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A Dirac comb is an infinite series of Dirac delta functions spaced at intervals of T A so-called uniform "pulse train" of Dirac delta measures, which is known as a Dirac comb , or as the Sha distribution, creates a sampling function, often used in digital signal processing (DSP) and discrete time signal analysis.
A well-known example of a one-dimensional singular potential is the Schrödinger equation with a Dirac delta potential. [5] [6] The one-dimensional Dirac delta prime potential, on the other hand, has caused controversy. [7] [8] [9] The controversy was seemingly settled by an independent paper, [10] although even this paper attracted later ...
the Kronecker delta function; the Feigenbaum constants; the force of interest in mathematical finance; the Dirac delta function; the receptor which enkephalins have the highest affinity for in pharmacology [1] the Skorokhod integral in Malliavin calculus, a subfield of stochastic analysis; the minimum degree of any vertex in a given graph
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ l ə ˈ p l ɑː s /), is an integral transform that converts a function of a real variable (usually , in the time domain) to a function of a complex variable (in the complex-valued frequency domain, also known as s-domain, or s-plane).
In control theory the impulse response is the response of a system to a Dirac delta input. This proves useful in the analysis of dynamic systems; the Laplace transform of the delta function is 1, so the impulse response is equivalent to the inverse Laplace transform of the system's transfer function.
In terms of the Dirac delta "function" δ(x), a fundamental solution F is a solution of the inhomogeneous equation LF = δ ( x ) . Here F is a priori only assumed to be a distribution .
The graph of the Dirac comb function is an infinite series of Dirac delta functions spaced at intervals of T. In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula := = for some given period . [1]
The impulse response for each voltage is the inverse Laplace transform of the corresponding transfer function. It represents the response of the circuit to an input voltage consisting of an impulse or Dirac delta function. The impulse response for the inductor voltage is