Questions tagged [fourier-analysis]
Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.
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Why does this Fourier transform not match the formula?
From this page:
So I'm trying to get that result in Mathematica. From the fourier formula above, we can see that {a, b} = {1,-1}.
However, the code below returns a different result.
...
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2
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81
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Can I take the Fourier transform of a PDE in both sides? [duplicate]
I want to know if it is possible to use a PDE in the function FourierTransform instead of a function.
Consider for example the simple case for the heat equation
...
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1
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1
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Nonlinear Schrödinger Equation With Periodically Varying Function
I am trying to solve Equation. 42 from https://labsites.rochester.edu/agrawal/wp-content/uploads/2019/08/paper_2019_03.pdf
The equation I am trying to solve is a nonlinear Schrödinger equation
More ...
2
votes
2
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Collision of two waves with phase difference
I am trying to produce collisional figures from this paper https://arxiv.org/pdf/1803.07165.pdf.
But failed to see the phase effect. In my case it just passes through one another. It basically solve a ...
1
vote
1
answer
61
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Inverse Fourier Transform and the sign of the Shifted Delta
I am using the sign convention of FourierParameters->{0, -2 Pi} for calculating the inverse FT of $Aexp(-2\iota\pi f K)$, where $A$, $K$ are real numbers >0 ...
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I am trying to solve nonlinear Schrödinger equation with dipolar interaction
I am trying to solve numerically Equation number (29) with the help of Eq.(32) and (34) from this paper https://arxiv.org/pdf/1506.03283.pdf.
for
...
0
votes
1
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Convolution theorem if one function depends on the reciprocal space in a non-trivial way
I would like to write the following integral in terms of a convolution:
\begin{equation}
H(x_1,x_2) = \int dt e^{\mathrm{i} t (x_1+x_2)/2} f(t,x_1,x_2) g(t),
\end{equation}
where $f(t,x_1,x_2)$ ...
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Implementing the Shift Property of the Fourier Transform in Mathematica
I am trying to determine the Fourier tranform of a time shifted (t-b) Lorentzian function in Mathematica. With the zero centered Lorentzian (b=0), the Integrate function with the conditions that all ...
- 121
0
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1
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81
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Obtaining Inverse Fourier Transforms by "FourierTransform" vs. "Integrate" Option [duplicate]
I am trying to calculate the inverse Fourier transform of "1" using two approaches. One using the Integrate option and the other with InverseFourierTransform, so the function looks like the ...
- 121
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How to use FindSequenceFunction to obtain the general expression of Fourier series?
I want to get cosine series of the following functions.
$f(x)=\left\{\begin{array}{cc}\cos x, & 0 \leqslant x<\frac{\pi}{2} \\ 0, & \frac{\pi}{2} \leqslant x \leqslant \pi\end{array}\right.$...
- 1,365
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Why does the following integral not evaluate? [closed]
I am a complete beginner to Mathematica. I am trying to evaluate a Fourier integral (see below). Here $\mu(\vec{r})$ is a mass density with units $[\frac{u}{mm^3}]$, and its Fourier transform is ...
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Why would the computation time be hugely different for the same computation expressed in different but totally equivalent forms?
I was trying to plot an interpolation function from fourier data. The plot was very fast and straightforward when I used the following code:
...
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1
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Mathematica `fourier` get different result with python `np.fft` [closed]
In python,I run fft as below:
...
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Integrate does not converge while Fourier transform does
Let us say I want Mathematica to compute the integral
$$\int dx \, \text{sign} (x) \, \frac{1}{1+x^2} = 0 \, .$$
Indeed
...
- 257
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0
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TransformedField between "Cartesian" and "Polar"
When I do
f[x_, y_] := Exp[-Sqrt[x^2 + y^2]]
ft = FourierTransform[f[x, y], {x,y}, {u,v}, FourierParameters -> {0, 2*Pi} ]]
The result is
$$\frac{2 \pi }...
