1. Write a Matlab function that takes a 2-d matrix (8bit gray-image) as a parameter, computes the 2D discrete cosine Transform for the input matrix, and returns the output matrix (the transformed 2D matrix). The function should be included inside an M file. Hint: You should implement the 2D discrete cosine Transform from scratch. Do not call the matlab function dct2(). 2. Use the LZW compression algorithm to compress the string: CDCCCDCC Show the steps by filling the table below: Encoder table String table Output Representing codeword String code