Accomplishment of fractional fourier transform by culmination of identities and applications

Abstract

In mobile communication, normally communication is intended to establish between the transmitter and receiver under the scenario where the transmitter / receiver or both having their respective movements, the consequence of the relative motion of receiver is to introduce a Doppler shift in the received frequency which in turn making the frequency components received as time-variant. This nonstationary behavior of the signal enforced the analysis of the signal to be performed in time-frequency plane. The fractional Fourier transform (FRFT), which is also known as generalization of Fourier transform (FT), has been established as a better mathematical tool to tackle this state of affair of the signal. The efficacy of the FRFT, as a transforming tool, is also investigated in 2-dimensional signal processing applications viz., encryption and watermarking. In both the cases of encryption and watermarking, the FRFT provides two more number of security options per FRFT block which can be used as decryption keys. Actually, these keys are generated in terms of the transformation order related with the column wise and row wise transformation and this beneficial feature can be originated only with the FRFT. Thus, the FRFT proved to be a better technique, in terms of the greater number of keys offered by this method, in context to the Fourier transform. Finally, this study succeeded in pushing the FRFT towards a complete and perfect Integral Transform.