Application of Exponential window to design a digital nonrecursive FIR filter

It has been proposed that the Exponential window provides better side-lobe roll-off ratio than Kaiser window which is very useful for some applications such as beam forming, filter design, and speech processing. In this paper the second application i.e. design of digital nonrecursive Finite Impulse Response (FIR) filter by using Exponential window is proposed. The far-end stopband attenuation is most significant parameter when the signal to be filtered has great concentration of spectral energy. In a sub-band coding, the filter is intended to separate out various frequency bands for independent processing. In case of speech, e.g. the far-end rejection of the energy in the stopband should be more so that the energy leakage from one band to another is minimum. Therefore, the filter should be designed in such a way so that it can provide better far-end stopband attenuation (amplitude of last ripple in stopband). Digital FIR filter designed by Kaiser window has a better far-end stopband attenuation than filter designed by the other previously well known adjustable windows such as Dolph-Chebyshev and Saramaki, which are special cases of Ultraspherical windows, but obtaining a digital filter which performs higher far-end stopband attenuation than Kaiser window will be useful. In this paper, the design of nonrecursive digital FIR filter has been proposed by using Exponential window. It provides better far-end stopband attenuation than filter designed by well known Kaiser window, which is the advantage of filter designed by Exponential window over filter designed by Kaiser window. The proposed schemes were simulated on commercially available software and the results show the close agreement with proposed theory.