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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4
votes
2answers
143 views

InverseFourierTransform takes forever

I am trying to find InverseFourierTransform of the following function, but the code below does not give me a result. I do not get any error messages but the calculation just does not end. Any Help? ...
3
votes
1answer
62 views

Problem with Inverse Laplace Transform in Mathematica

I am trying to calculate the following inverse Laplace transform $$ f(t) = \mathcal{L}^{-1}\left[ \left(\frac{1}{s+a}\right)^{n+1}\left( \frac{1}{s+b}\right)^{n} \right](t) $$ with $s$ being the ...
1
vote
1answer
80 views

InverseLaplaceTransform not working

I am trying to find the Inverse Laplace transform of a function I previously obtained from a Laplace transform, but the result obtained does not agree with the initial function. Why is this happening? ...
3
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1answer
162 views

Fourier transform of Log[RealAbs[x]]^2

At least one of the outputs (highly likely both) ...
0
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0answers
38 views

Solving a System and taking inverse Laplace/Fourier Transforms

I have a set of linear equations for 4 quantities which have been both Fourier transformed and Laplace transformed. The system needs to be solved for the quantities and then each of the quantities ...
0
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2answers
63 views

Impulse response function h(t) of Gauss functions as a stimulus and response

From the basics of the signal theory the impulse response function (IRF) can be calculate like (L=Laplace transformation): L[x(t)]= X(s) , L[y(t)]= Y(s) and transfer function H(s)= Y(s)/X(s), then IRF ...
1
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0answers
319 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. ...
1
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1answer
120 views

Generate this contour plot

I have the following complex function: ...
0
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0answers
67 views

Teach Mathematica analytical continuation of the gamma function

If I ask Mathematica to compute the gamma function for me Integrate[Exp[-s] s^(a - 1), {s, 0, Infinity}] It dutifully returns to me ...
2
votes
2answers
121 views

Finding the global maximum of a function

I've the following code: ...
1
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1answer
79 views

Integrate 2D Gaussian over a segment

I have the following 2D Gaussian: ...
7
votes
1answer
710 views

Correct way of simplifying the result of an integral

Many times Mathematica gives enormous results to simple problems. One uses the program more for trouble than for not knowing how to solve the problem. As an ejemplo I present this integral that ...
0
votes
2answers
75 views

Solving proplem by Laplace transform [closed]

I want to solve these ODE's by Laplace transformation and graph it dx1/dt = 38/1180 x3(t) + (1 + sin⁡(t)) - 38/2900 x1(t), x1(0) = 0 dx2/dt = 18/2900 x1(t) - 18/850 x2(t), x2(0) = 0 dx3/dt = 20/...
5
votes
3answers
722 views

Mathematica and MatLab giving different results from inverse Laplace transform [closed]

The questionis is as this Given the transfer function gs = (5*s + 4)/(s^4 + 4*s^3 + 2*s^2 + 3*s); and the input signal ...
3
votes
1answer
171 views

Inverse Laplace transform of this complicated function

I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
17
votes
5answers
1k views

Laplace transform of $\frac{1-\cos (t)}{t}$

In the documentation, it states that The Laplace transform of a function $f(t)$ is defined to be $\int_0^{\infty } f(t) e^{-s t} \, \mathrm{d}t$. But why can Mathematica not get the Laplace ...
5
votes
1answer
271 views

Fourier transform of Exp[x]/x

Could you please explain why Mathematica gives the following expression when taking Fourier transform of $\exp(\lambda z)/\lambda$? $$\frac{-\log(-z)+\log(z)}{\sqrt{2\pi}}$$ Why the answer does not ...
4
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0answers
7k 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 ...
1
vote
0answers
57 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 ...
3
votes
1answer
2k views

How to do continuous Fourier transform?

I want to do a Fourier transform to the below function by Mathematica. How can I do it? Here $c$, $d$, $a$, $L$ are constants. $$ w(r)= \left\{ \begin{array}{ll} -\frac{c}{\epsilon r} & ...
3
votes
1answer
143 views

How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
2
votes
1answer
96 views

Solving 2D convection-conduction equation via using Fourier integral transform: the disappearance of the convection term?(with code)

I am currently solving a 2D convection-conduction equation. The convection is only working on the x direction. The governing equation and its associated conditions are given as where T is the ...
0
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0answers
50 views

What is the representation of the Harmonic Number being used by Mma in this result?

The Fourier Transform of the function F[x_] = (m/Sqrt[\[Lambda]])*Tanh[(Sqrt[x^2]*m)/Sqrt[2]] where all variables are real, and $m>0$ is given by (Mma 11.0) ...
0
votes
1answer
62 views

Solutions of ODE from Mathematica and Laplace transform differ

The equation is $p'(t)=k_1s_0{e}^{-k_1t}-k_2p(t)$ The solution with Mathematica DSolve[p'[t] == k1*s0*E^(-k1*t) - k2*p[t], p[t], t] $p(t) = -(k_1/(k_1-k_2)) ...
4
votes
1answer
256 views

How to speed up the integral in NDSolve?

