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  2. Heaviside step function - Wikipedia

    en.wikipedia.org/wiki/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.

  3. Fundamental solution - Wikipedia

    en.wikipedia.org/wiki/Fundamental_solution

    Denote the convolution of functions F and g as F ∗ g. Say we are trying to find the solution of Lf = g(x). We want to prove that F ∗ g is a solution of the previous equation, i.e. we want to prove that L(F ∗ g) = g.

  4. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    If f is a Schwartz function, then τ x f is the convolution with a translated Dirac delta function τ x f = f ∗ τ x δ. So translation invariance of the convolution of Schwartz functions is a consequence of the associativity of convolution. Furthermore, under certain conditions, convolution is the most general translation invariant operation.

  5. Step function - Wikipedia

    en.wikipedia.org/wiki/Step_function

    The product of a step function with a number is also a step function. As such, the step functions form an algebra over the real numbers. A step function takes only a finite number of values. If the intervals , for =,, …, in the above definition of the step function are disjoint and their union is the real line, then () = for all .

  6. Analog signal processing - Wikipedia

    en.wikipedia.org/wiki/Analog_signal_processing

    A unit step function, also called the Heaviside step function, is a signal that has a magnitude of zero before zero and a magnitude of one after zero. The symbol for a unit step is u(t). If a step is used as the input to a system, the output is called the step response.

  7. Step response - Wikipedia

    en.wikipedia.org/wiki/Step_response

    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.

  8. Step potential - Wikipedia

    en.wikipedia.org/wiki/Step_potential

    The step potential is simply the product of V 0, the height of the barrier, and the Heaviside step function: = {, <, The barrier is positioned at x = 0, though any position x 0 may be chosen without changing the results, simply by shifting position of the step by −x 0.

  9. Rectangular function - Wikipedia

    en.wikipedia.org/wiki/Rectangular_function

    Plot of normalized ⁡ function (i.e. ⁡ ()) with its spectral frequency components.. The unitary Fourier transforms of the rectangular function are [2] ⁡ = ⁡ = ⁡ (), using ordinary frequency f, where is the normalized form [10] of the sinc function and ⁡ = ⁡ (/) / = ⁡ (/), using angular frequency , where is the unnormalized form of the sinc function.