#TITLE_ALTERNATIVE# - Anestasia (NIM 10103014), Maria
ABSTRACT: Frames play a fundamental role in signal processing. A frame expansion of vector, which corresponds to overcomplete generalizations of basis expansion, is more effective than bases itself in dealing with errors detecting of signal transmissions. Parseval frames are the particular class of frames having similar properties as orthonormal bases, which grow rapidly because of its simplicity to compute. In this final project, we will discuss the Hilbert spaces that lead us to the frames theory, some properties of Parseval frames, as well as an algorithm to compute Parseval frames for a subspace generated by an arbitrar finite sequence of vectors in a finite-dimensional Hilbert spaces. For the last section, several examples will be given to visualize further insight into the algorithm.