SYNTHESIS AND CHARACTERIZATION OF NEW WINDOW FAMILIES WITH THEIR APPLICATIONS

Abstract

Window functions are mostly used in truncating the data series to some finite limits. The data that are beyond the truncation point are simply ignored. To reflect the lost information, the coefficients of the data series could be modified. This windowed series may be processed more efficiently than the original one. Window functions are often applied in diverse engineering disciplines to produce realizable systems. There are many differing functional forms which comprise a subset of classical windows known to most engineers. This particular study focuses on the development and characterization of new window families and their performance evaluation in some applications. Prior to synthesis of new window families, for the first time a classification of all the available window functions based on their time and frequency domain characteristics is made and all the window functions along with their discrete and continuous time domain expressions are tabulated accordingly. Simultaneously, the optimality of Dolph-Chebyshev window and its drawbacks, responsible for its less applicability, are also studied. This insight of the world of windows as well as an understanding of the various trade-offs in between parameters of a window function and their appropriate applicability gave a real impetus in developing the novel window families. The novel window families developed are the polynomial window family (with a subset of this family as binary coefficient window) and the combinational window families (by taking linear combinations of the lag and data windows). The newly designed polynomial window family has its parameters as order dependent. The subset called binary coefficient window was derived with the help of binary polynomials. This window family, i.e. binary coefficient window, has an advantage that the temporal weightings can be calculated easily. The combinational window families came up after a generalized theory with appropriate terminology was formulated for designing them. On the basis of thorough

study of possible combinations some empirical relations came to be deduced. Four combinational window families are now reported and included in them is one combination of two data windows which does not follow the empirical conditions (as laid down necessary for such combinational window families). In this way, a negative approach for the validation of empirical conditions is also performed. These resultant window functions possess the merits of both the standard windows as also of Z-window functions, viz. simple expressions in both the domains, good overall spectral characteristics and the steerable side-lobe dip property. These combinational window families are defined on single variable as is the case of other variable window functions. The proposed window families were also tested as baseband symbol pulse shapes in full response signaling offset quadrature binary modulation systems and as tapers or smoothers in spectrum analysis. Their performance is found comparable with the other existing ones.