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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Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
163 views

Implementation of the Riesz transform

Implementing the Hilbert transformation \begin{equation}H(f)(x) = \frac{1}{\pi}\lim_{\varepsilon \to 0} \int_{|x-y|>\varepsilon} \frac{1}{x-y}f(y) \, dy,\end{equation} appropriate for 1-...
7k 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 ...
54 views

Is InverseMellinTransform unaware of second Barnes lemma?

Consider evaluating ...
132 views

Integral Representation of DiracDelta

I would like to get dirac delta from integral definition, of course if I ask Integrate[Exp[I x t],{x,-Infinity,Infinity}] I get that the integral does not ...
485 views

Region of convergence in Inverse laplace transform

Lets say we have a function in the s domain. Let it be H(s)=1/(s+1). It has one pole. If we consider the region to the right of the pole as the ROC, we would one function in the time domain when we ...
388 views

Computation of a Fresnel Diffraction pattern with Discrete Hankel Transform

In the next link: Computation of Hankel Transform using FFT (Fourier) Rainer implemented a great solution given in the next reference: Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Computation ...
32 views

Verifying a cosine FourierTransform

On page 31 of this standard reference we have the following relation: I wanted to use mathematica to verify this transform numerically for some example values. So I type in: ...
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Different Results under Inverse Laplace Transform

I am getting different results from the following commands: ...
102 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? ...
116 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 ...
236 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 g=\left(\textrm{e}^{\left(\frac{-0.008372\textrm{i}+0.008372\textrm{...
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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] where all variables are real, and $m>0$ is given by (Mma 11.0) ...
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Generate this contour plot

I have the following complex function: ...
34 views

MellinTransform yields DiractDelta function

I want to do a Mellin transform for the following function psi[x_] := Sum[1 - E^(-x/2^h), {h, 0, Infinity}] If I try ...
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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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 ...