# 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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143 views

### InverseFourierTransform takes forever

I am trying to find InverseFourierTransform of the following function, but the code below does not give me a result. I do not get any error messages but the calculation just does not end. Any Help? ...
62 views

### Problem with Inverse Laplace Transform in Mathematica

I am trying to calculate the following inverse Laplace transform $$f(t) = \mathcal{L}^{-1}\left[ \left(\frac{1}{s+a}\right)^{n+1}\left( \frac{1}{s+b}\right)^{n} \right](t)$$ with $s$ being the ...
80 views

### InverseLaplaceTransform not working

I am trying to find the Inverse Laplace transform of a function I previously obtained from a Laplace transform, but the result obtained does not agree with the initial function. Why is this happening? ...
162 views

### Fourier transform of Log[RealAbs[x]]^2

At least one of the outputs (highly likely both) ...
38 views

### Solving a System and taking inverse Laplace/Fourier Transforms

I have a set of linear equations for 4 quantities which have been both Fourier transformed and Laplace transformed. The system needs to be solved for the quantities and then each of the quantities ...
63 views

### Impulse response function h(t) of Gauss functions as a stimulus and response

From the basics of the signal theory the impulse response function (IRF) can be calculate like (L=Laplace transformation): L[x(t)]= X(s) , L[y(t)]= Y(s) and transfer function H(s)= Y(s)/X(s), then IRF ...
319 views

### Mathematica 12 returns a “greater::nord” error when Mathematica 11 does not

In the following code Talbot's method is made use of to invert Laplace's transforms. ...
120 views

### Generate this contour plot

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

### Teach Mathematica analytical continuation of the gamma function

If I ask Mathematica to compute the gamma function for me Integrate[Exp[-s] s^(a - 1), {s, 0, Infinity}] It dutifully returns to me ...
121 views

### Finding the global maximum of a function

I've the following code: ...
79 views

### Integrate 2D Gaussian over a segment

I have the following 2D Gaussian: ...
710 views

### Correct way of simplifying the result of an integral

Many times Mathematica gives enormous results to simple problems. One uses the program more for trouble than for not knowing how to solve the problem. As an ejemplo I present this integral that ...
75 views

### Solving proplem by Laplace transform [closed]

I want to solve these ODE's by Laplace transformation and graph it dx1/dt = 38/1180 x3(t) + (1 + sin⁡(t)) - 38/2900 x1(t), x1(0) = 0 dx2/dt = 18/2900 x1(t) - 18/850 x2(t), x2(0) = 0 dx3/dt = 20/...
722 views

### Mathematica and MatLab giving different results from inverse Laplace transform [closed]

The questionis is as this Given the transfer function gs = (5*s + 4)/(s^4 + 4*s^3 + 2*s^2 + 3*s); and the input signal ...
171 views

964 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 ...
72 views

### Solving a system of two differential equation using Laplace Transform [duplicate]

I was trying to solve a system of two differential equation using Laplace Transform with Mathematica, but couldn't get any implementation for it. How do you reckon this can be solved? Consider this ...
68 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 ...
197 views

### How do I plot a Laplace transform?

I have been looking everywhere for help on this issue and cannot find a solution that works. Here is the assignment. I have figured out how to find the Laplace transform, but I do not know how to ...
146 views

### InverseFourierTransform very slow

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

### Package for fast spherical harmonic transform in Mathematica?

Mathematica's implementation of the Fast Fourier Transform is, naturally, much faster than computing the discrete transform yourself using Sum. The analog of the ...
57 views

### How to find discrete Z-transform of a list of complex numbers

Can we find the discrete Z-transform of a list of complex numbers in Mathematica? Similar to the function Fourier for the discrete Fourier transform, do we have a ...
199 views

### I can't get the inverse Laplace transform in terms of the unit step function

I tried this: ...
86 views

### Inverse Laplace transform - Getting a compact solution

I had the following inverse laplace transform: ...
48 views

### Peculiar result of InverseHankelTransform

In using the HankelTransform and its inverse I find that the inverse does not lead to the initial input. I begin with r (the independent variable) in the denominator but end up with r0 (a constant) in ...
71 views

### Laplace transform giving incorrect result

In Mathematica: LaplaceTransform[Exp[-Exp[-t]], t, s] Out:= Gamma[s]-Gamma[s,1] But performing InverseLaplaceTransform on the ...
64 views

### Difference between FourierTransform and LaplaceTransform [duplicate]

There is an equation for example： eqn=D[c[x, t], t] == d D[c[x, t], x, x]; When I make a LaplaceTransform of it: ...
275 views

### Problem using Hankel transform

Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and ...
70 views

### Collect terms in Fourier Transform

I want to collect terms in x from a product of polynomials and Fourier transform. So I try following code: ...
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 $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
52 views

### Mellin transform of $x^p$ seems to miss a factor of $2\pi$
Bug introduced in 11.1 or earlier and fixed in 11.3 On Mathematica 11.1.1.0 the Mellin transform of $x^p$ is evaluated as $\delta(p+s)$, while I think it should be $2\pi\,\delta(p+s)$: ...