orthonormal basis and orthogonal basis

[RAJARSHI ROY CHAUDHURI]

We know that  orthonormal basis set of signals can be used for linear decomposition of a signal x(t). Can't we just use orthogonal basis set of signals for linear decomposition of a signal x(t)?Why is orthonormality condition necessary? 

[NOC16 March - May]

Hi,

yes you are right. Orthogonality and orthonormality are one and the same things except the fact that in the latter case we have norm equal to 1. Now having norm of a vector as 1 is something that is additional that one would want since it helps out in carrying calculations. If we want to find out the projections of a vector onto a different vector space (which is essentially what is meant by decomposing a signal as a linear combination of its basis) then we always don't have to take care of the constants involved in the inner products. So this in some sense reduces our efforts in calculations. 

I hope that this would clear your doubts.

Thanks

TA