freq

Orthogonality of 2 signals (functions) means, as you've written, that their inner product is equal to zero. Your formula is almost right, but the complex conjugate sign must be considered:

I = int(x1•x2*) = 0. If this is true, 2 functions are orthogonal.

It's necessary to define the orthogonality interval. Usually it's considered to be inf, but sometimes it is shrank to finite boundaries. If orthogonality is valid on both finite and infinite intervals, these functions have the double orthogonality

In frequency domain orthogonality is checked the same way:

I = (1/2pi)* int(X1•X2*) = 0, where X1 and X2 are the Fourier transforms of x1 and x2 respectively.

According to Parseval formula int(x1•x2*) = (1/2pi)*int(X1•X2*) = 0. That is, orthogonality may be checked either in time or frequency domains.

If 2 signals don't overlap in any of these domains, they are definetely orthogonal. In all the other cases  we need to check it. Very often 2 signals overlap on time span and frequency span, but they are orthogonal (Haar, Walsh functions, etc.)

With respect,

Dmitrij

Orth in time and freq

thanx
but this means that if a signal is othogonal in it it must be orthogonal in freq too
is this right?

Re: Orth in time and freq

yes, this property is called time-frequency equivalence