Spectral Variability in Fixed Windows using Fractional Fourier Transform: Application in Power Spectral Density Estimation

Abstract

In statistical signal processing, power spectral density estimation is a frequency domain analysis in which power contents of a signal are measured with respect to frequency components of that signal. The power estimation of a signal can be carried out more precisely by using a window with a narrower 3-dB bandwidth and higher side-lobe attenuation. Theoretically, these two spectral parameters show trade-off in variable windows and remain constant in fixed windows. In this work, spectral behavior of fixed windows has been elaborated using Fractional Fourier Transform (FRFT) keeping their inherent time domain behavior intact. The FRFT is an extension of conventional Fourier transform with an additional variable parameter, known as rotation angle, which makes it more flexible and useful in various signal processing applications viz. power estimation and designing of tunable transition band FIR filters. In this article, variability in 3-dB bandwidth and sidelobe attenuation of fixed windows has been achieved by exploiting the available flexibility in FRFT and obtained variability has been applied in the estimation of signal power. Simulation results demonstrate that both of these two spectral parameters are improved and hence, trade-off problem between resolution and spectral leakage in the power spectral density estimation is overcome upto an extent.