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 rolloff 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. The results show that the filters designed by cosh window provide better far end stopband attenuation than the filters designed by Kaiser window.

A Comparative Study of Performance of Different Window Functions for Speech Enhancement

“…The performance of window function in different applications relies on the spectral characteristics of a window. For example, in digital filter design and image processing, the ripple ratio or main lobe to side lobe energy ratio (MSR) are more essential as compared to the side lobe roll-off ratio, while in speech processing, the side lobe roll-off ratio is more important [16][17][18][19].…”

“…Window functions are widely used in digital signal processing for various applications of signal analysis [16][17][18][19]. A window is time-domain weighting function.…”

“…For the speech applications, higher side lobe ratio is required. Therefore, to improve the spectral characteristics, many window functions have been developed such as Kaiser, Saramaki, Cosh, and Exponential [16][17][18][19]. In above context, therefore, in this paper, an improved method based on DCT for speech enhancement using different window functions is presented from slight modification in Soon and Koh algorithm [7].…”

“…This window function gives fairly good frequency resolution as compared to other window functions. However, in speech processing, one more important spectral parameter, called side lobe roll-off ratio (S) is more essential as compared to other spectral characteristics of window function [16][17][18][19]. For the speech applications, higher side lobe ratio is required.…”

The Effect of Exponential/Cosine Hyperbolic/ Polynomial/ Kaiser Window Parameters Cg-Icg-Enbw-Sl on the SNR Improvement of MST Radar Signals

“…Since the use of an inappropriate window can lead to corruption of the principal spectral parameters, hence it is important to consider the criteria by which the choice of data weighting window to be selected for optimum results [4]. Here we will observe the effects of "α α α α or m" in recently proposed adjustable windows based on the Exponential [5] and Cosine Hyperbolic [6] and Polynomial [7] Window Functions on the SNR of RADAR returns.…”