On the MMA.SE, there have been several question on how to solve equations including integral using NDSolve, see example 1, example 2, and example 3. Many people, ...
5
votes
1answer
198 views

Solving partial differential equation involving Hilbert transform

While solving one research paper published in Physical Review Letters, I came across the following equation and I am unable to solve it. $$\frac{\partial f}{\partial t}−(\mathcal{H}(f)\left(\frac{\...
2
votes
2answers
104 views

Evaluating FourierTransform like integral manually

I am trying to evaluate Integrate[x^2*Exp[I k (x - 1)], {k, -∞, ∞}, {x, -∞, ∞}] Since $\frac{1}{2\pi}\int_{-\infty}^{\infty} e^{ik(x-1)} d{k}$ is $\delta(x-1)$, ...
9
votes
1answer
2k views

How can I invert a Laplace transform numerically?

I have a very complicated expression, which I want to transform using the inverse Laplace transform. The built-in function InverseLaplaceTransform doesn't work. So,...
1
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3answers
112 views

How to obtain that result of the integral in Mathematica?

I would like to integate this equation: Integrate[Exp[I*(t1-t2)*ω, {ω, -∞, ∞}] According to a textbook, I know the answer is $2\pi\delta(t_1 - t_2)$, where $\...
1
vote
1answer
964 views

How to solve Laplace transform question for a system in Mathematica

I know how to use the LaplaceTransform function but am struggling to do this with a system with two ODEs. This is my question: Use Mathematica and the Laplace ...
0
votes
0answers
72 views

Solving a system of two differential equation using Laplace Transform [duplicate]

I was trying to solve a system of two differential equation using Laplace Transform with Mathematica, but couldn't get any implementation for it. How do you reckon this can be solved? Consider this ...
2
votes
0answers
68 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 ...
3
votes
1answer
197 views

How do I plot a Laplace transform?

I have been looking everywhere for help on this issue and cannot find a solution that works. Here is the assignment. I have figured out how to find the Laplace transform, but I do not know how to ...
0
votes
1answer
146 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
12
votes
1answer
413 views

Package for fast spherical harmonic transform in Mathematica?

Mathematica's implementation of the Fast Fourier Transform is, naturally, much faster than computing the discrete transform yourself using Sum. The analog of the ...
1
vote
1answer
57 views

How to find discrete Z-transform of a list of complex numbers

Can we find the discrete Z-transform of a list of complex numbers in Mathematica? Similar to the function Fourier for the discrete Fourier transform, do we have a ...
1
vote
1answer
86 views
2
votes
1answer
48 views

Peculiar result of InverseHankelTransform

In using the HankelTransform and its inverse I find that the inverse does not lead to the initial input. I begin with r (the independent variable) in the denominator but end up with r0 (a constant) in ...
1
vote
1answer
71 views

Laplace transform giving incorrect result

In Mathematica: LaplaceTransform[Exp[-Exp[-t]], t, s] Out:= Gamma[s]-Gamma[s,1] But performing InverseLaplaceTransform on the ...
2
votes
1answer
64 views

Difference between FourierTransform and LaplaceTransform [duplicate]

There is an equation for example: eqn=D[c[x, t], t] == d D[c[x, t], x, x]; When I make a LaplaceTransform of it: ...
3
votes
1answer
275 views

Problem using Hankel transform

Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and ...
0
votes
1answer
70 views

Collect terms in Fourier Transform

I want to collect terms in x from a product of polynomials and Fourier transform. So I try following code: ...
7
votes
2answers
1k views

Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
1
vote
0answers
52 views

Inverse Laplace transform of powers with an arbitrary index

Tried for Inverse Laplace transform (ILT) for the following: L[s] = (L /(L + s) w + Q /(Q + s) (1 - w))^n $L[s]$ can also be written as $$L[s]=\sum_{k=0}^n\...
3
votes
0answers
61 views

Is `InverseMellinTransform` unaware of second Barnes lemma?

Consider evaluating ...
4
votes
2answers
164 views

Numerical Laplace transform error

I'm running Mathematica 11.3.0.0. The inverse Laplace transform of $1/(s^2-1)$, evaluated at $t=1$ gives ...
0
votes
1answer
70 views

Evaluating a Fourier integral

Is it possible to evaluate the following integral? $$\int \frac{(x-x_0) \: dx \: dy \: e^{i k_x x + i k_y y}}{((x-x_0)^2+(y-y_0)^2+4 h^2)^{\frac{5}{2}}}$$ As a first try, I evaluated ...
0
votes
0answers
51 views

How can I eliminate InverseLaplaceTransform returning complex

I tried this: F = InverseLaplaceTransform[ 1/((1 + s^2) (1 + (s + 1/2)^2)) + Exp[-Pi*s]*1/((1 + s^2) (1 + (s + 1/2)^2)), s, t] But it returns an answer ...
3
votes
1answer
196 views

Mellin transform of $x^p$ seems to miss a factor of $2\pi$

Bug introduced in 11.1 or earlier and fixed in 11.3 On Mathematica 11.1.1.0 the Mellin transform of $x^p$ is evaluated as $\delta(p+s)$, while I think it should be $2\pi\,\delta(p+s)$: ...