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.

Filter by
Sorted by
Tagged with
1
vote
0answers
31 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 ...
0
votes
0answers
29 views

How to automate the transformation into spherical coordinates of a region

I've this region: S = { (x,y,z) ∈ R^3 | 2 * Sqrt[x^2+y^2] <= z <= 1 + x^2 + y^2} Now I would like to transform the coordinates into spherical ones, so as to ...
1
vote
0answers
75 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}\...
2
votes
0answers
56 views

InverseRadon function - possible bug?

I have to calculate a 2-dimensional radially symmetric distribution from a single projection. I know that InverseRadon should actually do the job, but I get the ...
0
votes
1answer
55 views

Assume that the value of an integral is real

I would like to give a condition that the integral I am handling are not complexes. Consider ...
0
votes
1answer
147 views

Are there some programs about inverse Fourier and Laplace transfroms?

To be more exact, I have a function F[w_,s_], where $w$ is the Fourier transform of $x$ and $s$ is the Laplace transform of $t$. Now I want to perform the double inverse transforms $s\to t$ and $w\to ...
1
vote
0answers
146 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\\\...
2
votes
1answer
90 views

How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
1
vote
0answers
54 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 ...
1
vote
0answers
44 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: ...
3
votes
1answer
51 views

Numerical Laplace Transform of InterpolatingFunction

What are some ways to find the numerical Laplace transform of an InterpolatingFunction? (I know that numerical Laplace transforms are rarely used but my application requires a numerical evaluation). ...
3
votes
0answers
60 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 ...
1
vote
1answer
54 views

Laplace transform of Heaviside step function of free variables

In A First Course in Differential Equations with Modeling Applications, Tenth Edition (Zill, 2013) it's stated that if $$\mathcal{U(x)}= \begin{cases} 0,\;x < 0 \\ 1,\;x \geq 0 \...
0
votes
1answer
82 views

Inverse Fourier Transform and peculiar results

In order to get Fourier and Inverse Transform of a function $f(x)$ I write the following commands: As far I can see that Nominator in the quotient of INF[x] is ...
6
votes
1answer
195 views

InverseMellinTransform producing two different results for the same input?

Consider the expression expr = Gamma[1 + s]/Gamma[1 - s] Gamma[-s]^2; and a slightly simplified version of the same ...
4
votes
2answers
71 views

LaplaceTransfrom with time shifting

Hi I'm wondering if there's some workaround to get Mathematica to use time-shifting identities for Laplace and Inverse Laplace transforms. My examples are below. ...
2
votes
2answers
125 views

Issues with Fourier transform in M.12.1.0

I am using M. Version: 12.1.0. In version 10, I got the result right away.So, Why mathematica (12.1.0) is not able to solve this problem? ...
4
votes
2answers
149 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? ...
2
votes
1answer
86 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
90 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? ...
0
votes
0answers
44 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
votes
2answers
91 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 ...
0
votes
0answers
71 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 ...
3
votes
1answer
176 views

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

At least one of the outputs (highly likely both) ...
1
vote
0answers
329 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
vote
1answer
85 views

Integrate 2D Gaussian over a segment

I have the following 2D Gaussian: ...
0
votes
2answers
85 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
761 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 ...
2
votes
2answers
153 views

Finding the global maximum of a function

I've the following code: ...
3
votes
1answer
249 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}, ...
1
vote
0answers
78 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
182 views

How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
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} & ...
7
votes
1answer
717 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 ...
2
votes
1answer
117 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
votes
1answer
66 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
289 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, ...
2
votes
2answers
108 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 $\delta(x-1)$, ...
5
votes
1answer
241 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{\...
1
vote
1answer
134 views

Generate this contour plot

I have the following complex function: ...
1
vote
3answers
122 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
2k 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 ...
2
votes
0answers
74 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
266 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 ...
1
vote
1answer
66 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 ...
2
votes
1answer
50 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
80 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
66 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: ...
0
votes
1answer
75 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: ...