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7 votes

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

The frequency content of the interpolated signal is significantly influenced by the interpolation basis. If you have a band-limited function that you have adequately sampled (i.e. satisfying Nyquist ...
coolguy1000000's user avatar
6 votes

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

The interpolation indeed affects the Fourier transform. @Steve already gives the correct answer in general, but I want to give you an example that helps the intuition more. Think for example that you ...
Wolfgang Bangerth's user avatar
3 votes
Accepted

MKL/FFTW performance of batch 1-D FFTs

From the old document: IntelĀ® Math Kernel Library FFT to DFTI Wrappers, A314775-001US: All transforms require additional memory to store the transform coefficients. When performing multiple FFTs of ...
Anton Menshov's user avatar
  • 8,672
3 votes
Accepted

Segmentation fault when broadcasting FFTW wisdom with MPI

The backtrace showed the following: ...
Hannes's user avatar
  • 111
3 votes

C++ libraries for Fast Fourier Transform in high precision

You might want to take a look at the Eigen C++ matrix class library. http://eigen.tuxfamily.org/index.php?title=Main_Page There is an FFT class in the unsupported section of the library but my ...
Bill Greene's user avatar
  • 6,144
2 votes
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FFT Poisson Solver for non-uniform grid

First, there are non-uniform mesh FFT variations that you could use without having to do the coordinate transformation. Second, the FFT is not easily applicable to the transformed problem. The reason ...
Wolfgang Bangerth's user avatar
2 votes

Wrong amplitude of convolution using numpy fft

You actually do recover the convolution, but as it is discussed in the comments, there is a normalization issue due to discretization. According to the documentation, ...
matthiaw91's user avatar
2 votes
Accepted

MPI support for discrete Fourier transform (DFT) in Python

I think you are looking for mpi4py-fft, which is a Python package (BSD-2 licensed) with its wrappers on the serial FFTW library. From pretty extensive mpi4py documentation: Parallel FFTs are ...
Anton Menshov's user avatar
  • 8,672
2 votes
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Computation of triple nested loops as a convolution product?

Let us write it as \begin{equation} A_j = \sum_{l'=1}^{NL} S_{jl'}L_{l'} \end{equation} Where \begin{equation} S_{jl'} = \sum_{k= 0}^{K-1}[T_k\epsilon_{l'\text{mod} R,k}]e^{2\pi i \frac{k}{K}j} \...
Ian Bush's user avatar
  • 616
1 vote

FFTW on subarray with MPI

The whole point of the guru interface is to do complicated FFTs without copying the data into contiguous arrays. This advantage is not very important if data needs ...
alfC's user avatar
  • 113
1 vote

Generating initial velocity field

The method produces a velocity field in Fourier space, where $k_1,k_2,k_3$ are the components of the wave vector $k \in {\mathbb R}^3$. In order to get a velocity field in physical space, you need to ...
Wolfgang Bangerth's user avatar
1 vote

C++ libraries for Fast Fourier Transform in high precision

ARPREC (http://crd-legacy.lbl.gov/~dhbailey/mpdist/) is an arbitrary-precision C++/Fortran package and contains an FFT implementation. Apfloat (http://www.apfloat.org/apfloat/) is another C++ ...
gpavanb's user avatar
  • 572
1 vote

FFT parallel processing in MPI

I would definitely advise going FFTW-route anyway. FFTW is a high-quality library with good documentation that can be used in a convenient way in your project without requiring many modifications or ...
Anton Menshov's user avatar
  • 8,672

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