Other Definitions of Main Lobe WidthOur simple definition of main-lobe band-width (distance between zero-crossings) works pretty well for windows in the Blackman-Harris family, which includes the first six entries in Table 5.1. (See §3.3 for more about the Blackman-Harris window family.) However, some windows have smooth transforms, such as the Hann-Poisson (Fig.3.21), or infinite-duration Gaussian window (§3.11). In particular, the true Gaussian window has a Gaussian Fourier transform, and therefore no zero crossings at all in either the time or frequency domains. In such cases, the main-lobe width is often defined using the second central moment.6.5
A practical engineering definition of main-lobe width is the minimum distance about the center such that the window-transform magnitude does not exceed the specified side-lobe level anywhere outside this interval. Such a definition always gives a smaller main-lobe width than does a definition based on zero crossings.
Simple Sufficient Condition for Peak Resolution