- 19
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fast fourier transformation question
I was testing fft on mathematica using simple functions and ran into problems.
I first tried a simple cos function with the following code:
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What integrals can `FourierTransform` evaluate that `Integrate` cannot?
FourierTransform can make sense of integrals that diverge according to Integrate.
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How to fourier transform a numerical solution?
I numerically solved a wave equation and want to fourier transform the solution uwave1(t,x,z) at a particular instant of time t and position z. The code is as follows:
...
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1
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1
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How to calculate Fourier series for an arbitray non-periodic function defined in arbitray interval by setting FourierParemters or by rescale? How?
I am struggling to understand the Fourier series in Mathematica.
I don't find a way to calculate Fourier series for a general function which is not periodic and defined on a interval but not on ...
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generating 1/f noise
the spectrum of noise δε(t) is S(ω)=<|δε(ω)|²>, where δε(ω) is a Fourier coef. of δε(t). And the relationship between the variance σ² of a zero-mean δε(t) and the spectrum is
……(I),
where ωl（ωh）...
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How to get the Inverse Fast Fourier Transform (ifft) of a dataset? [closed]
I'm looking at the inverse fast Fourier transform as calculated by Matlab. In the question "What's the correct way to shift zero frequency to the center of a Fourier Transform?" the way to ...
- 1,100
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2
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Mathematica Fourier Transform not responding
I am trying to do Fourier Transformation on the following function Izzn, which is essentially just a lot of trigonometric function, whose Fourier transformation are all well defined. However, when I ...
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How can I use fast Fourier transform (FFT) to solve a PDE (heat equation)?
I'm trying to solve a one-dimensional heat equation (PDE) with the Fourier transform numerically, in the way it was done here. The equation:
,
is subject to the initial condition:
,
where U(x,t) is ...
- 1,100
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68
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Why does the reported primary frequency with Mathematica's discrete Fourier transform scale with the length of the input signal?
I am testing Mathematica's DFT algorithm using one of the test cases provided in the documentation, of a noisy sine function with a frequency of 0.15 cycles per sample:
...
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3
votes
1
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115
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How to conciliate results between Fourier and FourierTransform?
I can't match the analytical results of a continuous-time Fourier transformation with the results I get from a discrete Fourier transform using Fourier[] in ...
- 113
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1
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How can I get the power spectrum density and separate low and high frequencies?
Good day everyone,
I'm new in mathematica.
I got these values over time (each value was obtained every 100 milliseconds):
...
- 51
3
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0
answers
40
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Spectrogram/SpectrogramArray output
Is there/ What is the trick to get the output of the STFT as {Fourier coeff., freq, time} format from Spectrogram/SpectrogramArray/anything else?
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How to solve Coupled a Parabolic and Elliptic PDE in NDSolve?
I want to solve a mixed PDE Parabolic-Elliptic system in 3-dimension (rectangular coordinate), as shown below:
The respective code version with parameters value, boundary and initial conditions is,
<...
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What is 0 dB in Periodogram?
Consider some sound:
ViolinNote = Sound[SoundNote["G", 1, "Violin"]]
We may plot the periodogram:
...
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How does Fourier work with arbitrary FourierParameters?
Mathematica's Fourier function allows you to insert an arbitrary real number in the exponent of the discrete Fourier transform, via ...
- 265
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0
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Analyzing anomalies of Bluetooth audio generation with Mathematica
I' m working on an audio generator for physics lab, using an Android device and Bluetooth . However, the response of the Bluetooth speaker is wrong.
When programmed to deliver, say 3150 Hz, it may ...
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How to visualize overtones in Mathematica?
I would like to visualize the difference in sounds extracted by different musical instruments, which is due to different overtones. In order to do this, I define the following samples:
...
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Need help plotting a wavefunction generated from a sum of eigenstates [closed]
I am a beginner in Mathematica. I am trying to plot the time evolution of a non-eigenstate wavefunction as a sum of eigenstates.
So I start with an eigenstate of an infinite square well, then expand ...
