/* * Fast discrete cosine transform algorithms (C#) * * Copyright (c) 2017 Project Nayuki. (MIT License) * https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms * * Permission is hereby granted, free of charge, to any person obtaining a copy of * this software and associated documentation files (the "Software"), to deal in * the Software without restriction, including without limitation the rights to * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of * the Software, and to permit persons to whom the Software is furnished to do so, * subject to the following conditions: * - The above copyright notice and this permission notice shall be included in * all copies or substantial portions of the Software. * - The Software is provided "as is", without warranty of any kind, express or * implied, including but not limited to the warranties of merchantability, * fitness for a particular purpose and noninfringement. In no event shall the * authors or copyright holders be liable for any claim, damages or other * liability, whether in an action of contract, tort or otherwise, arising from, * out of or in connection with the Software or the use or other dealings in the * Software. */ using System; public sealed class FastDctLee { /* * Computes the unscaled DCT type II on the specified array in place. * The array length must be a power of 2. * For the formula, see https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II . */ public static void Transform(double[] vector) { if (vector == null) throw new NullReferenceException(); int n = vector.Length; if (n <= 0 || ((n & (n - 1)) != 0)) throw new ArgumentException("Length must be power of 2"); Transform(vector, 0, n, new double[n]); } private static void Transform(double[] vector, int off, int len, double[] temp) { // Algorithm by Byeong Gi Lee, 1984. For details, see: // See: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.118.3056&rep=rep1&type=pdf#page=34 if (len == 1) return; int halfLen = len / 2; for (int i = 0; i < halfLen; i++) { double x = vector[off + i]; double y = vector[off + len - 1 - i]; temp[off + i] = x + y; temp[off + i + halfLen] = (x - y) / (Math.Cos((i + 0.5) * Math.PI / len) * 2); } Transform(temp, off, halfLen, vector); Transform(temp, off + halfLen, halfLen, vector); for (int i = 0; i < halfLen - 1; i++) { vector[off + i * 2 + 0] = temp[off + i]; vector[off + i * 2 + 1] = temp[off + i + halfLen] + temp[off + i + halfLen + 1]; } vector[off + len - 2] = temp[off + halfLen - 1]; vector[off + len - 1] = temp[off + len - 1]; } /* * Computes the unscaled DCT type III on the specified array in place. * The array length must be a power of 2. * For the formula, see https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-III . */ public static void InverseTransform(double[] vector) { if (vector == null) throw new NullReferenceException(); int n = vector.Length; if (n <= 0 || ((n & (n - 1)) != 0)) throw new ArgumentException("Length must be power of 2"); vector[0] /= 2; InverseTransform(vector, 0, n, new double[n]); } private static void InverseTransform(double[] vector, int off, int len, double[] temp) { // Algorithm by Byeong Gi Lee, 1984. For details, see: // https://www.nayuki.io/res/fast-discrete-cosine-transform-algorithms/lee-new-algo-discrete-cosine-transform.pdf if (len == 1) return; int halfLen = len / 2; temp[off + 0] = vector[off + 0]; temp[off + halfLen] = vector[off + 1]; for (int i = 1; i < halfLen; i++) { temp[off + i] = vector[off + i * 2]; temp[off + i + halfLen] = vector[off + i * 2 - 1] + vector[off + i * 2 + 1]; } InverseTransform(temp, off, halfLen, vector); InverseTransform(temp, off + halfLen, halfLen, vector); for (int i = 0; i < halfLen; i++) { double x = temp[off + i]; double y = temp[off + i + halfLen] / (Math.Cos((i + 0.5) * Math.PI / len) * 2); vector[off + i] = x + y; vector[off + len - 1 - i] = x - y; } } }