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Questions tagged [integral-transforms]

Questions about transforms of functions by means of integration, such as Fourier transforms and Laplace transforms. Many integral transforms can be inverted by means of another integral transform.

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Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
highBandWidth's user avatar
6 votes
0 answers
247 views

Implementation of the Riesz transform

Implementing the Hilbert transformation \begin{equation}H(f)(x) = \frac{1}{\pi}\lim_{\varepsilon \to 0} \int_{|x-y|>\varepsilon} \frac{1}{x-y}f(y) \, dy,\end{equation} appropriate for 1-...
confused's user avatar
5 votes
1 answer
14k views

Fourier Transform of Absolute Value

If you ask Mathematica to provide the Fourier Transform of a singular functions it is likely to provide an answer that while nearly correct, is technically incorrect and it will do so without a word ...
JEP's user avatar
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4 votes
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85 views

Is `InverseMellinTransform` unaware of second Barnes lemma?

Consider evaluating ...
Kagaratsch's user avatar
4 votes
0 answers
180 views

Integral Representation of DiracDelta

I would like to get dirac delta from integral definition, of course if I ask Integrate[Exp[I x t],{x,-Infinity,Infinity}] I get that the integral does not ...
MaPo's user avatar
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3 votes
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How does Mathematica obtain this result?

FullSimplify[ Sqrt[2 π] InverseFourierTransform[1/(x^2 - a^2), x, p], Element[a, Reals]] Gives the output ...
user824530's user avatar
3 votes
0 answers
156 views

Strange result with Laplace transform

The following code: f[x_] := HeavisideTheta[1 - x]/x InverseLaplaceTransform[ f[t], t, x]/x Returns 1/x. But this should not be ...
Anixx's user avatar
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3 votes
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159 views

Convolution using the Laplace integral transform of certain functions

I am trying to convolve two functions: $f(t) = e^{- t}$ $g(t) = e^{-(e^{-t})^2}$ $(f*g)(t) = \int_{0}^{t} f(t-\tau)g(\tau) d\tau = \int_{0}^{t} e^{-(t-\tau)} e^{-(e^{-\tau})^2} d\tau$ Using the ...
dtn's user avatar
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3 votes
0 answers
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Region of convergence in Inverse laplace transform

Lets say we have a function in the s domain. Let it be H(s)=1/(s+1). It has one pole. If we consider the region to the right of the pole as the ROC, we would one function in the time domain when we ...
Danny's user avatar
  • 31
3 votes
0 answers
686 views

Computation of a Fresnel Diffraction pattern with Discrete Hankel Transform

In the next link: Computation of Hankel Transform using FFT (Fourier) Rainer implemented a great solution given in the next reference: Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Computation ...
Eduardo's user avatar
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2 votes
0 answers
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Efficient powers of DPR1 matrices

I'm looking to compute the following quantity for $A$ where $A$ is a convergent positive definite $d\times d$ diagonal + rank1 matrix (DPR1). $$f(s)=\operatorname{Tr}(A^s)$$ Earlier answer answer by ...
Yaroslav Bulatov's user avatar
2 votes
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Is this a bug in InverseLaplaceTransform or LaplaceTransform?

Let us consider in version 13.1 on Windows 10 ClearAll["Global`*"]; a = InverseLaplaceTransform[s*Log[(s - 1)/(s + 1)], s, x] ...
user64494's user avatar
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2 votes
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InverseLaplaceTransform gives inconsistent results

These should give the same results, but they do not: InverseLaplaceTransform[1/Sqrt[x] HeavisideTheta[x + 1], x, y] InverseLaplaceTransform[1/Sqrt[x], x, y] ...
Anixx's user avatar
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2 votes
0 answers
98 views

Solving a finite Hilbert transform from 2D thin wing theory

I have a problem where I know $w(x) =1$ and want to find $u(x)$. It's a well-known problem I am recreating, from a 1972 paper. Note the paper doesn't solve the problem, the integral equation, it just ...
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2 votes
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Verifying a cosine FourierTransform

On page 31 of this standard reference we have the following relation: I wanted to use mathematica to verify this transform numerically for some example values. So I type in: ...
Kagaratsch's user avatar
2 votes
0 answers
430 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
Peter Zimmerman's user avatar
2 votes
0 answers
160 views

Incorrect output from InverseFourierTransform

Bug introduced in 8.0.4 or earlier and fixed in 9.0.1 or earlier I am trying to compute the inverse Fourier transform of this expression ...
Goulifet's user avatar
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1 vote
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How can I write the code for an inverse integral transform?

