orthogonal basis functions

[Jiahn K]

What does basis functions being ‘orthogonal ‘ mean exactly?
In the lecture slides, I actually can see some points where for example the basis function with the most lower frequency overlaps with a basis function which as a bit higher frequency than that.

Of course I could approximate the points in the diagrams but I’d like to know what being orthogonal exactly means!

[Simon]

Orthogonal means that the correlation between any pair of basis functions is zero. This property is necessary for there to be a unique set of coefficients when we analyse a given signal using a set of basis functions.

Think of it as “there is no amount of one basis function contained in any other one”, or as “if we analyse a signal that happens to be the same as one of the basis functions, that coefficient and that coefficient only will be non-zero”.

[Author]

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