# 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 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 ...
796 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. ...
136 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 ...
193 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 ...
470 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 ...
857 views

### Inverse Laplace transform

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

### Z-Transforms and Floor Functions

When I take the $Z$-Transform of the Floor function: ZTransform[ Floor[x], x, z] I get ...
369 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: ...
113 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 ...
355 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] ...
1k 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 ...
130 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, ...
6k 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 ...
777 views

### Integrating over Bessel Function erroreous? (Hankel Transform)

Bug introduced in 8.0.4 or earlier and persists through 11.0.1 or later The Hankel Transform is given by Integrate[f[x] x BesselJ[0, x t], {x, 0, Infinity}] It ...
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). ...
1k views

### Inverse Laplace transform not obtained

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