# File fft.hxx¶

FFT routines

Copyright 2010 B.D.Dudson, S.Farley, M.V.Umansky, X.Q.Xu

Contact: Ben Dudson, bd512@york.ac.uk

This file is part of BOUT++.

BOUT++ is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

BOUT++ is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with BOUT++. If not, see http://www.gnu.org/licenses/.

Functions

void rfft(const BoutReal *in, int length, dcomplex *out)

Returns the fft of a real signal using fftw_forward

The fftw_forward returns out_k = sum_{j=0}^(length-1) in_j*exp(-2*pi*j*k*sqrt(-1)/length)

Thus, out_k must be divided by ‘length’ in order for DFT[IDFT[in]] = in where IDFT is the inverse fourier transform. See the the fftw user manual for details.

Parameters
• in: Pointer to the 1D array to take the fourier transform of
• length: Number of points in the input array
• out: Pointer to the complex 1D array which is the FFT of in

void irfft(const dcomplex *in, int length, BoutReal *out)

Take the inverse fft of signal where the outputs are only reals.

This is done through a call to fftw_plan_dft_c2r_1d which is calling fftw_backwards.

That is out_k = sum_{j=0}^(length-1) in_j*exp(2*pi*j*k*sqrt(-1)/length)

See the the fftw user manual for details.

Parameters
• in: Pointer to the 1D array to take the inverse fourier transform of
• length: Number of points in the input array
• out: Pointer to the complex 1D array which is IFFTed

void DST(const BoutReal *in, int length, dcomplex *out)

Discrete Sine Transform

in and out arrays must both be of the same length

void DST_rev(dcomplex *in, int length, BoutReal *out)

Inverse Discrete Sine Transform

in and out arrays must both be of the same length

namespace bout

SNB model

namespace fft

Functions

void rfft(const BoutReal *in, int length, dcomplex *out)

Returns the fft of a real signal using fftw_forward

The fftw_forward returns out_k = sum_{j=0}^(length-1) in_j*exp(-2*pi*j*k*sqrt(-1)/length)

Thus, out_k must be divided by ‘length’ in order for DFT[IDFT[in]] = in where IDFT is the inverse fourier transform. See the the fftw user manual for details.

Parameters
• in: Pointer to the 1D array to take the fourier transform of
• length: Number of points in the input array
• out: Pointer to the complex 1D array which is the FFT of in

void irfft(const dcomplex *in, int length, BoutReal *out)

Take the inverse fft of signal where the outputs are only reals.

This is done through a call to fftw_plan_dft_c2r_1d which is calling fftw_backwards.

That is out_k = sum_{j=0}^(length-1) in_j*exp(2*pi*j*k*sqrt(-1)/length)

See the the fftw user manual for details.

Parameters
• in: Pointer to the 1D array to take the inverse fourier transform of
• length: Number of points in the input array
• out: Pointer to the complex 1D array which is IFFTed

void DST(const BoutReal *in, int length, dcomplex *out)

Discrete Sine Transform

in and out arrays must both be of the same length

void DST_rev(dcomplex *in, int length, BoutReal *out)

Inverse Discrete Sine Transform

in and out arrays must both be of the same length

void fft_init(bool fft_measure)

Should the FFT functions find and use an optimised plan?

void fft_init(Options *options = nullptr)

Should the FFT functions find and use an optimised plan?

If options is not nullptr, it should contain a bool called “fftw_measure”. If it is nullptr, use the global Options root

Array<dcomplex> rfft(const Array<BoutReal> &in)

Returns the fft of a real signal in using fftw_forward.

Array<BoutReal> irfft(const Array<dcomplex> &in, int length)

Take the inverse fft of signal in where the outputs are only reals. Requires the length of the original real signal

length is required because input signals to the forward transform of length n and n + 1 both produce ffts of length (n / 2) + 1 i.e. it’s not possible to recover the length of the original signal from the fft alone.

Expects that in.size() == (length / 2) + 1