jube-fork/Accord.Math/Transforms/CosineTransform.cs

// Accord Math Library
// The Accord.NET Framework
// http://accord-framework.net
//
// Copyright © César Souza, 2009-2017
// cesarsouza at gmail.com
//
// Copyright © Diego Catalano, 2013
// diego.catalano at live.com
//
//    This library 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.
//
//    This library 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 this library; if not, write to the Free Software
//    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
//

namespace Accord.Math
{
    using System;
    using AForge.Math;

    /// <summary>
    ///   Discrete Cosine Transformation.
    /// </summary>
    /// 
    /// <remarks>
    /// <para>
    ///    A discrete cosine transform (DCT) expresses a finite sequence of data points
    ///    in terms of a sum of cosine functions oscillating at different frequencies. 
    ///    DCTs are important to numerous applications in science and engineering, from
    ///    lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small 
    ///    high-frequency components can be discarded), to spectral methods for the 
    ///    numerical solution of partial differential equations.</para>
    ///    
    /// <para>
    ///    The use of cosine rather than sine functions is critical in these applications:
    ///    for compression, it turns out that cosine functions are much more efficient,
    ///    whereas for differential equations the cosines express a particular choice of 
    ///    boundary conditions.</para>
    ///   
    /// <para>
    ///   References:
    ///   <list type="bullet">
    ///     <item><description>
    ///       Wikipedia contributors, "Discrete sine transform," Wikipedia, The Free Encyclopedia,
    ///       available at: http://en.wikipedia.org/w/index.php?title=Discrete_sine_transform </description></item>
    ///     <item><description>
    ///       K. R. Castleman, Digital Image Processing. Chapter 13, p.288.
    ///       Prentice. Hall, 1998.</description></item>
    ///   </list></para>
    /// </remarks>
    /// 
    public static class CosineTransform
    {

        /// <summary>
        ///   Forward Discrete Cosine Transform.
        /// </summary>
        /// 
        public static void DCT(double[] data)
        {
            double[] result = new double[data.Length];
            double c = Math.PI / (2.0 * data.Length);
            double scale = Math.Sqrt(2.0 / data.Length);

            for (int k = 0; k < data.Length; k++)
            {
                double sum = 0;
                for (int n = 0; n < data.Length; n++)
                    sum += data[n] * Math.Cos((2.0 * n + 1.0) * k * c);
                result[k] = scale * sum;
            }

            data[0] = result[0] / Constants.Sqrt2;
            for (int i = 1; i < data.Length; i++)
                data[i] = result[i];
        }

        /// <summary>
        ///   Inverse Discrete Cosine Transform.
        /// </summary>
        /// 
        public static void IDCT(double[] data)
        {
            double[] result = new double[data.Length];
            double c = Math.PI / (2.0 * data.Length);
            double scale = Math.Sqrt(2.0 / data.Length);

            for (int k = 0; k < data.Length; k++)
            {
                double sum = data[0] / Constants.Sqrt2;
                for (int n = 1; n < data.Length; n++)
                    sum += data[n] * Math.Cos((2 * k + 1) * n * c);

                result[k] = scale * sum;
            }

            for (int i = 0; i < data.Length; i++)
                data[i] = result[i];
        }


        /// <summary>
        ///   Forward 2D Discrete Cosine Transform.
        /// </summary>
        /// 
        public static void DCT(double[,] data)
        {
            int rows = data.GetLength(0);
            int cols = data.GetLength(1);

            double[] row = new double[cols];
            double[] col = new double[rows];

            for (int i = 0; i < rows; i++)
            {
                for (int j = 0; j < row.Length; j++)
                    row[j] = data[i, j];

                DCT(row);

                for (int j = 0; j < row.Length; j++)
                    data[i, j] = row[j];
            }

            for (int j = 0; j < cols; j++)
            {
                for (int i = 0; i < col.Length; i++)
                    col[i] = data[i, j];

                DCT(col);

                for (int i = 0; i < col.Length; i++)
                    data[i, j] = col[i];
            }
        }

        /// <summary>
        ///   Inverse 2D Discrete Cosine Transform.
        /// </summary>
        /// 
        public static void IDCT(double[,] data)
        {
            int rows = data.GetLength(0);
            int cols = data.GetLength(1);

            double[] row = new double[cols];
            double[] col = new double[rows];

            for (int j = 0; j < cols; j++)
            {
                for (int i = 0; i < col.Length; i++)
                    col[i] = data[i, j];

                IDCT(col);

                for (int i = 0; i < col.Length; i++)
                    data[i, j] = col[i];
            }

            for (int i = 0; i < rows; i++)
            {
                for (int j = 0; j < row.Length; j++)
                    row[j] = data[i, j];

                IDCT(row);

                for (int j = 0; j < row.Length; j++)
                    data[i, j] = row[j];
            }
        }
    }
}