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/usr/include/libavcodec/avfft.h is in libavcodec-dev 6:11.12-1~deb8u1.

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/*
 * This file is part of Libav.
 *
 * Libav 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 2.1 of the License, or (at your option) any later version.
 *
 * Libav 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 Libav; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 */

#ifndef AVCODEC_AVFFT_H
#define AVCODEC_AVFFT_H

/**
 * @file
 * @ingroup lavc_fft
 * FFT functions
 */

/**
 * @defgroup lavc_fft FFT functions
 * @ingroup lavc_misc
 *
 * @{
 */

typedef float FFTSample;

typedef struct FFTComplex {
    FFTSample re, im;
} FFTComplex;

typedef struct FFTContext FFTContext;

/**
 * Set up a complex FFT.
 * @param nbits           log2 of the length of the input array
 * @param inverse         if 0 perform the forward transform, if 1 perform the inverse
 */
FFTContext *av_fft_init(int nbits, int inverse);

/**
 * Do the permutation needed BEFORE calling ff_fft_calc().
 */
void av_fft_permute(FFTContext *s, FFTComplex *z);

/**
 * Do a complex FFT with the parameters defined in av_fft_init(). The
 * input data must be permuted before. No 1.0/sqrt(n) normalization is done.
 */
void av_fft_calc(FFTContext *s, FFTComplex *z);

void av_fft_end(FFTContext *s);

FFTContext *av_mdct_init(int nbits, int inverse, double scale);
void av_imdct_calc(FFTContext *s, FFTSample *output, const FFTSample *input);
void av_imdct_half(FFTContext *s, FFTSample *output, const FFTSample *input);
void av_mdct_calc(FFTContext *s, FFTSample *output, const FFTSample *input);
void av_mdct_end(FFTContext *s);

/* Real Discrete Fourier Transform */

enum RDFTransformType {
    DFT_R2C,
    IDFT_C2R,
    IDFT_R2C,
    DFT_C2R,
};

typedef struct RDFTContext RDFTContext;

/**
 * Set up a real FFT.
 * @param nbits           log2 of the length of the input array
 * @param trans           the type of transform
 */
RDFTContext *av_rdft_init(int nbits, enum RDFTransformType trans);
void av_rdft_calc(RDFTContext *s, FFTSample *data);
void av_rdft_end(RDFTContext *s);

/* Discrete Cosine Transform */

typedef struct DCTContext DCTContext;

enum DCTTransformType {
    DCT_II = 0,
    DCT_III,
    DCT_I,
    DST_I,
};

/**
 * Set up DCT.
 *
 * @param nbits           size of the input array:
 *                        (1 << nbits)     for DCT-II, DCT-III and DST-I
 *                        (1 << nbits) + 1 for DCT-I
 * @param type            the type of transform
 *
 * @note the first element of the input of DST-I is ignored
 */
DCTContext *av_dct_init(int nbits, enum DCTTransformType type);
void av_dct_calc(DCTContext *s, FFTSample *data);
void av_dct_end (DCTContext *s);

/**
 * @}
 */

#endif /* AVCODEC_AVFFT_H */