Design of high-quality low-order nonrecursive digital filters using the window functions

The aim of the thesis study is to present a new window function (or simply window) to provide better nonrecursive filter characteristics than the filters designed by the windows in the literature. To achieve this aim, four windows - namely Exponential, Cosh, modified Cosh and modified Kaiser - are proposed.The Exponential and Cosh windows are derived by replacing the modified Bessel function of first kind of order zero in the Kaiser window with the exponential and cosine hyperbolic functions, respectively. Unlike the Kaiser window, they have an advantage that they have no power series expansion in their time domain representations. The spectrum design equations are established for these windows. The simulation results show that compared to the Kaiser window for the same window length and mainlobe width, they provide very good sidelobe roll-off ratio characteristic - which may be useful for some applications. But, in terms of the ripple ratio, the Kaiser window performs better results. As for the comparison with the three-parameter Ultraspherical window, the Exponential window performs better in ripple ratio characteristic for narrower mainlobe width and larger sidelobe roll-off ratio with fixing the window length, mainlobe width and sidelobe roll-off ratio. For wider mainlobe width and smaller sidelobe roll-off ratio, it performs worse ripple ratio. The Cosh window performs better ripple ratio characteristic for wider mainlobe width and larger sidelobe roll-off ratio. But, for narrower mainlobe width and smaller sidelobe roll-off ratio, the Ultraspherical window provides better results.Third and fourth proposed window functions are the modified Cosh and modified Kaiser windows which are derived by proposing a third adjustable parameter to the two-parameter Cosh and Kaiser windows, respectively. The simulation results show that they provide superior ripple ratio characteristics compared to the Kaiser and Cosh windows.As for the applications of the proposed windows in the design of nonrecursive digital filters, the filter design equations for the Exponential and Cosh windows are obtained, and then they are compared with the Kaiser window. The simulation results show that the Kaiser window provides better results in terms of the minimum stopband attenuation. But, the Exponential and Cosh windows are better in terms of the maximum stopband attenuation which may be useful for some applications. The optimum solutions for the modified Cosh and modified Kaiser windows are found, and then the simulation results show that these two modified windows performs very good results in terms of the minimum stopband attenuation compared to the Kaiser window.The comparisons with the well known window functions in literature show that the proposed modified Cosh and modified Kaiser windows can provide the best quality in terms of the minimum stopband attenuation for a fixed filter order, and also provide lowest filter order for a fixed minimum stopband attenuation.