# Questions tagged [fourier-transform]

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### Reducing the frequency resolution for a short pulse by applying the SVEA - how to keep frequency?

If I have a single light pulse, I can define it as (within certain boundaries, and $A$ a gaussian function) $$E(t) = A(t)\cdot\exp(-i\omega_0 t)$$ After applying an FFT over it, I can then shift the ...
1answer
34 views

### How to obtain the exact value of wavelength from a 2D FFT amplitude vs wavenumber plot like it is obtainable from 1D FFT amplitude vs wavenumber plot?

I have a two dimensional multi modal spatial signal generated from a MATLAB code using sinusoidal functions of different wave numbers, amplitudes and phases. What I want to know is that if I have the ...
1answer
58 views

### Improving efficiency of FFT for large time window and single frequency pulses

Spectral methods for pulse propagation usually require at least one FFT and one iFFT for each step. In my case I have a two-dimensional radially symmetric electric field (one dimension in space, one ...
1answer
74 views

### Reason behind different outputs for Fast Fourier Transform in Numpy and Matlab

Here is the output of Numpy np.fft.ifft([0, 4, 0, 0]) array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) # may vary Here is the output of Matlab ...
0answers
40 views

### Fourier transform in finite element

I have a finite element solver where I am using tetrahedral elements. I am solving for electric potentials and then calculate the current densities in each element, which are constant in each element. ...
2answers
102 views

0answers
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### Problems with simulation of a spatial filter 4f setup (Python)

I have a question about my code which computes numerically the output field of a 4f setup with a pinhole in the middle which works as a spatial filter. My setup consists of two lenses with 50mm focal ...
0answers
30 views

### Scale of x-axis for Fourier transform

Consider a function $f(t)$ and its Fourier transform $F(\omega)$. The amplitude of the Fourier transform $F(\omega)$ depends on the frequency $\omega$ and thus also depends on the scale of the $t$-...
2answers
588 views

### Computing numeric derivative via FFT - SciPy

I wrote the following code to compute the approximate derivative of a function using FFT: ...
1answer
147 views

### How to define a dimensionless Objective function for determining how peaked a curve is?

I have attached 2 plots for FFT spectra. One is considered good and one is bad. The good one is classified on the basis of how closely spaced the frequencies and the bad is based on how multiple ...
0answers
34 views

1answer
412 views

### Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
2answers
127 views

### DFT of $g(\omega) \exp(i C \omega^2)$. How to do it ,if uniform sampling requires too much memory?

I have a following problem : I want to transform a function $g(\omega) \exp(i C \omega^2)$. $g(\omega)$ is real and limited. It changes slowly compered to $\exp(i C \omega^2)$. I have a black box that ...
0answers
48 views

### The sign of Schrodinger equation

I have a question for the format of Schrodinger equation $$\psi(x,t) = \int_0^\infty c_n e^{-iE_nt/\hbar} \psi_n(x)$$ Why do we have $i$ instead of $-i$?
1answer
60 views

### FFT of “implicitly” uniform data

I am trying to take a Fourier transform of a density field estimated from mock galaxy survey catalogs. Basically, you start with a list of galaxy positions, then you bin these positions over some ...
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96 views

### Discrete sine and cosine transform for mixed derivatives

Using sine and cosine transforms to solve Poisson's equation with Dirichlet boundary conditions seem quite standard nowadays (see, e.g., here or Table 2 in this paper). In the case of Poisson's ...
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### What is the inverse Laplace transform algorithm that is most accurate given the fewest frequencies considered?

Based on your empirical knowledge. This paper suggests a nonlinearly accelerated Fourier series approach, such as the one proposed here, but I have one constraint: we should be able to express the ...
2answers
128 views

### How to solve diffusion equation in Fourier space when mobility is not constant

I want to solve non-classic diffusion equation in Fourier space. The equation is $$∂c/∂t=-∇.J$$ Where $J$ is $$J= -M.∇μ$$ Where M is mobility. It depends on c and $\mu$ is $$μ= g(c) - \nabla^2c$$ ...
1answer
377 views

### High precision Discrete Fourier Transform in c

I'm trying to do a high precision discrete fourier transform on a signal. To examine the precision, I use a gaussian function as the signal, because the fourier transform is also a gaussian function. ...
0answers
100 views

### Code for solving the heat equation on the semi-infinite rod

Cross posted in mathematica.SE. Question : I want to test the solution which is given below is right by Matlab/Maple/Mathematica. Please look the post in mathstackexhange or Please look below. ...
1answer
83 views

### fft with non uneven spacing between the value of the signal

I am trying to implement in C or C++ a solution for a fft and Ifft when the signal values are not obtained at a constant rate, making it having a desviation between the values and the periodic ones. I ...
0answers
80 views

### Can x-ray back-projection be converted to hard-field magnetic induction tomography?

This is a question about hard-field back-projection as used in x-ray tomography, applied magnetic induction tomography. Al-Zeibak and Saunders have shown that x-ray filtered backprojection can be ...
0answers
53 views

### Beam propagation over extremely short distances

I like to simulate the free-space propagation of an electric field (beam radius ~ 1-10 cm) over extremely short distances (~ 5-10 cm). The reason is that the field is focused by a lens with a very ...
1answer
145 views

### Hankel transform from paper works only for certain functions

I implemented an algorithm for solving the Hankel transformation based on a paper. My problem is: It works very good for the functions suggested in the paper (as test functions), it works pretty ok ...