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17
votes
1answer
409 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 ...
-2
votes
0answers
39 views

Finding Laplace Transform [closed]

With the following DE y"(t)+5 y'(t) +6y(t)= t 0 How do I find the Laplace Transform to find the IVP??? I've tried everything and I can't figure it out.
0
votes
0answers
37 views

How can i obtain the inverse transform

The inverse Fourier transform is defined as: $$\mathcal{F}^{-1}[g](x) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} g(k) e^{i k x} d k$$ I can't get an inverse Fourier Transform to ...
10
votes
1answer
425 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 ...
1
vote
0answers
34 views

Different Results under Inverse Laplace Transform

I am getting different results from the following commands: ...
0
votes
0answers
58 views

Another question about inverse Laplace transform

Given $r = 0.06;\quad \theta = 105;\quad \kappa = 1;\quad x_0 = 100;\quad K = 100;\quad \sigma = 0.10;\quad T = 0.25;$ Define $ \nu = -\kappa/\sigma^2 - 0.5;\quad p = \kappa*\theta/\sigma;\quad q = ...
3
votes
1answer
24 views

Possible incompatibility between ReplaceAll and LaplaceTransform

I have a large symbolic expression containing many terms of the form, LaplaceTransform[u2[z], z, s], with various functions for the first argument. I wish to ...
0
votes
0answers
33 views

How can I get left-sided-sequence with InverseZTransform

InverseZTransform[z^2/((4 - z)*(z - 1/4)), z, n, Assumptions -> {1/4 < Abs[z] < 4}] (* -(1/15) 4^-n (-1 + 16^(1 + n)) *) the result is not true.It only ...
3
votes
1answer
77 views

Table with power law indexing

I am using the Drubin numerical inversion out of Laplace space, and need to see how the function performs over a wide range of values, covering multiple logrithmic cycles. However, the inversion is ...
2
votes
0answers
88 views

How to Mellin transform a complicated Log integrand?

I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this: $$ \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
0
votes
1answer
60 views

InverseFourierTransform very slow

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

Laplace Transform of a Multidimensional Partial Differential Equation

I'm trying to use Mathematica to solve a multidimensional partial differential equation using Laplace tranforms. The PDE is as follows: $$ \frac{{\partial T}}{{\partial t}} = \frac{{{\partial ...
4
votes
1answer
77 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 ...
2
votes
0answers
74 views

How to do the Fourier transform of a picture? [duplicate]

I want to generate Fourier transforms of a picture. the transform can represent the diffraction pattern of the picture. Basically, if I have a picture. Then, the result should look like this: For ...
0
votes
1answer
59 views

$\tt DiracDelta$ behaves incorrectly on multidimensional integral [duplicate]

Is there a reason why this seems to work: Integrate[DiracDelta[x] F[x], {x, -Infinity, Infinity}] F[0] But this does not: ...
6
votes
2answers
311 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
64 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? ...
3
votes
0answers
115 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. ...
9
votes
1answer
178 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 ...
7
votes
1answer
630 views

Integrating over Bessel Function erroreous? (Hankel Transform)

Bug introduced in 8.0.4 or earlier and persists through 10.2. The Hankel Transform is given by Integrate[f[x] x BesselJ[0, x t], {x, 0, Infinity}] It is ...
4
votes
2answers
141 views

Calculate the Bromwich Integral (Inverse Laplace Transform)

How can I calculate the Bromwich Integral in Mathematica? If I enter this as code it gives me just the same: $$\frac{1}{2\pi i}\int_{\alpha-\infty i}^{\alpha+\infty i} \left(e^{st}\cdot ...
34
votes
1answer
2k views

Mathematica 9 cannot solve this Integral. Mathematica 8 could. Is this a bug?

