Benutzer:SprinterSB/Formeln

sin oder -sin in einer verrauschten Kurve finden

Applet

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$$S(a,b) = \sum_{i=1}^n (f(x_i)-m(x_i))^2$$

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$$\int_0^{2 \pi/b} |a\cdot\mathrm{sin}(b x) | \mathrm{d}x = 4 |a/b|$$

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$$(f\star g)(x) = \int_{-\infty}^\infty f(y)\,g(x-y) \,dy \qquad \mathrm{Faltung\ von\ }f\mathrm{\ und\ }g$$

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$$(f\star t)_n = \sum_{i=-K}^K t_i \cdot f_{n+i} \qquad\mathrm{mit}\qquad 1 = \sum_{i=-K}^K t_i$$

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$$F(x,y) = \int_{x-y}^{x+y} f(t)\,dt$$

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Transistor oder Mosfet

$$dP = \frac{R_\mathrm{FET}}{(R_\mathrm{FET}+R)^2}U^2 \, dt \qquad\mathrm{mit}\qquad R_\mathrm{FET}=R_\mathrm{FET}(t)$$

$$\Delta P_\mathrm{FET} = U^2 \cdot \int_0^{\Delta t} \frac{R_\mathrm{FET}}{(R_\mathrm{FET}+R)^2} \, dt \sim \frac{U^2}{R} \Delta t \quad\Rightarrow\quad P_\mathrm{switch} \sim \frac{U^2}{R}\,f\,\Delta t \quad\mathrm{und}\quad P_\mathrm{on} \approx R_\mathrm{on}\frac{U^2}{R^2}$$

$$P_\mathrm{FET} \approx P_R\cdot \left(\kappa\cdot f\cdot \Delta t + \frac{R_\mathrm{on}}{R}\right)$$