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flsmhs, a smoothed step function, or Heaviside function, with a continuous first derivative and overshoot on both sides of the step. The overshoot ensures that the integral from 0 to infinity is correct. y=flsmhs(x,scale) approximates the logical expression y = (x>0) by smoothing the transition within the interval
−scale < x < scale; that is, the scale value is half of the smoothing zone s. fldsmhs is the derivative of the smoothed Heaviside function. |
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flsmsign, a smoothed sign function with a continuous first derivative. y = flsmsign(x,scale) approximates the function y = sign(x) by smoothing the transition within the interval −scale < x < scale. fldsmsign is the derivative of the smoothed sign function.
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flc1hs, a smoothed Heaviside function with a continuous first derivative without overshoot. Its syntax is similar to the functions just described. The definition of flc1hs is the following:
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flc2hs, a smoothed Heaviside function with a continuous second derivative without overshoot. Its syntax is similar to the functions just described. The definition of flc2hs is the following:
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The smoothed functions accept any unit in their input arguments with the limitation that both arguments must have the same unit. The output is always without unit, except for the special derivative functions of fldsmhs and fldsmsign, which will get a unit of one over the input argument’s unit.
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