Nonrecursive digital FIR filter design by 3-parameter Hyperbolic Cosine window: A high quality low order filter design

Abstract

In this paper, nonrecursive digital filters design using 3-parameter Hyperbolic Cosine window (3-parameter Cosh window for short) is investigated. The 2-parameter Cosh window has been investigated in literature that is modified by introducing a new third parameter. The quality and performance of filter designed by proposed window are compared with the well-known adjustable windows in literature such as the ultraspherical, Saramaki, Kaiser, Dolph-Chebyshev, 2-parameter Cosh and Modified Kaiser window. Simulation results show that the filters designed by proposed 3-parameter Cosh window provide higher quality in terms of the minimum stopband attenuation for a fixed order, and yield lower order for a fix minimum stopband attenuation compared to the filters designed by other windows. The far-end stopband attenuation has more significance when the filtered signal has great concentration of spectral energy. In a sub-band coding, the filter is an intended to separate out various frequency bands for independent processing. In the case of speech, e.g. the far-end rejection of the energy in the stopband should be more so that the energy leak from one band to another is a minimum and the simulation results show that the filter designed by proposed window provides the maximum (better) far-end stopband attenuation that is figure of merit.