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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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 ...
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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 ...
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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 ...
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314 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. ...
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1answer
77 views

Integrate 2D Gaussian over a segment

I have the following 2D Gaussian: ...
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2answers
70 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/...
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3answers
706 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 ...
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2answers
111 views

Finding the global maximum of a function

I've the following code: ...
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1answer
163 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}, ...
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54 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 ...
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1answer
124 views

How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
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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} & ...
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709 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 ...
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1answer
88 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 ...
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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) ...
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1answer
58 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)) ...
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1answer
253 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, ...
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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 $\delta(x-1)$, ...
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1answer
191 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{\...
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1answer
117 views

Generate this contour plot

I have the following complex function: ...
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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 $\...
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68 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 ...
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1answer
897 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 ...
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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 ...
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1answer
184 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 ...
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1answer
52 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 ...
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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 ...
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1answer
66 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 ...
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1answer
59 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: ...
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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: ...
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49 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\...
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61 views

Is `InverseMellinTransform` unaware of second Barnes lemma?

Consider evaluating ...
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2answers
155 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 ...
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1answer
389 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 ...
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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 ...
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50 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 ...
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1answer
264 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 ...
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1answer
94 views

Plotting a sum for a series of sine and cosine all within the same height on the x-y axis? [closed]

The limits of the graph should be (0,1) on the x and y axis but mine is [1,11] on x-axis and [0,7] on the y axis. Any idea what to do? ...
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1answer
62 views

Transform expression involving Erfc back and forth with Laplace transform and its inversion

It's a problem I encountered when answering this question and I think it's worth starting a new question for it. Consider the following expressions: ...
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2answers
335 views

Is it possible to find the transfer function of these three differential equations using Mathematica

Imagine you are attempting to obtain a model of a device with two inputs [u1, u2] and three outputs [O1, O2, x] from the Lagrangian. After some of Lagrangian work, you find the following three ...
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2answers
82 views

Can I use `LaplaceTransform` to find an $f$ such that $f(t)-f(t-a)= g(t)$ for some given $g$?

Suppose I know the difference between an unknown function $f$ and its delayed version, can I use LaplaceTransform to find $f$? I didn't succeed in this toy example:...
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39 views

InverseLaplaceTransform@LaplaceTransform does not reproduce the original expression

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1answer
184 views

Can the product of an exponential and a hypergeometric function be expressed as a Meijer-G function?

Let $0<\alpha< 1$. Can the function $\qquad e^{-\alpha x}U(a,b,x),$ where $U(a,b,z)$ is the hypergeometric U function be expressed as a Meijer-G function? The closest I found was here which ...
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1answer
83 views

Inverse Laplace transform - Getting a compact solution

I had the following inverse laplace transform: ...
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1answer
88 views

Inverse Laplace transform of a symbolic expression

I'd like to get the inverse Laplace transform of a symbolic expression. The output of my code is equal to the input? How can I modify the code to obtain the correct result? All k and V1 are positives....
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1answer
335 views

2D Fourier transform of annulus

I have an annulus and I'd like to the take the 2D Fourier transform of it, my code: ...
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1answer
148 views

FourierParameters causing function not to simplify

When evaluating this expression, Mathematica simplifies the result: FourierTransform[FourierTransform[u[t], t, s], s, t] This simplifies to ...
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1answer
809 views

Solving the heat equation on the semi-infinite rod

Cross posted in scicomp.SE. I want to test the solution which is given below is right by Mathematica. Please look the post in mathstackexhange or Please look below. Question: Solve the ...
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1answer
185 views

The inverse Laplace Transform of a real proper rational function must be real

How does one get Mathematica to return a real answer when using InverseLaplaceTransform? Tried using Re and ...