Orthogonal Signals Question

Is the sole criterion for two signals to be orthogonal a cross correlation
type relationship? Could two signals that have some frequency cancellation
when added together still be viewed as orthogonal?

For example. if x(t) has fourier transform X(f), which has a magnitude of
1 over some BW, B. And y(t) has fourier transform Y(f), has a magnitude of
1 over the same band.

If the sole requirement for signals to be orthogonal is int(x(t)*y(t))dt =
0 over a time interval and x(t)^2 + y(t)^2 = (x(t)+y(t))^2., this is an
enery/power like criterion' and the equation doesnt necessarily say
X(f)+Y(f) have to equal 1.41 over that the bandwith B. The equation just
alludes to the energy in the 2 singals needing to be preseved, not
necessarily the energy in any one particular frequency.

Could there be frequency cancellation/addtion in X(f)+Y(f) and the signals
still be deemed orthogonal as long as the power is conserved?

I hope im asking this question the right way..

On Oct 9, 10:03&#4294967295;am, "westocl" <cwest...@hotmail.com> wrote:
> Is the sole criterion for two signals to be orthogonal a cross correlation
> type relationship? Could two signals that have some frequency cancellation
> when added together still be viewed as orthogonal?


I dont think any canceallation would occur, because that would imply
that one of them has a component projected into the other's space.
I can see a frequency addition taking place (as the vector sum
increases because the two signals are orthogonal) but I cannot see a
subtraction.

I might be mistaken here though.
Look at the sine and cosine as an example, the amplitude of their sums
(or difference) is always bigger than their individual components.

On Oct 9, 9:03&#4294967295;am, "westocl" <cwest...@hotmail.com> wrote:
> Is the sole criterion for two signals to be orthogonal a cross correlation
> type relationship? Could two signals that have some frequency cancellation
> when added together still be viewed as orthogonal?
>
> For example. if x(t) has fourier transform X(f), which has a magnitude of
> 1 over some BW, B. And y(t) has fourier transform Y(f), has a magnitude of
> 1 over the same band.
>
> If the sole requirement for signals to be orthogonal is int(x(t)*y(t))dt =
> 0 over a time interval and x(t)^2 + y(t)^2 = (x(t)+y(t))^2., this is an
> enery/power like criterion' and the equation doesnt necessarily say
> X(f)+Y(f) have to equal 1.41 over that the bandwith B. The equation just
> alludes to the energy in the 2 singals needing to be preseved, not
> necessarily the energy in any one particular frequency.

You seem to have an unusual definition of orthogonality.
If [x(t)]^2 + [y(t)]^2 = [x(t) + y(t)]^2 for all t, then it must
be that for each value of t, x(t)y(t) = 0, that is, at least
one of the two signals is 0.  If this is so, then obviously
int(x(t)*y(t))dt = 0 over *any* time interval because the
integrand is always 0.  A less restrictive (and very much
more widely accepted) definition of orthogonality (for all
time or over some specified time interval) is that the
inner product int(x(t)*y(t))dt have value 0 where the integral
is over all time, or over the specified time interval, whichever
is appropriate.

westocl wrote:
> Is the sole criterion for two signals to be orthogonal a cross correlation
> type relationship? Could two signals that have some frequency cancellation
> when added together still be viewed as orthogonal?

> For example. if x(t) has fourier transform X(f), which has a magnitude of
> 1 over some BW, B. And y(t) has fourier transform Y(f), has a magnitude of
> 1 over the same band.

> If the sole requirement for signals to be orthogonal is int(x(t)*y(t))dt =
> 0 over a time interval and x(t)^2 + y(t)^2 = (x(t)+y(t))^2., 

The ones I am used to have a w(t) weighting term.  It is often 1, but
in some cases it is another function.

http://en.wikipedia.org/wiki/Orthogonal#Orthogonal_functions

-- glen