Analysis and Design of Fractional Domain Filtering Utilizing Fractional Tools

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 non-stationary 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 proposed work can be divided into two broader segments. The first segment includes the efforts made in establishing the translation invariance concept of fractional convolution and correlation to show that these are no more partial invariant by expanding some convolution and correlation related identities. The second segment comprises the filtering application in FrFT. The beneficial role of the FrFT in the filtering application lies in the capability of the FrFT in localizing the non-stationary (chirp) signals in time-frequency plane. This ascertains the superiority of FrFT domain filtering over time-domain and frequency domain filtering in the case of overlapping band limited signal and noise. Thus, FrFT proved to be a better technique in the context to other transformation techniques.