Let *x*(*t*) be a finite energy signal. We consider the scalar product of two functions _{i}(*t*) and _{k}(*t*) of finite energy, represented as follows:

where _{k}*(*t*) denotes the complex conjugate of _{k}(*t*).

A family {_{k}(*t*)} of finite energy functions is called orthonormal if it verifies the following relations:

A family {_{k}(*t*)} is complete if any vector of the space can be approximated as closely as possible by a linear ...

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