From Frequencies to the Forecasting Processes

This communication aims to show and explain the frequency influences over the signal evolutions. We draw an operational analogy between the modulations and the detection of periodic and aperiodic behaviours. Consequently g(t) is related to G(s) its Laplace picture as a frequency generator. To win more easiness in the structure analysis we will use the "Bond Graph" methodology and therefore we shortly notice its main specificities.

After the description of the reactivity which causes the technological memory we show the operational connection from this one to the (pole - zero) pairs and underline the delivered future characteristics. From inspecting the Laplace space we remark that any root locus = {R L} structure corresponds to a set of Newton's fields what supplies a divergence field in the (Lp.sp.) = Laplace space. This Laplace distribution helps for determining the g(t) evolution characteristics. From the {R L} it is possible to deduce the system decomposition into a first-order one and a set of second-order ones, what brings a drastic analysis reduction of forecasting processes. The convolution of a system g(t) with an inflow signal x(t) will be transfered in a (Lp.sp.) what yields the angular convolution of both {R L} stars. In (Lp.sp.), are injected horizontal conjugated heliphasors for each fixed frequency pair with exp(-Δσ) as damping variation of the amplitude, resulting from the imaginary graduation and vertical damped or amplified Fourier phasors supporting (Δωι) frequency variation for exp(-σκ) as fixed amplitude. The supply of synchronous curves following the time evolution along the {R L}, acts as an extension of the Fourier wavelets. Afterwards we deduce a shortage of the (Lp.sp.) into a sector of the 2° stability quadrant. This accessible window is defined by the uppermost possible frequency.

An extended (Lp.sp.) configuration describes the evolution and the management of a library or a documentation centre. For this last use, the informations will be located in the first quadrant where we can display the obtained gains and developments (= information increase) on the real axis and the use frequency of each knowledge on the imaginary one. This configuration shows the interest grade for each type of knowledge and will supply a valuable guidance to improve the future development.