In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula Ш   T ⁡ ( t )   :=...

and Cauchy. 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...

2005. The frequency domain representation of a perfect frequency comb is like a Dirac comb, a series of delta functions spaced according to f n = f 0 + n...

\xi x}\,d\xi =D_{n}(2\pi x),} and comb n ⁡ ( x ) {\displaystyle \operatorname {comb} _{n}(x)} goes to the Dirac comb Ш {\displaystyle \operatorname {\text{Ш}}...

impulse at zero. It may be considered to be the discrete analog of the Dirac comb. The Kronecker delta is also called degree of mapping of one surface into...

} In other words, the periodization of a Dirac delta δ , {\displaystyle \delta ,} resulting in a Dirac comb, corresponds to the discretization of its...

input function/waveform is periodic, the Fourier transform output is a Dirac comb function, modulated by a discrete sequence of finite-valued coefficients...

of a Dirac delta function is the Dirac comb. Likewise, the periodic summation of an integrable function is its convolution with the Dirac comb. If a...

practice (not discussed above) is to handle that divergence via Dirac delta and Dirac comb functions. But the same spectral information can be discerned...

of poles spaced along the jω axis. Dirac comb Fabry–Pérot interferometer Roger Russell. "Hearing, Columns and Comb Filtering". Retrieved 2010-04-22. "Acoustic...

is the Dirac comb both equations yield the Poisson summation formula and if, furthermore, u ≡ δ {\displaystyle u\equiv \delta } is the Dirac delta then...

delta functions is called a Dirac comb. Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with s ( t ) {\displaystyle...

impulse response equal to a rect function, and with input being a sequence of dirac impulses scaled to the sample values. The filter can then be analyzed in...

and δ {\displaystyle \delta } is the Dirac delta function. In other words, the Fourier transform is a Dirac comb function whose teeth are multiplied by...

integral Dirac delta function Dirac comb Dirac measure Dirac operator Dirac algebra 5997 Dirac, an asteroid The various Dirac Medals Dirac (software) DiRAC supercomputing...

transform purposes, sampling is modeled as a product between s(t) and a Dirac comb function. The spectrum of a product is the convolution between S(f) and...

mathematically equivalent method uses the Dirac comb and proceeds by convolving one sinc function with a series of Dirac delta pulses, weighted by the sample...

interpreted as the coefficients of a linear combination of Dirac delta functions, forms a Dirac comb. If additionally truncation is applied, one obtains finite...

with equality achieved when x or X is a Dirac mass, or more generally when x is a nonzero multiple of a Dirac comb supported on a subgroup of the integers...

_{n=0}^{\infty }\delta (t-nT)} be a sampling impulse train (also called a Dirac comb) and x q ( t ) = d e f x ( t ) Δ T ( t ) = x ( t ) ∑ n = 0 ∞ δ ( t − n...

The Dirac comb of period 2π, although not strictly a function, is a limiting form of many directional distributions. It is essentially a wrapped Dirac delta...

one and both equations yield the Dirac-comb identity. Another example is to let g {\displaystyle g} be the Dirac comb and f ≡ rect ∈ E ′ {\displaystyle...

infinity at x = 2πn in a significant way: it is the Fourier series of a Dirac comb. The ordinary, Cesàro, and Abel sums of this series involve limits of...

(t-nT).} Therefore, an alternative definition of DTFT is: The modulated Dirac comb function is a mathematical abstraction sometimes referred to as impulse...

Sha when they use the term Shah function for what is otherwise called a Dirac comb. The shuffle product is often denoted by ш. ش : Arabic letter ش श: Devanagari...

equal to translations and modulations of a suitably normalized Kronecker comb of period A {\displaystyle A} where A {\displaystyle A} is any exact integer...

a Dirac delta measure (flash) and a constant finite rectangular window, in combination. For example, a sensitivity window comprising a Dirac comb combined...

basis vector. A fundamental wrapped distribution is the Dirac comb, which is a wrapped Dirac delta function: Δ 2 π ( θ ) = ∑ k = − ∞ ∞ δ ( θ + 2 π k )...

René Descartes Dirac equation Dirac delta function Dirac comb Dirac spinor Dirac operator  See also: List of things named after Paul Dirac Mathematics,...

domain representation uses the Fourier series coefficients to modulate a Dirac comb: S ( f )   ≜   ∑ n = − ∞ ∞ S [ n ] ⋅ δ ( f − n P ) , {\displaystyle S(f)\...