fourier.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2020, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */
#pragma once

#include <mrpt/math/CMatrixDynamic.h>
#include <mrpt/math/CVectorDynamic.h>

namespace mrpt::math
{
/** \addtogroup fourier_grp Fourier transform functions
 *  \ingroup mrpt_math_grp
 * @{ */

/** Computes the FFT of a 2^N-size vector of real numbers, and returns the
 * Re+Im+Magnitude parts.
 * \sa fft2_real
 */
void fft_real(
    CVectorFloat& in_realData, CVectorFloat& out_FFT_Re,
    CVectorFloat& out_FFT_Im, CVectorFloat& out_FFT_Mag);

/** Compute the 2D Discrete Fourier Transform (DFT) of a real matrix, returning
 * the real and imaginary parts separately.
 * \param in_data The N_1xN_2 matrix.
 * \param out_real The N_1xN_2 output matrix which will store the real values
 * (user has not to initialize the size of this matrix).
 * \param out_imag The N_1xN_2 output matrix which will store the imaginary
 * values (user has not to initialize the size of this matrix).
 * \sa fft_real, ifft2_read, fft2_complex
 *  If the dimensions of the matrix are powers of two, the fast fourier
 * transform (FFT) is used instead of the general algorithm.
 */
void dft2_real(
    const CMatrixFloat& in_data, CMatrixFloat& out_real,
    CMatrixFloat& out_imag);

/** Compute the 2D inverse Discrete Fourier Transform (DFT)
 * \param in_real The N_1xN_2 input matrix with real values.
 * \param in_imag The N_1xN_2 input matrix with imaginary values.
 * \param out_data The N_1xN_2 output matrix (user has not to initialize the
 * size of this matrix).
 *  Note that the real and imaginary parts of the FFT will NOT be checked to
 * assure that they represent the transformation
 *    of purely real data.
 *  If the dimensions of the matrix are powers of two, the fast fourier
 * transform (FFT) is used instead of the general algorithm.
 * \sa fft_real, fft2_real
 */
void idft2_real(
    const CMatrixFloat& in_real, const CMatrixFloat& in_imag,
    CMatrixFloat& out_data);

/** Compute the 2D Discrete Fourier Transform (DFT) of a complex matrix,
 * returning the real and imaginary parts separately.
 * \param in_real The N_1xN_2 matrix with the real part.
 * \param in_imag The N_1xN_2 matrix with the imaginary part.
 * \param out_real The N_1xN_2 output matrix which will store the real values
 * (user has not to initialize the size of this matrix).
 * \param out_imag The N_1xN_2 output matrix which will store the imaginary
 * values (user has not to initialize the size of this matrix).
 *  If the dimensions of the matrix are powers of two, the fast fourier
 * transform (FFT) is used instead of the general algorithm.
 * \sa fft_real, idft2_complex,dft2_real
 */
void dft2_complex(
    const CMatrixFloat& in_real, const CMatrixFloat& in_imag,
    CMatrixFloat& out_real, CMatrixFloat& out_imag);

/** Compute the 2D inverse Discrete Fourier Transform (DFT).
 * \param in_real The N_1xN_2 input matrix with real values, where both
 * dimensions MUST BE powers of 2.
 * \param in_imag The N_1xN_2 input matrix with imaginary values, where both
 * dimensions MUST BE powers of 2.
 * \param out_real The N_1xN_2 output matrix for real part (user has not to
 * initialize the size of this matrix).
 * \param out_imag The N_1xN_2 output matrix for imaginary part (user has not
 * to initialize the size of this matrix).
 * \sa fft_real, dft2_real,dft2_complex
 *  If the dimensions of the matrix are powers of two, the fast fourier
 * transform (FFT) is used instead of the general algorithm.
 */
void idft2_complex(
    const CMatrixFloat& in_real, const CMatrixFloat& in_imag,
    CMatrixFloat& out_real, CMatrixFloat& out_imag);

/** Correlation of two matrixes using 2D FFT
 */
void cross_correlation_FFT(
    const CMatrixFloat& A, const CMatrixFloat& B, CMatrixFloat& out_corr);

/** @} */

}  // namespace mrpt::math