We’re rewarding the question askers & reputations are being recalculated! Read more.

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
14
votes
1answer
465 views

Workarounds for a possible bug in the linearity of FourierTransform

This is somewhat similar to this question, except the problem I am encountering is to do with Fourier transforms of scalar multiples of functions and their derivatives. I wish to input ...
27
votes
4answers
10k views

Implementing discrete and continuous Hilbert transforms

What is an efficient and accurate Mathematica implementation of the Hilbert transform, for both continuous and especially discretely sampled functions? This transform relates phase and amplitude in ...
6
votes
1answer
564 views

Implement finite Fourier transforms

Recently I came across finite Fourier transforms, which can be used for solving certain type of boundary value problem (BVP) of linear partial differential equation (PDE) with constant coefficient. ...
22
votes
1answer
1k views

Numerical inverse Laplace-Hankel transform

When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
15
votes
1answer
355 views

Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
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
1answer
742 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 ...
4
votes
1answer
242 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, ...
15
votes
1answer
5k views

Computation of Hankel Transform using FFT (Fourier)

To address circularly symmetric cases of 2-D Fourier Transformations, the so-called Hankel Transform can be applied (for a detailed derivation of the relation between the 2-D Fourier transform and the ...
10
votes
1answer
1k views

Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
5
votes
1answer
164 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{\...
8
votes
2answers
341 views

Why does InverseLaplaceTranform give an incorrect solution?

Bug introduced in 9.0.1, fixed in 11.1. I was trying to answer this question, but I ended up asking this. Method 1 A workaround is to differentiate the ODE once, ...
3
votes
2answers
147 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 ...
5
votes
1answer
539 views

Solving PDE involving Hilbert transform numerically

I'm trying to solve the following equation numerically: $$u_{tt}-\mathcal{H}(u_x)=A^2_{xx},$$ where $\mathcal{H}$ is the Hilbert transform and $A$ is a prescribed forcing function which we assume ...
4
votes
1answer
61 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: ...
1
vote
2answers
307 views

Why does InverseFourierTransform gives different result to doing it by hand? [duplicate]

When I can calculate an inverse fourier transform by the built-in function InverserFourierTransform, the result is different from what I calculate by definition ...
0
votes
1answer
843 views

Inverse Laplace transform

For this expression: $ (1 - Exp[-Sqrt[1+s] x])/(1+s)$ How to make the Inverse Laplace Transform analytically? ...
0
votes
0answers
106 views

Multidimensional DFT of function

Assume that we have a well-defined real-valued functionf[x,y,z] whose (inverse) Fourier transform is impossible to solve for symbolically and numerically using ...