Development of Efficient Algorithms for Filtering and Spectral Analysis Using FRFT

Abstract

In studies of discrete time systems, signal processing and analysis are two important newlineoperations. The processing of signal is required to achieve the desired properties in the newlinesignal, while the analysis is done if the study of signal constituents is needed. Filtering is the newlinemost important signal processing operation required to extract the desired signal from form newlinethe noise corrupted information. There are two main categories of digital filters, viz., infinite newlineimpulse response (IIR) and finite impulse response (FIR). This particular work focuses on newlinedevelopment of new and efficient algorithms for FIR filtering using window functions. The newlinework critically examines the utility of window functions in FIR filtering from different newlineperspectives. Fixed, variable and steerable side lobe dip windows have been used in this newlinework for filtering. newlineThe Zhong (Z)-Window (ZW) is a popular steerable side-lobe (SSLD) window. Its newlineparameters can be varied by steering dips in its side-lobes. New empirical design newlinerelationships for ZW based FIR filters have been established in this work. The performance newlineof these filters has been observed to be better than Kaiser Window (KW) filters. newlineApplicability of these filters has been established in multi-rate signal processing for the newlinedesigning of quadrature mirror filter banks which can be used for the suppression of images newlineassociated with interpolators. newlineWindow parameters such as maximum side-lobe level (MSLL), half main-lobe width newline(HMLW), and side-lobe fall-off rate (SLFOR) play an important role in the performance of newlineFIR filters. In this work, characterization of these window parameters has been carried out in newlinefractional Fourier domain. As the fractional Fourier domain has got one additional degree of newlineiv newlinefreedom, window functions in this domain offer more flexible and optimum solutions for newlinefiltering and spectral analysis applications. newlineSome real time filtering applications require a tunable Transition Bandwidth (TBW).