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searching for Inverse Laplace transform 24 found (37 total)

alternate case: inverse Laplace transform

State-transition equation (519 words) [view diff] exact match in snippet view article find links to article

} So, the state-transition equation can be obtained by taking inverse Laplace transform as x ( t ) = L − 1 [ ( s I − A ) − 1 ] x ( 0 ) + L − 1 ( s I −

Wiener filter (2,953 words) [view diff] exact match in snippet view article find links to article

inverse Laplace transform) S x + ( s ) {\displaystyle S_{x}^{+}(s)} is the causal component of S x ( s ) {\displaystyle S_{x}(s)} (i.e., the inverse Laplace

RC circuit (2,913 words) [view diff] exact match in snippet view article find links to article

{in} }(s)\,.} The impulse response for each voltage is the inverse Laplace transform of the corresponding transfer function. It represents the response

RL circuit (3,341 words) [view diff] exact match in snippet view article find links to article

_{R}}\end{aligned}}} The impulse response for each voltage is the inverse Laplace transform of the corresponding transfer function. It represents the response

Infinite impulse response (2,915 words) [view diff] exact match in snippet view article find links to article

{\displaystyle Y(z)=T(z)} Now the output of the analog filter is just the inverse Laplace transform in the time domain. y ( t ) = L − 1 [ Y ( s ) ] = L − 1 [ T (

Impulse invariance (1,062 words) [view diff] exact match in snippet view article find links to article

H_{c}(s)=\sum _{k=1}^{N}{\frac {A_{k}}{s-s_{k}}}\,} Thus, using the inverse Laplace transform, the impulse response is h c ( t ) = { ∑ k = 1 N A k e s k t

Hamburger moment problem (1,175 words) [view diff] exact match in snippet view article find links to article

probability density function can often be found by applying the inverse Laplace transform to the moment generating function m ( t ) = ∑ n = 0 m n t n n

Analog signal processing (1,620 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X(s)=\int _{0^{-}}^{\infty }x(t)e^{-st}\,dt} and the inverse Laplace transform, if all the singularities of X(s) are in the left half of the

Constraint counting (1,397 words) [view diff] exact match in snippet view article find links to article

[Fp](m,n)+[Fq](m,n)}{\omega ^{2}+m^{2}+n^{2}}}} Applying the inverse Laplace transform gives [ F u ] ( t , m , n ) = [ F p ] ( m , n ) cos ⁡ ( m 2 +

Multidimensional transform (4,600 words) [view diff] case mismatch in snippet view article find links to article

so by formulating a circuit as a state-space and expanding the Inverse Laplace Transform based on Laguerre function expansion. The Laguerre method can

Transfer function (2,497 words) [view diff] exact match in snippet view article find links to article

{H(s)}{s-j\omega _{0}}}} , and the temporal output will be the inverse Laplace transform of that function: g ( t ) = e j ω 0 t − e ( σ P + j ω P ) t −

Maple (software) (2,648 words) [view diff] exact match in snippet view article

{\frac {1}{s-c}}+{\frac {A}{(s-c)^{2}}}+{\frac {2B}{(s-c)^{3}}}} inverse Laplace transform inttrans:-invlaplace(1/(s-a), s, x); e a x {\displaystyle e^{ax}}

Dynamic light scattering (4,231 words) [view diff] exact match in snippet view article find links to article

analyzing the autocorrelation function can be achieved through an inverse Laplace transform known as CONTIN developed by Steven Provencher. The CONTIN analysis

Stretched exponential function (2,268 words) [view diff] case mismatch in snippet view article find links to article

[citation needed] The same reference also shows how to obtain the inverse Laplace Transform for the stretched exponential exp ⁡ ( − s β ) {\displaystyle \exp

LC circuit (5,471 words) [view diff] exact match in snippet view article find links to article

_{0}^{2}}}\,,} Which can be transformed back to the time domain via the inverse Laplace transform: v ( t ) = L − 1 ⁡ [ V ( s ) ] {\displaystyle v(t)=\operatorname

Perturbation theory (quantum mechanics) (15,890 words) [view diff] exact match in snippet view article

|n^{(0)}\rangle } . For k = 2 {\displaystyle k=2} , one has to consider the inverse Laplace transform ρ n , 2 ( s ) {\displaystyle \rho _{n,2}(s)} of the two-point

Linear canonical transformation (3,109 words) [view diff] exact match in snippet view article find links to article

transform when θ = 90 ∘ . {\displaystyle \theta =90^{\circ }.} The inverse Laplace transform corresponds to θ = − 90 ∘ . {\displaystyle \theta =-90^{\circ

Two-sided Laplace transform (1,995 words) [view diff] exact match in snippet view article find links to article

{s}})}}\,F_{2}(s)\,ds} This theorem is proved by applying the inverse Laplace transform on the convolution theorem in form of the cross-correlation. Let

Z-transform (4,524 words) [view diff] exact match in snippet view article find links to article

{\bigg .}X^{*}(s)=X(z){\bigg |}_{\displaystyle z=e^{sT}}} The inverse Laplace transform is a mathematical abstraction known as an impulse-sampled function

Group delay and phase delay (5,881 words) [view diff] exact match in snippet view article find links to article

frequency, and L − 1 {\displaystyle {\mathcal {L}}^{-1}} is the inverse Laplace transform. H ( s ) {\displaystyle \displaystyle H(s)} is called the transfer

Fractional calculus (7,146 words) [view diff] exact match in snippet view article find links to article

dependence on s. Taking the derivative of C(x,s) and then the inverse Laplace transform yields the following relationship: d d x C ( x , t ) = d 1 2 d

Aquilanti–Mundim deformed Arrhenius model (4,903 words) [view diff] case mismatch in snippet view article find links to article

"Pressure-Dependent Rate Constant Predictions Utilizing the Inverse Laplace Transform: A Victim of Deficient Input Data". ACS Omega. 3 (7): 8212–8219

Rate equation (7,441 words) [view diff] exact match in snippet view article find links to article

vector. Let L − 1 {\displaystyle {\mathcal {L}}^{-1}} be the inverse Laplace transform from s {\displaystyle s} to t {\displaystyle t} . Then the time-evolved

Stable count distribution (7,739 words) [view diff] exact match in snippet view article find links to article

{D}{4}}\right)={\frac {2a}{\sigma ^{2}}}} . From Section 4 of, the inverse Laplace transform H α ( k ) {\displaystyle H_{\alpha }(k)} of the Mittag-Leffler