Discrete signal representation using triangular basis functions

This thesis deals with the representation of discrete signals using triangular basis functions. Signals are usually represented by Fourier series expansions where the basis functions are cosine and sine functions which are all mutually orthogonal. The triangular basis functions used here are called TRIC (triangular cosine) and TRIS (triangular sine) functions. The TRIC and TRIS functions are like their cosine and sine function counterparts except that they are linear. The TRIC and TRIS functions are not all mutually orthogonal, though most of them are. A matrix method of representing discrete signals using TRIC and TRIS functions is presented. A discrete triangular transform matrix is developed and a method of deriving this matrix is presented. A Fortran program is written to derive the discrete triangular transform matrix and to prove the reconstruction of several basic functions like impulse, step, pulse and sinusoidal waveforms.