Using python, do not use inbuilt functions like fft from either numpy, opencv or other libraries.

def discrete_cosine_tranform(self, matrix): """Computes the discrete cosine transform of the input matrix  takes as input:  matrix: a 2d matrix  returns a matrix representing discrete cosine transform"""   return matrix def magnitude(self, matrix): """Computes the magnitude of the inverse DFT 

 takes as input:  matrix: a 2d matrix  returns a matrix representing magnitude of the inverse dft"""   return matrix