October 2006
Intermediate to advanced
369 pages
8h 11m
English
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3.2. The Fourier transform of continuous signals
3.2.1. Summary of the Fourier series decomposition of continuous signals
3.2.1.1. Decomposition of finite energy signals using an orthonormal base
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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