How can I code any type of integral transform with its inverse integral transform in Mathematica which gives the correct results and properties? Below is the example for Elzaki transform: ...
Kishor Kshirsagar's user avatar
1 vote
1 answer
99 views

Question about numerical integration of a double integral

I am trying to numerically integrate the following double integral in Mathematica for different values of t. ...
HadamardN2's user avatar
1 vote
0 answers
61 views

Inverting Laplace transform numerically for a set of points

Computing inverse of Laplace transform numerically in Mathematica seems very slow and requires $k$ calls for $k$ points. Is there a faster way to do it for a set of $k$ points, ie $k\approx 1000$? <...
Yaroslav Bulatov's user avatar
1 vote
0 answers
74 views

Incorrect result of InverseFourierTransform

When executing in 13.2 on Windows 10, the command FourierTransform[DiracDelta@Cos[x], x, s] results in ...
user64494's user avatar
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1 vote
0 answers
183 views

Inverse Laplace in mathematica

I can't even get an inverse Laplace for this expression numerically in mathematica, is there a way to inverse this equation below? I have also tried to use fixt talbot package for a numerical ...
Ali AlCapone's user avatar
1 vote
0 answers
34 views

Replace subexpression with variable in result from Laplace transform

I'd like to clean up the result I obtained from an inverse Laplace transform: First of all, I'd like to replace the square root expressions in the hyperbolic function arguments (part encircled in ...
Hans's user avatar
  • 11
1 vote
0 answers
89 views

Implementing the Shift Property of the Fourier Transform in Mathematica

I am trying to determine the Fourier tranform of a time shifted (t-b) Lorentzian function in Mathematica. With the zero centered Lorentzian (b=0), the Integrate function with the conditions that all ...
AChem's user avatar
  • 123
1 vote
0 answers
86 views

Closed form for integral with SinIntegral

MMA can't solve this integral: $$\int_0^{\pi } \text{sinc}(x) \text{Si}(2 x) \, dx$$ The I use FourierSinTransform to find closed form,but I try a verify result is ...
Mariusz Iwaniuk's user avatar
1 vote
0 answers
50 views

Performing operator expression on a function

What I want. I write an operator expression, and Mathematica performs it on a function. Examples: E^(b D): f[x] -> f[x+b] ...
Anixx's user avatar
  • 3,585
1 vote
0 answers
70 views

Numerically obtaining inverse 2D Laplace transform

I wonder if there is a function in Mathematica (or code) that can help obtaining inverse 2D Laplace transform of a function, f(s1,s2) which is the 2D Laplace transform of a function F(t1,t2) in (s1,s2)...
Refaat Galal's user avatar
1 vote
0 answers
113 views

How to plot integral of a gradient function

For $f : \mathbb{R} \longrightarrow \mathbb{R}$ continously differentiable and $\phi \in [0,\pi/2]$ let $$F(x) = \int \frac{f'(x)-\cot \phi}{1+ f'(x) \cot \phi} d x$$ be a clockwise 'rotation' of $f$. ...
JHT's user avatar
  • 1,005
1 vote
0 answers
154 views

Simplify trigonometric functions to take the Laplace transform

I have one trigonometric function which is simplified as f[t_, RV_, H_] := 0.000308148 H Cos[0.172439 RV Sin[2 \[Pi] t]] It is an input to one ODE which I want to ...
hesamaero's user avatar
  • 489
1 vote
0 answers
52 views

HankelTransform problem

Somewhere in the following code there is a bug. The result should not be zero! FunctionExpand@HankelTransform[Sqrt[r] Cos[r], r, k, 1/2] I think the answer should ...
SolutionExists's user avatar
1 vote
0 answers
63 views

Adding a module to teach Mathematica the Laplace transform of particular Mittag-Leffler functions

Mathematica 11.3 is not aware of a useful Laplace transform LaplaceTransform[t^(-a) MittagLefflerE[a, a, t^a], t, s] which for ...
florin's user avatar
  • 1,798
1 vote
0 answers
145 views

Calculate a nested integral

I wish to plot the following probability on Mathematica: $$ \pi=n\cdot\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty}\left[\int_{-\infty}^{z_{1}}G\left(z-z_{2}\right)\cdot f\left(z_{2}\right)dz_{2}\...
Avocaddo's user avatar
1 vote
0 answers
166 views

Can this boundary value problem leading to a partio-integral DE be solved using finite Fourier or any integral transform?

I asked the three-dimensional version of this problem here which lead to a trivial solution. I have now tried it in 2-D $$\frac{\partial \theta_h}{\partial x} + b_h (\theta_h - \theta_w) = 0, \tag 1\\\...
Avrana's user avatar
  • 297
1 vote
0 answers
120 views

Is it possible to take the Laplace transform of a Hankel function with Mathematica?

