The Evaluations of the Inverse .Transform of Eight Often-used Waveforms by Mobius Transform-The Inverse Transform of Their Fourier Series

摘要

Applying the Mobius transform to the eight often-used waveforms and the evaluations of their inverse transform as well as the inverse transform of their Fourier series, were investigated. Then the results, the sine, cosine and general periodic function expanded on these waveforms and the formula for evaluating the expanding coefficients on these non-orthogonal function set were derived. Perhaps more important, in the evaluation process, another non-orthogonal function set were deduced, which are orthogonal to the former set that the integral of their product in a period T was orthogonal. These two function set orthogonal to each other, as the modulation function set and the demodulation function set, could play an important role in the information modulatingdemodulating.