08-17-2017, 12:23 AM
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A little bit of history .
Jean Baptiste Joseph Fourier (1768 1830)
MGP: Leibniz - Bernoulli - Bernoulli - Euler - Lagrange - Fourier Dirichlet - .
1787: Train for priest (Left but Never married!!).
1793: Involved in the local Revolutionary Committee.
1974: Jailed for the first time.
1797: Succeeded Lagrange as chair of analysis and mechanics at cole Polytechnique.
1798: Joined Napoleon's army in its invasion of Egypt.
1804-1807: Political Appointment. Work on Heat. Expansion of functions as trigonometrical series. Objections made by Lagrange and Laplace.
1817: Elected to the Acad mie des Sciences in and served as secretary to the mathematical section. Published his prize winning essay Th orie analytique de la chaleur.
1824: Credited with the discovery that gases in the atmosphere might increase the surface temperature of the Earth (sur les temp ratures du globe terrestre et des espaces plan taires ). He established the concept of planetary energy balance. Fourier called infrared radiation "chaleur obscure" or "dark heat .
Mallat's multiresolution framework
Design method of most of the practically relevant discrete wavelet transforms (DWT)
Wavelet Banding
Filtering the predictors
relative to the signature of
the predictands eliminates
noise.
In this simple case the
forecast is perfect.
In complicated geophysical
time series where coefficients
vary with time, spurious
modes are eliminated and
Bayesian statistical schemes
are less confused .