The following two functions are the fundamental solutions of the wave equation and its Laplace transform (the modified Helmholtz equation) in two dimensions, respectively, when the speed of wave ...
ManUtdBloke's user avatar
1 vote
0 answers
111 views

Numerical Definite Integral of Numerical Laplace Transform

I'm having problem taking the numerical definite integral of a numerical Laplace transform that depends on two variables due to NIntegrate:inumr errors: ...
Rpj's user avatar
  • 249
1 vote
0 answers
418 views

Mathematica 12 returns a "greater::nord" error when Mathematica 11 does not

In the following code Talbot's method is made use of to invert Laplace's transforms. ...
freddy-baudine's user avatar
1 vote
0 answers
325 views

Taking numerical Laplace transform of a tabulated data with Mathematica?

I am relatively new to the use of Mathematica in the context of numerical evaluations, therefore I would greatly appreciate a detailed answer and would like to express my gratitude towards any help in ...
Rohit Jain's user avatar
1 vote
0 answers
267 views

Can Mathematica verify the Cahen - Mellin integral?

Can Mathematica verify the Cahen-Mellin integral? When I try Integrate[Gamma[1 + I s]/Zeta[3]^(1 + I s), {s, -Infinity, Infinity}] I just get the input back. ...
Kagaratsch's user avatar
1 vote
0 answers
187 views

Inverse Laplace Transform Failing: $\frac{1}{\exp (\beta \tau )-a}$

I have tried various approaches to get the solution to this inverse transform but all so far are failing. ...
Alexander McFarlane's user avatar
1 vote
0 answers
119 views

Different Results under Inverse Laplace Transform

I am getting different results from the following commands: ...
Hugo Andrade's user avatar
1 vote
0 answers
131 views

InverseLaplaceTransform provides a wrong answer?

Question is revised as below: I'm trying to define a function involving inverse of a Laplace Transform for a rational function, but Mathematica provides a wrong result. Can anyone help on this? ...
Tim's user avatar
  • 11
1 vote
0 answers
204 views

Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
Gappy Hilmore's user avatar
1 vote
0 answers
285 views

The inverse Fourier transform of a rather complex function

I am using Mathematica 7.0 and trying to find the Fourier transform of a rather complex function g. The function g is defined by $$g=\left(\textrm{e}^{\left(\frac{-0.008372\textrm{i}+0.008372\textrm{...
Pauliina's user avatar
0 votes
0 answers
94 views

LaplaceTransform doesn't work

I have code: A = 1; ω0 = 5*10^6; τ0 = 3*10^-3*Sqrt[2/Log[2]]/(5.85*10^3); s0[t_] = A*E^(-t^2/τ0^2)*Cos[ω0*t]; Phi[ω_] = LaplaceTransform[s0[t], t, ω] The last ...
Cpp Nosavvier's user avatar
0 votes
0 answers
135 views

Implementing the 3D Radon transform

I am wondering how to implement the Radon transform, the 3D Radon transform, that is, given a 'density' function $f: \mathbb{R}^3\to \mathbb{R}$ The Radon transform of $f$ is $$Rf(s,w)= \int_{x\cdot w=...
NotaChoice's user avatar
0 votes
0 answers
46 views

How to do variable change for a general Fourier series? I failed at first step :(

Well, firtly, I think I should define a general rule for Fourier series, but I fails. Below is my code including several attempts. Anys helps are greatly appreciated, thanks. ...
op-luffy's user avatar
0 votes
0 answers
149 views

Solving coupled integro-differential equations using Laplace transform

I have two coupled integrodifferential equations, as shown in the image attached. I am trying to solve them using a Laplace transform, as follows ...
Jose Enrique Aroca's user avatar
0 votes
0 answers
181 views

How to plot this FourierTransform?

I need to find the Fourier transform and plot the function: Delta(x-xo) I've already tried to write it as: FourierTransform [DiracDelta[x - Subscript[x, 0]], x, w] ...
Marina Nebot's user avatar
0 votes
0 answers
46 views

Possible bug in InverseZTransform

Try x1n=InverseZTransform[1/(1-(1/z))//Factor,z,n] x2n=InverseZTransform[1/(1-(1/z)),z,n] DiscretePlot[x1n,{n,-10,10}] DiscretePlot[x2n, {n,-10,10}] The result ...
Napoleone Bavaresco's user avatar
0 votes
0 answers
52 views

Need help to understand the code

Here is the code by P. Valko and J. Abate for finding numerical inverse Laplace transform by trapezoidal's rule. Can someone willing to explain this code? I don't understand this part: ...
user516076's user avatar