Analysis of PC6 window function using fractional Fourier transform

Abstract

Fractional Fourier transform (FRFT) is a linear transform generalizing Fourier transform (FT) that plays an important role in the field of signal processing and analysis. FRFT contains an adjustable parameter α, which it rotates the signal in the time frequency plane and represents the signal in an intermediate domain between time and frequency. FRFT provides a measure about the angular distribution of signal's energy in time frequency plane. FT is a special case of FRFT when angle α is equal to π/2. This paper presents mathematical model for obtaining FRFT of PC6 window function. The different parameters of this window function are also obtained with the help of simulation results. A comparison of window function parameters is presented using FT and FRFT. Also comparison of this window function with Hanning window function is presented in terms of Side Lobe Fall off Rate (SLFOR). For different values of FRFT order, PC6 window function shows variation in different parameters. Thus by changing the FRFT order, the minimum stop band attenuation of the resulting window function can be controlled.