- 101
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Fourier coefficient of $\frac{1}{5 + 4\cos(x)}$ wrong
I've been trying to use Mathematica to compute the Fourier coefficient of
$$
f(x) = \frac{1}{5 + 4\cos(x)},
$$
which is a $2\pi$ periodic function. Inputting
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How to symbolically manipulate the closed form series output from the easyFourier package?
EasyFourier by @xzczd is a nice package to obtain a Fourier series in closed form, e.g.
f = x^2
easyFourierTrigSeries[f, {x, -\[Pi], \[Pi]}, \[Infinity]]
However, ...
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extracting phase from sinusoidal data
I am dealing with data which are essentially are sinusoidal with various degrees of noise. I have an interest in extracting the phase of the data and rather than simply fitting a sine wave, I would ...
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1
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Power spectrum of a signal in negative frequency domain
I have a signal with fc = 308 kHz and B = 30 kHz and some white noise added. The signal is sampled at samplFreq = 4fc.
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0
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Fourier transform of $ \exp{\left(\text irx/\sqrt{1-\text ix}\right)}/(1-\text ix) $
I want to calculate the following Fourier transform:
$$u(r,t) = \int_{-\infty}^{\infty}\text d\omega\ \frac{1}{1-\text i\omega}\, \exp\left\{\frac{\text ir \omega}{\sqrt{1-\text i \omega}} +\text i\...
- 9
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Is there a function in Mathematica to combine/decompose sinusoids? [closed]
Lets say I have some combination of an arbitrary number of sinusoids with potentially varying magnitudes, phase angles and frequencies that I would like to compose into a singular sinusoid, is there a ...
0
votes
1
answer
92
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Microfluctuations analysis and Power spectrum
I measured a parameter over time and obtained the values below:
0,627896 0,205004 0,259237 1,059125 0,832184 0,587992 0,565537 0,527323 0,460228 0,471958 0,26696 0,75367 ...
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2D Poisson equation with Piecewise RHS - symbolic solution?
I'm trying to solve the following 2D Poisson equation symbolically:
$$
-\nabla^2 u(x,y) =
\begin{cases}
1-\text{sech}\left(\frac{w}{2 d}\right) \cosh \left(\frac{x}{d}\right)
& -w/2 \leq ...
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Debugging code with Plot function. Full details
This is some code:
The first plot (with the f[x,3]) gives me a graph.
The second plot (with the 'numerical' form of f[x,3] given) does give me a plot
How can I fix this so that the first line gives me ...
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Useless result of Integrate
Considering a Fourier sine series, I calculate
int = Integrate[Log[1 + Sin[x]]*Sin[i*x], {x, 0, Pi}, Assumptions -> i ∈ PositiveIntegers]
...
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0
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Raising awareness about a Fourier analysis issue [closed]
I have just posted a query on Wolfram's own forum: https://community.wolfram.com/groups/-/m/t/2299913?p_p_auth=HBTdYN1c
This is because it allows me to share the notebook I am working on and therefore ...
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Issues to compute and plot a function with some Fourier analysis
I'm currently in an internship and I have to construct a model that involve Fourier transform of 2 orbitals. My issue is that when I run the programm, the function evluateton non numerical values : &...
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How to obtain a normalized fourier transform?
In my code I solved a differential equation system, then I made a fourier transform of the solution in differents times, this is my code
...
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4
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Challenge: Computing the Fourier Series of a List Plot!
I have a bunch of data points (copied from Mathematica below), which I have 'ListPlotted'
I would now like to compute the Fourier series of this function (after doing a Fourier transform I assume? Or ...
- 103
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0
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120
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Fourier transform not working! [closed]
The FourierTransform doesn't seem to work on the following function:
...
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Fourier transform of DawsonF not recovered by using Erfi
Bug introduced in 8 or earlier and fixed in 12.2
I wish to compute the Fourier transform related to the Dawson function:
FourierTransform[1/u DawsonF[1/u], u, x]
...
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