Analysis of Kaiser and Gaussian Window Functions in the Fractional Fourier Transform Domain and Its Application

Abstract

Fractional Fourier transform (FRFT) is generalization of Fourier transform. It has an adjustable parameter in the form of $$\alpha$$ rotational angle that makes it more useful in the various fields of science and engineering. In this paper, an analysis of Kaiser and Gaussian window functions is obtained in the FRFT domain. The behavior of these window functions is observed in terms of spectral parameters along with their special cases. The effect of their behavior is applied in FIR filter implementation and tunes its transition band. By changing the order of the FRFT, the variation in the transition width of windowed FIR filter is obtained which makes it possible to vary the stop-band attenuation. While designing a new filter, this tuning method saves significant time to compute filter coefficients. To validate the results, tuning of the FIR filter with Gaussian and Kaiser window functions is achieved in FRFT domain and the performance of the filter is measured in terms of stop-band attenuation.