Gaussian
Integral normalized to 1; a changes the width of the distribution, b its center..
Gaussian multiplied by noise
Gaussian with stochastic error as a factor to the Gaussian value. The error level is defined by c. Activation of the p slider creates a new stochastic distribution at the same level, as any other change.
Gaussian with added noise
Gaussian with stochastic error as an additive to the Gaussian value. The error level is defined by c. Activation of the p slider creates a new stochastic distribution at the same level as any other change.
Normalized Poisson distribution: The formula of the normalized Poisson distribution (integral = 1) includes the function Faculty ( p! ). This simulation contains special code for its calculation, which is accessed as p_Faculty . Inside this file it can be used in other formulas too. To be able to use the value at -xmax as initial value of integration, the zero point of the Poisson distribution is shifted to -xmax.
Three Modulation schemes following: x corresponds to time; b is the carrier frequency, c/5 the modulation frequency. In practical systems the carrier frequency is large compared to the modulation frequency b>>c/5. The factor 5 serves to adjust the relation to the default setting b = 1, c = 1.
Amplitude modulation y = sin(bx)*cos(c/5*x).
Phase modulation y = sin (bx+cos(c/5*x)).
Frequency modulation y = sin(bx*cos(c/5*x))).
Relativistic length contraction x = v/velocity_of_light c; v: velocity of the object.
Relativistic mass increase x = v/velocity_of_light c; v: velocity of the object.
Planck´s radiation law (x +2): wave length in μm; b defines temperature (unit 1000o K). To suppress the physically irrelevant branch for x < 0 the origin is shifted by 2 units.