Cosine Hyperbolic Window Family with its Application to FIR Filter Design

Abstract

In this paper a new class of adjustable window functions based on cosine hyperbolic function is proposed. The proposed window, namely cosh window for short, has been derived in the same way of the derivation of Kaiser window but it has the advantage of having no power series expansion in its time domain function. The spectral characteristic of cosh window is studied, and its performance is compared with Kaiser window in terms of the ripple ratio and sidelobe roll-off ratio for the same window length and normalized mainlobe width. Simulation results show that cosh window provides better sidelobe roll-off characteristic which may be useful for some applications such as filter design and beamforming. It is also shown that the combination of the proposed window with Hamming window can perform better ripple ratio compared to Kaiser window and its combination with Hamming window. The last spectrum comparison of the proposed window is performed with ultraspherical window for the same window length, mainlobe width and sidelobe rol-off ratio, and the results show that the proposed window performs better ripple ratio than 3-parameter ultraspherical window for wider mainlobe width and larger sidelobe roll-off ratio. Moreover, the paper presents the application of the proposed window in the area of FIR filter design. The filter design equations for cosh window to meet the given lowpass filter specification are established, and the comparison with Kaiser window is performed.