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Questions tagged [fftw]

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38 views

MKL/FFTW performance of batch 1-D FFTs

MKL and FFTW offer 1-D FFTs that can operate on many inputs simultaneously - in other words, they can batch-transform the columns of some input matrix. Is the performance of these multi-transforms ...
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0answers
40 views

FFTW on subarray with MPI

With the guru interfaces of FFTW, I can apply transforms only to parts of a multidimensional array by modifying the fftw_iodim ...
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0answers
52 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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0answers
119 views

Use of multidimensional FFTW and normalisation factor

I am using the FFTW MPI in C. I have a simple question. Quoting from fftw.org The multi-dimensional transforms of FFTW, in general, compute simply the separable product of the given 1d ...
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1answer
131 views

FFT Poisson Solver for non-uniform grid

I have a 3D solver for the incompressible Navier-Stokes equations which uses a FFT library for the Poisson equation with a uniform grid on all directions. In 2D the Poisson equation is given by: $$ ...
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0answers
36 views

Computing IFFT for only $k$ samples in a high dimensional signal

I have a very high dimensional signal, say $15$ dimensions. Across each dimension the width is $N$ points. So total number of points is $N^{15}$. I already have the FFT given to me. Only low frequency ...
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0answers
39 views

Extracting Real Part of Twiddle Factors from `fftw_plan`

When calculating a type-II DCT with FFTW, you create an fftw_plan, via ...
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0answers
45 views

Integrating the 2d vorticity equation on periodic boundaries

This question is a follow-up of https://stackoverflow.com/questions/44718160/solve-a-linear-system-for-fft-coefficients At some time (kt), the FT of the vorticity (omega) satisfies: ...
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0answers
652 views

Wrong amplitude of convolution using numpy fft

I try to convolve a rectangle function in [-1/2, 1/2] with itself using fft. The convolution should be a tent shaped function, see figure below. The code is below. In the 3rd to last line I add /50 ...
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2answers
848 views

Fourier transform by FFT : by using cubic splines to interpolate between data points, do we change the frequency content of the Fourier transform?

I have a data file with some points equally spaced. These represent some function. I have to calculate the Fourier transform of this set of points. The thing is, I'm tempted to take a cubic spline of ...
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2answers
228 views

Generating initial velocity field

I am trying to generate initial velocity field which satisfies incompressible flows condition. To formulate this I am using Rogallo's procedure formulation which is given by $$ \tilde{u}(k) = \frac{\...
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0answers
155 views

Python DFT library using MPI

I am looking for a discrete Fourier transform (DFT) library that can be run with MPI on Python. Usually, in other language (C, fortran) FFTW is used. There's a Python wrapper for FFTW called pyFFTW, ...
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0answers
167 views

Solving a 3D (almost radial) convolution with FFT

I have a 3D integral that is almost a radial convolution of the form $$ \int d^{3}k'h(\mathbf{k'})g(|\mathbf{k-k'}|) $$ and I am looking for a fast and efficient algorithm (e.g. FFT) to solve it ...
4
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2answers
8k views

C++ libraries for Fast Fourier Transform in high precision

I am looking for a C++ library for Fast Fourier Transform (FFT) in high precision (e.g., using high precision real data types similar to mpfr_t in MPFR or ...
3
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0answers
256 views

How to obtain values in physical space for a given spectrum?

My question falls under purview of turbulent flows. I want to add an initial perturbation, for which I have a given energy spectrum (say$ E(k)=ak^4e^{-bk^2} $). The steps involved in getting these ...
6
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1answer
2k views

computing turbulent energy spectrum from isotropic turbulence flow field in a box

I have my 3 dimensional velocity flow-field u, v and w at a given instant of time from DNS using pseudo-spectral method. I need to calculate the energy spectrum ( in Fourier space ) as a function of ...
4
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1answer
122 views

Computing Fourier representation of space dependent advection operator via FFT

Consider the following equation on the circle: $$\dfrac{\partial p(x,t)}{\partial t} = a(x)\dfrac{\partial p(x,t)}{\partial x} \equiv L(p) \enspace ,$$ where $L$ is the operator acting on $p(x,t)$. ...
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0answers
58 views

Broadening spectral data by using FFT's

I obtain numerical discrete data of the form $$ S_{raw}(\omega) = \sum_{j}w_{j} \delta(\omega-\omega_{j}) $$ to compare the result with experimental data the delta peaks need to be broadened ...
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0answers
539 views

radially averaged power spectrum of a binary image does not look like power law

It has been known that Fourier power spectrum somehow obeys power law therefore the slope of the spectrum can be used to calculate the fractal dimension of an image. Many people have used it for ...
3
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1answer
241 views

precision loss in non-trigonometric, periodic functions using FFTW and NaNs after marching forward in time (Fortran)

I have developed a pseudospectral solver of the Navier-Stokes equations using FFTW. I tested my formulation of right hand sides (RHS) of the NS equations against standard trigonometric functions (...
0
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1answer
428 views

FFT parallel processing in MPI

I am working now in Beowulf Cluster and parallel processing, I want code for Fast Fourier transfer functions written in any language, e.g., C/C++. Without using FFTW library based on message passing ...
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1answer
585 views

Time array from frequency array in FFT using Python

I have done a Fourier transformation of two signals (in time) $S_1(t),S_2(t)$ using numpy's fft which will give me $S_1(f),S_2(f)$. The corresponding frequency grid ...
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1answer
71 views

Which version of FFTW

At the moment, I'm installing the "GADGET-2" application. In its documentation it says "Note that the MPI-capable version 2.x of FFTW is required, the new version 3 lacks MPI capability at this point. ...
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2answers
406 views

DST using FFT routine

Please can you help me with my problem? On Wikipedia, in article Discrete sine transform, this is written (chapter Computation): "Although the direct application of these formulas would require O(N2) ...
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2answers
80 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 ...
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1answer
2k 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 ...
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0answers
150 views

FFT - function only in sine series? Can be done with MKL / Lapack? [duplicate]

please can I ask, how one can make from function sine series (Fourier transform) with MKL? I can do "normal" exponential FFT with MKL (Lapack of course), how can I say that I want only sine series? ...
1
vote
1answer
171 views

Discrete convolution

please can I ask a bit stupid question? Let say I need to solve an equation in a form $\frac{\partial X}{\partial t}=\sum_k M_k * X_{n-k}$ How can I do the discrete convolution numerically? I will say ...
9
votes
1answer
2k 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 ...
12
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4answers
849 views

Scalability of Fast Fourier Transform (FFT)

To use the Fast Fourier Transform (FFT) on uniformly sampled data, e.g. in connection with PDE solvers, it is well known that the FFT is an $\mathcal{O}(n\log(n)$) algorithm. How well do the FFT scale ...
7
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1answer
486 views

How can I tell VASP 5.2 is compiled with FFTW3?

When VASP 5 was released, the performance was mostly slower than our make of VASP 4.6. I wrote it off as an optimization issue, and went on in my life. Then, in VASP 5.2, with the release notes, I ...