Advanced Algorithmic Evaluation for Imaging, Communication and Audio Applications: Eigenvalue Decomposition Using the Catapult Algorithmic Synthesis Methodology

This report discusses the hardware implementation of “eigenvalue decomposition”. Eigenvalue decomposition is used in a wide range of applications for imaging, communication and audio such as image recognition using KL conversion, high-speed communication using MIMO antenna, and electric/sound wave arrival direction estimation using MUSIC method. It is expected that more than four antennas will be required in many cases for future MIMO communications and electric wave arrival direction estimation with MUSIC method applications. With four antennas, the matrix size will be 4x4 with complex numbers and the computational load will be increased, so we were interested in verifying whether the method to obtain eigenvalues directly from the eigenvalue equation was reasonable or not. Therefore, we developed two effective algorithms in ANSI C++ to obtain eigenvalues and synthesized them with Catapult® to compare the area versus the number of cycles at the algorithm level, respectively.