On the use of filter design programs for generating spectral windows

In processing long sequences of data either for the purpose of filtering or spectal analysis, one generally divides the data into segments. The elements of each segment are usually multiplied by a set of weights, referred to as a "window", to reduce certain undesired effects of the division into short sequences (see Ref. 1). A simple effective way to design a window is to use one of the many window functions such as the Hanning, Hamming (1) or Kaiser (2) windows. These are defined by simple formulas in which parameters can be selected so that the frequency response of the window will have the desired center-lobe width and side-lobe attenuation. These procedures have the advantage that they require no more than a pocket calculator. On the other hand, if one is equipped with a large computer with filter design programs such as those in the IEEE Program Book (3), one may find it easier, in some cases, to design better windows by the direct calculation of an optimized filter. The present work shows the results of computations of FIR filters and how they compare with Hanning, Hamming and Kaiser windows. We get, for typical filter parameters, a side-lobe attenuation of 31.5 dB for the Hanning window, 42.0 dB for the Hamming window, 41.0 dB for the Kaiser window and 47.2 dB for the FIR window.