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Step function. In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. An example of step functions (the red graph).
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time.
In signal processing, control theory, electronics, and mathematics, overshoot is the occurrence of a signal or function exceeding its target. Undershoot is the same phenomenon in the opposite direction. It arises especially in the step response of bandlimited systems such as low-pass filters. It is often followed by ringing, and at times ...
Heaviside step function. The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙 ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use.
Stepped-up basis. The tax code of the United States holds that when a person (the beneficiary) receives an asset from a giver (the benefactor) after the benefactor dies, the asset receives a stepped-up basis, which is its market value at the time the benefactor dies ( Internal Revenue Code § 1014 (a)). A stepped-up basis can be higher than the ...
Stiff equation. In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms ...
In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. [1] These values may be expressed as ratios [2] or, equivalently, as percentages [3] with respect to a given reference value. In analog electronics and digital electronics ...
Final value theorems for obtaining have applications in probability and statistics to calculate the moments of a random variable. Let be cumulative distribution function of a continuous random variable and let be the Laplace–Stieltjes transform of . Then the -th moment of can be calculated as. The strategy is to write.