DCT and Entropy Coding Source Code (MATLAB Simulation Implementation)

Source Code for DCT and Entropy Coding (Simulated using MATLAB)

In this project, we will conduct simulations using MATLAB and develop source code for Discrete Cosine Transform (DCT) and entropy coding. Through this process, we will gain deep insights into the principles and implementation methods of these two encoding techniques. We will write code from scratch, progressively implementing DCT and entropy coding algorithms to better understand their working mechanisms.

First, we will introduce the principles of Discrete Cosine Transform (DCT) and write corresponding MATLAB code to implement it. DCT is a technique widely used in image and audio compression that transforms signals into a set of coefficients that can represent the original signal more efficiently. We will study the mathematical definition and algorithmic steps of DCT, implementing it using MATLAB functions like dct2() for 2D transforms or developing our own DCT matrix multiplication approach for educational purposes. This implementation will be used in subsequent simulation experiments.

Next, we will introduce the concepts and principles of entropy coding and develop corresponding MATLAB code implementations. Entropy coding is a lossless compression technique that reduces data redundancy by leveraging statistical properties of the signal. We will study the fundamental principles of entropy coding, including Shannon coding and Huffman coding algorithms. For Huffman coding implementation, we will create MATLAB functions to build Huffman trees based on symbol probabilities, generate code dictionaries, and perform encoding/decoding operations. These implementations will be utilized in our simulation experiments.

By completing this project, we will not only gain comprehensive understanding of DCT and entropy coding principles and implementation methods, but also deepen our comprehension through simulation approaches. We will implement these algorithms through source code development and verify their effectiveness through simulation experiments. This will be a challenging yet fascinating and beneficial project that helps enhance our programming and signal processing skills, particularly in implementing core compression algorithms using MATLAB's matrix operations and data structure capabilities.