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.

29 questions with no upvoted or accepted answers
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8
votes
0answers
1k views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
5
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0answers
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-...
4
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0answers
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 ...
3
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0answers
54 views

Is `InverseMellinTransform` unaware of second Barnes lemma?

Consider evaluating ...
3
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0answers
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 ...
3
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0answers
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 ...
3
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0answers
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 ...
2
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0answers
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: ...
2
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0answers
294 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
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0answers
135 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
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0answers
38 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 ...
1
vote
0answers
61 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 ...
1
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0answers
46 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\...
1
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0answers
39 views

LaplaceTransform vs Integrate with inconsistent result

I am trying to evaluate the following integral, which happens to be a laplace transform $$ G(x,x';z)=\frac{1}{i\hslash}\int_0^{\infty}dt \exp\left(\frac{izt}{\hslash}\right)\sqrt{\frac{m}{2\pi i \...
1
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0answers
124 views

Can Mathematica verify the Cahen - Mellin integral?

Can Mathematica verify the Cahen-Mellin integral? When I try Integrate[Gamma[1 + I s]/Zeta[3]^(1 + I s), {s, -Infinity, Infinity}] I just get the input back. ...
1
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0answers
153 views

Inverse Laplace Transform Failing: $\frac{1}{\exp (\beta \tau )-a}$

I have tried various approaches to get the solution to this inverse transform but all so far are failing. ...
1
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0answers
249 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
1
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0answers
87 views

Different Results under Inverse Laplace Transform

I am getting different results from the following commands: ...
1
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0answers
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? ...
1
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0answers
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 ...
1
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0answers
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{...
0
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0answers
46 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) ...
0
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1answer
80 views

Generate this contour plot

I have the following complex function: ...
0
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0answers
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 ...
0
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0answers
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 ...
0
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0answers
38 views
0
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0answers
102 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 ...
0
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0answers
76 views

Understanding Mathematica's InverseZTransform Function

I'm trying to find the Inverse Z Transform of the following: InverseZTransform[(1 - ρ)/(1 - ρ z), z, n] and I get from Mathematica the result ...
0
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0answers
35 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 ...