Questions on the computational aspects of Fourier analysis, including the various applications of the fast Fourier transform (FFT).
2
votes
2answers
61 views
how can a 2-d fft be constructed to an equivalent matrix?
When I use the cvx matlab toolbox, I met a puzzled problem. The function of fft (or dct, wavelet, etc.) cannot be recognized by the type of 'cvx'. For the 1-d fft, it can be constructed to an ...
1
vote
1answer
42 views
How can I quantify the error of FFT-based poisson solvers?
I have an FFT code that solves a particular case of the steady Euler equations where a Poisson equation is solved, what is a good way to quantify the error? Is what I am doing ok?
Since I do not have ...
0
votes
0answers
30 views
How to distinguish between the different frequency domains? [migrated]
Sometimes the terms 'Fourier domain', 'complex frequency domain', 'Frequency domain' and 's domain' are used interchangeably.
Take those answers here for example: ...
1
vote
1answer
53 views
Von Neumann Stability Analysis
I came across the following task recently:
Use the von-Neumann stability analysis to investigate the stability of the discrete form of $\frac{\partial c}{\partial x} = \frac{\partial^2 c}{\partial ...
3
votes
1answer
47 views
How to do local FFT on huge 3D vector data cell mesh and visualize it spatially?
Simulation type:
I'm running a simulation with the OOMMF micromagnetics package
http://math.nist.gov/oommf/
where are magnet is represented by a mesh of 3 million cells, it gets excited by a ...
0
votes
0answers
34 views
Discrete Fourier Transform Vs. Inverse Discrete Fourier Transform (Division by Number of Samples) [closed]
I've noticed that there are two possible notations for both DFT and IDFT.
The First One
DFT:
$$
y_i = \sum_{j = 0}^{n - 1} x_j \cdot \omega_n^{i \cdot j}, i = 0, \dots, n - 1
$$
IDFT:
$$
x_i = ...
1
vote
1answer
57 views
Error analysis of WENO scheme
I have three questions regarding WENO schemes
1) How to actually compute the smoothness indicators $\beta_j$ for required order of polynomial? Any reference which explains the algorithm will be ...
1
vote
1answer
52 views
Order of MATLAB FFT frequencies
This wikibook states that the output of MATLAB's FFT corresponds with the wavenumbers ordered as:
...
1
vote
2answers
60 views
A function as a sum of serie of modified FFT coeff. of another function - multiplied by sum number
I solve such a problem.
Lets have a function $Y=\sum_{k=-\infty}^\infty i\hat Y e^{ik\pi y}$
and then I have a function which is defined as $X=\sum_{k=-\infty}^\infty ik^2\hat Y e^{ik\pi y}$.
I ...
4
votes
1answer
90 views
MPI-based Implementations of FFT
In a numerical computation, I am required to take a multi-dimensional FFT on a distributed-memory cluster. The data is currently distributed using a distributed array in PETSc (DMDA).
I initial ...
6
votes
1answer
189 views
Fast (approximate) evaluation of Chebyshev polynomial
Is there a preferred way how to implement a fast (approximate) evaluation of the Chebyshev interpolation polynomial on uniform grid (given the function values at the Chebyshev nodes)? My problem is ...
7
votes
1answer
175 views
Fourier transform for Neumann boundary condition
I need to solve system of two coupled partial differential equations numerically.
$\frac{\partial x_1}{\partial t} = c_1\nabla ^2 x_1 + f_1(x_1,x_2) \\$
$\frac{\partial x_2}{\partial t} = ...
2
votes
1answer
102 views
Numerically designing a periodic 1D curve that maximizes an integral area objective and satisfies value, derivative, and frequency constraints
I need to write MATLAB program (or use an existing one) to obtain Fourier series coefficients. Let's say the series is going to approximate a 1D curve. The boundary conditions are:
value of the ...
6
votes
2answers
286 views
How many Fourier magnitudes do I have to calculate before an FFT becomes more efficient than a DFT?
I need to compute only a small number of low frequency Fourier components of a complex 2-dimensional array. I'll be computing the same Fourier components over and over again as the input array ...
7
votes
1answer
224 views
Which fourier series is needed to solve a 2D poisson problem with mixed boundary conditions using Fast Fourier Transform?
I have heard that a fast fourier transform can be used to solve the poisson problem when the boundary conditions are all one type... Sine series for dirichlet, cosine for neumann, and both for ...
