The Construction of Orthonormal Bases and Riesz Bases 5121 Signal of Finite Energy

The time series or signals are often regarded as vectors, and can also be regarded as measurable functions. Then, one poses the integration Lebesgue theorem, which explains that a function f is integrable, if f is of finite energy:

The space of integrable functions is noted L1 (R) if f-2 | f1 (t) - f2(t) | dt = 0. This means that f1 and f2 can differ only on a set of points of measure zero. Roughly, it is said that they are equal almost everywhere. Moreover, the time series or signals which are the subject of transformations in the time-frequency planes are offered to the handling of scientists who practise the signal processing and define a metric and exploit the properties of vector spaces. The concepts of distance, norm, convergence, integration, orthogonality, projection, basis, are largely used and enriched.

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