THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

9.14 Data Windows and Selection of Weighting Functions 197Figure 9.19. Effect of window deviations in FFT scanning of noninteger number ofperiods.The discontinuities at the ends of the segments will engender a frequency spectrumdiffering from the true frequency content of the original signal. Aperiodic signalsmay also be misinterpreted on account of the finite length of sampling.The weighting or window function modifies the shape of the observation windowby tapering off both the leading and trailing edges of the data. Because theweighting function is used to obviate the effects of duration limiting, it increasesthe effective bandwidth. This increase is stated in terms of the noise bandwidthfactor (NBF) defined asEffective bandwidth with window functionNBF =(9.16)Effective bandwidth without window functionThe ideal value of NBF is unity. Another important consideration in the use ofweighting functions is the side-lobe ratio (SLR) or highest side-lobe level, expressedasSLR =Most sensitive out-of-band responsedB (9.17)Center of bandwidth responseA greater negative value of SLR (in decibels) is more desirable. But the selectionof the two parameters given by Equations (9.16) and (9.17) requires a compromise,i.e., a tradeoff between the steepness of the filter characteristic on one hand and theeffective bandwidth on the other. Table 9.1 lists the popular types of data windowsand their parametric values. The Hanning window (one period of a cosine-squaredfunction) constitutes a good choice for stationary signals, because that functionhas a zero value and slope at each end and thus renders a gradual transition overthe discontinuity of data. Figure 9.20 illustrates the rectangular, Hanning, andHamming weighting functions.