All Questions
Tagged with mathematica fourier-analysis
17
questions
1
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1
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95
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Fourier transform of incomplete gamma function
Ultimately I am interested in the Fourier transform of
$$
e^{-i\zeta}(-i\zeta)^{-2\epsilon}\Gamma(2\epsilon,-i\zeta)
$$
in a series expansion around $\epsilon=0$, so to first order in
$$
\lim_{\...
- 133
0
votes
0
answers
649
views
Inverse Fourier transform of sign function
I am a bit puzzled by the following Mathematica outputs:
{FourierTransform[Sign[x], x, y], InverseFourierTransform[Sign[x], x, y]}
$$\frac{i \sqrt{2/\pi}}y, \quad ...
- 677
0
votes
0
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46
views
Fourier Series on Mathematica
Trying to find the first few terms of the Fourier series of $e^{x^2}$ on Mathematica, but my code doesn't seem to be working. It says the first few terms are all 0. Can anyone look at it and tell me ...
- 1
4
votes
1
answer
224
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May someone of you provide me (if possible) an expression for the F.T. of $\tan(x)$?
So here it is my problem: I need the Fourier Transform of the tangent function, namely:
$$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} \tan(x)\ e^{-ikx}\ dx$$
I tried for hours by hands and I got ...
- 26.3k
0
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0
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444
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Fourier-transform of non-analytic function
This question results from some afterthoughts from an earlier problem I posted in the mathematica-section (https://mathematica.stackexchange.com/q/130387/34999). So, I want to do the fourier-...
- 235
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0
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78
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Is this plot linear in the same way the Chebyshev function is linear?
The Dirichlet generating function for the von Mangoldt function is:
$$-\frac{\zeta '(s)}{\zeta (s)}=\lim_{c\to 1} \, \left(\frac{\zeta (c) \zeta (s)}{\zeta (c+s-1)}-\zeta (c)\right) \;\;\;\;\;\;\;\;\;(...
- 7,448
5
votes
2
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769
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Should I trust Mathematica or numerous other sources on this Fourier transform
Assume $a>0$
So Mathematica claims
$$F\{e^{-a|t|}\}(\omega) = \frac{a\sqrt{\frac{2}{\pi}}}{a^2+\omega^2}$$
However, I've read about another transform pair (page 3):
$$F\{e^{-a|t|}\}(\omega) = \...
- 1,755
0
votes
1
answer
671
views
Graphing Fourier transforms on a frequency versus intensity plot (how to deal with complex numbers)
I am trying to understand how Fourier transforms are used to make HNMR plots.
HNMR basically consists of hitting some molecules with some radiation and listening to the radio signal that results. ...
- 115
2
votes
1
answer
1k
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Fourier series of oscillation in form $\cos(2 \pi \frac{k}{T}+\phi)$
I would like to calculate the fourier coefficients of $\cos(2 \pi \frac{k}{T}+\phi)$ where $T \in \mathbb{N}$ is the period and is arbitrary but fixed, $k \in [1, N-1]$ is the number of oscillations ...
- 21
7
votes
1
answer
342
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Finding the period of the solution to $y'(x) = y(x) \cdot \cos(x + y(x))$ with Fourier transform; how to interpret complex result?
A question elsewhere on this site asks about detecting the frequency of oscillations in a system defined by differential equations.
The equation is $y'(x) = y(x) \cdot \cos(x + y(x))$. The solution ...
- 3,420
2
votes
0
answers
224
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What is the Fourier series of $e^{\mu\cos\theta}$?
Motivation: I want to solve this convolution problem on the circle: find $f$, given $g$ and
$$ g(\theta) = \int_{S^1} e^{\mu\cos(\theta-\phi)}g(\phi)\ d\phi. $$
To do this, I want to find the Fourier ...
- 33.3k
0
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1
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109
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fourier transforms with Woflram Alpha
I'm studying Fourier transform at the moment and I've noticed some weird irregularities between my textbook and Wolfram Alpha's answers.
Say I ask Wolfram the following:
fourier transform delta(t-...
- 807
1
vote
2
answers
328
views
Bessel function to $\sin(kr)$
$J_{\frac{1}{2}}(kr)=\frac{\sqrt{\frac{2}{\pi }} \text{Sin}[\text{kr}]}{\sqrt{\text{kr}}})$ This can be easily obtained by Mathematica,
How to do the details?
user52950
0
votes
1
answer
346
views
Inverse Fourier transform to find out $\hat c_1$
If we have an integration which is need to solve inversely $$a_0 e^{-r^2/R^2} = \int_0^\infty \hat{c}_1(k) \frac{\sin(k r)}{r} dk,$$
If I transform the $\sin(kr)$, then we get imaginary part.
Please ...
user52950
0
votes
1
answer
686
views
Fourier Transform for a Convolution
Alright, so I am using the Convolution property of Fourier Transforms to find a function $f(x)$. So the obvious equation: $h(x) = f(x) \ast g(x)$.
Definitions:
$$g(x)=Rect\left[\frac x w \right]$$...
- 1,449