Project 1:
In this project we will explore minimal norm solutions as well as Tikhonov regularisation. We will go through how truncated QR factorization can be used to efficiently compute the minimal norm solution of a underdetermined system. Additionaly we will study how singular value decomposition can be used in Tikhonov regularisation. The project will ultimately culminate into single channel source separation using techniques developed through the work on this project.
Project 2:
In this project we prove many of the fundamental properties of the discrete Fourier transform that lay the foundation for signal processing. Furthermore, we use the fundamental interpolant of translation invarient spaces based on the Dirichlet kernel to obtain higher resolution signals from sampling data. Lastly we use multidimensional FFT to smoothen dithered halftone pictures.