Cosh window family and its application to FIR filter design

In this paper a new class of adjustable windows based on the cosine hyperbolic function is proposed. The proposed window has been derived in the same way as the Kaiser window, but it has computational cost advantage due to having no power series expansion in its time domain representation. After the spectrum design equations for the proposed function are empirically obtained, comparisons with the Kaiser and ultraspherical windows in terms of various spectral characteristics are performed. Simulation results show that the proposed window performs better sidelobe roll-off ratio than the Kaiser window for the same window length and normalized mainlobe width. As for the comparison with the ultraspherical window, the proposed window provides better ripple ratio for wider mainlobe width and larger sidelobe roll-off ratio. It is also shown that the proposed function in combination with a Hamming window performs better in terms of the ripple ratio, than a similar combination of a Kaiser and Hamming windows. Moreover, the paper presents the application of the proposed window in finite impulse response (FIR) filter design. The results show that the filters designed by the proposed window provide better far end stopband attenuation than the filters designed by the Kaiser window.