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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). ...
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 ...
18
votes
1answer
455 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
5answers
575 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 ...
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 ...
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] ...
11
votes
2answers
4k views

Numerically obtaining the inverse Laplace transform of data

I have been using several Mathematica packages to do numerical inverse Laplace transforms on known (expressible in closed form) expressions, $\tilde{f}(s)$. I am now being confronted with the more ...
10
votes
1answer
429 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 ...
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 ...
8
votes
0answers
793 views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
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: ...
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 ...
6
votes
2answers
313 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 $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
6
votes
3answers
417 views

Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

fixed in 10.0.2 Update I have tried like these. I think there is a bug. ...
4
votes
2answers
145 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 ...
4
votes
2answers
599 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 ...
4
votes
3answers
489 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, ...
4
votes
2answers
213 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 $\frac{-i}{2 \pi}$ ...
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 ...
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 ...
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, ...
3
votes
1answer
81 views

Bilateral ZTransform

Is there support for bilateral Z-transform in Mathematica, or a third-party package?
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 ...
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. ...
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: $$F(s)=\frac{2}{s-1}-\frac{3}{(s+1)^2+4}$$ ...
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 ...
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} ...
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 ...
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
190 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. ...
1
vote
1answer
75 views
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 ...
1
vote
1answer
276 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 ...
1
vote
2answers
93 views

Unknown limit of an array of area integrals

Could someone explain why Mathematica can't finish computing this limit (this is a limit of an array, when n -> Infinity (n ...
1
vote
1answer
155 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 ...
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 ...
1
vote
0answers
34 views

Different Results under Inverse Laplace Transform

I am getting different results from the following commands: ...
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? ...
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: ...
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 ...
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 ...
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 ...
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 ...
1
vote
0answers
66 views

Inverse Z Transform returning complicated expression

I want to study how the Z transform changes with the sampling rate T, in a closed loop system. The command I'm using to do this is: ...
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
279 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
1answer
60 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
0
votes
1answer
141 views

Z-Transforms and Floor Functions

When I take the $Z$-Transform of the Floor function: ZTransform[ Floor[x], x, z] I get ...
0
votes
0answers
38 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 ...