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I have come across a condition which states that wavelets must satisfy the condition of orthogonality but I am not sure what is the EXACT reason behind that? Is it to ensure that the scaled version of a wavelet function and it's translates do not overlap while representing the original function??

I am quite new in this area so please try to explain it in a simple way.

Thank You !!!

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    Are you familiar with orthogonality in more traditional settings (i.e. Fourier analysis)? – 2017-02-16
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    Well, I just have a rough idea about the fact that the integration of the dot product of two functions over a period of time has to be ZERO for the two functions to be orthogonal. I don't know how orthogonality impacts fourier analysis as well. – 2017-02-16
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    Orthogonality is a large concept in linear algebra generically. Questions like [this](https://math.stackexchange.com/questions/399740/why-is-it-important-that-a-basis-be-orthonormal) get into it more. Without a linear algebra background, it might not be easy to see why this is useful. The short of it is that it makes computations much easier - If we have that $e_1,e_2,e_3$ are orthogonal, then $\langle a_1e_1+a_2e_2+a_3e_e, b_1e_1+b_2e_2+b_3e_3\rangle = a_1b_1|e_1|^2 + a_2b_2|e_2|^2+a_3b_3|e_3|^2$. If the basis is also normal the computation becomes much easier. – 2017-02-16
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    Is orthonormality the same as orthogonality ? The reason I ask this is that there is another thread which discusses the importance of orthonormality in linear algebra. Perhaps, I can draw some ideas from that. – 2017-02-16
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    They're similar, but not the same. Orthagonality says that if you have two basis vectors, their "dot product" (inner product) is 0 if they're not the same basis vector. Orthonormality says that additionally if they are the same basis vector, their dot product is 1. – 2017-02-16

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