I was trying to (re)calculate a problem of an older Wolfram blog post (Problem 11457, by M. L. Glasser) with Mathematica 9.0.0.0 (on OS X 10.8.2). ...
1
vote
0answers
55 views

Convergence conditions of the Laplace Transform [closed]

I have to calculate some Laplace Integrals but if I use LaplaceTransform then it does not give the conditions when the integral converges. Is there an option to get ...
1
vote
0answers
50 views

Transfer function in recursive form [closed]

To get transfer function in recursive form, I tried this: ...
4
votes
2answers
212 views

Analytic expression for a Complex Hilbert Transform in Mathematica

I need to solve the following integral equations for a problem I'm working on - $\frac{-i}{2 \pi}$ $\int_{-a}^{a} \mathrm{dt}\,\, \frac{e^{i k t}}{t + i \tau}$ and $\frac{-i}{2 \pi}$ ...
12
votes
0answers
201 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] ...
13
votes
1answer
3k 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 ...
1
vote
0answers
51 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 ...
3
votes
1answer
81 views

Bilateral ZTransform

Is there support for bilateral Z-transform in Mathematica, or a third-party package?
1
vote
0answers
72 views

Inverse Laplace computation Mathematica [closed]

I have a transfer function such as following, which I would like to find its inverse: F=(a*s^2)/(b*s^3+c*s^2+d*s+e) I have a numeric value for a b c d and e but ...
15
votes
5answers
572 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 ...
2
votes
1answer
167 views

Inverse Laplace Transform difficulty

I am asked to find the inverse Laplace transform of: $$F(s)=\frac{2s^2+s+13}{(s-1)((s+1)^2+4)}$$ I did the partial fraction decomposition by hand and got: $$F(s)=\frac{2}{s-1}-\frac{3}{(s+1)^2+4}$$ ...
4
votes
2answers
598 views

Bilateral Laplace Transform

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
1
vote
2answers
104 views

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

When I can calculate an inverse fourier transform by the built-in function InverserFourierTransform, the result is different from what I calculate by definition ...
2
votes
0answers
106 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 ...
1
vote
1answer
274 views

Discrete Fourier Transform of a vector defined on a 3D lattice

In my research I need to compute the Discrete Fourier transform of a vector defined on a 3D lattice (a cube) to the "reciprocal" lattice. This is quite new to me so before proceeding i wanted to be ...
4
votes
3answers
486 views

Integral of function involving Dirac delta

I am performing lots of simple calculations with dirac delta functions. It would be awesome if Mathematica could do this routine exercise for me, eliminating any possible human errors. For example, ...
1
vote
0answers
131 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 ...
2
votes
0answers
1k 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
1answer
109 views

Inverse Laplace transform only returning exponentials

The inverse Laplace transform is only returning exponentials. I know it is from the definition $$ \frac{1}{2\pi i}\int_{\gamma - i\infty}^{\gamma + i\infty}F(s)e^{st}ds = \sum\text{Res} $$ However, I ...
19
votes
3answers
7k 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 ...
3
votes
1answer
109 views

PrincipalValue option of Convolve not working in 9.0.1?

The PrincipalValue option of Convolve is used in this question to define the Hilbert transform. However, in Mathematica 9.0.1, ...
1
vote
1answer
188 views

Trouble with Fourier transform of Exp[-Sqrt[x]]

First time trying to do something "real" in Mathematica, I am having trouble getting it to calculate this Fourier transform. It runs for a long time, then just prints the input expression. ...
0
votes
2answers
163 views

Indirect transformation based on a list of data points

I have a set of data which describes the Intensity function $Int(q)$ as a function of $q$. The data list provided below provides the shape of $Int(q)$ versus $q$.How can I use this information to ...
0
votes
1answer
278 views

Inverse Laplace transform

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

Code for solving numerically an integro-differential equation

First of all, I want to greet the community. This is my first question, but I hope I will be able to help answering others members questions, although I am quite new working with Mathematica. I would ...
7
votes
3answers
585 views

Any way I can solve this integral?

So, Mathematica can't solve it. Any workaround? \begin{equation*} \int_0^\pi \frac{1}{\sin\left(\frac{\theta}{2}\right)^\beta + 1} \mathrm{d}\theta \end{equation*} The code is: ...
0
votes
1answer
140 views

Z-Transforms and Floor Functions

When I take the $Z$-Transform of the Floor function: ZTransform[ Floor[x], x, z] I get ...