# Does the “direction” of a signal physically matter?

I am thinking of the typical (sound, electromagnetic or whatever) signal which can be represented in time or frequency domain as a collection of infinite amplitudes for, respectively, each time-point or each frequency, so that one can say that this function (where the input is the time points or the frequencies, as the case may be, and output is their amplitudes) is a vector in a generalized sense (where coefficients are the amplitudes and the basis vectors could be represented by complex exponentials of the relevant time point or frequency, as the case may be).

So this vector, in a generalized sense, has clearly "magnitude" and one could think that it has "direction", in some sense, if we consider that we could play with the weight of the components, raising it here and lowering it there, so that the resulting signal sort of “points to somewhere else”, even if its magnitude remains the same.

Is this a simple theoretical speculation or does it have practical application in physics? Is there any real-life situation where you would need to ascertain or alter the “direction” of a signal for some practical purpose?

(Well, an obvious answer is that through this playing with the weights you generate a different signal and this will always have some practical utility, but I was wondering if, in the scientific literature or in practice, this is an expression that you would typically use in some common situations: let us change the "direction" of the signal to achieve this or that result.)

• I've removed a number of comments that were attempting to answer the question and/or responses to them. Please keep in mind that comments should be used for suggesting improvements and requesting clarification on the question, not for answering. – David Z Jul 19 at 19:51

• @Sierra, if you want me to be able to comment on it, you should define with mathematics, how, given a signal $x(t)$ or $X(f)$ are the magnitude and direction calculated. For example, one traditional definition of the magnitude would be $\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^{T}x^2(t) dt$. – The Photon Jul 19 at 20:28