Kaiser Windows and Transforms

Figure 3.24 plots the Kaiser window and its transform for $\alpha = \beta/\pi = 1,2,3$ . Note how increasing $\alpha$ causes the side-lobes to fall away from the main lobe. The curvature at the main lobe peak also decreases somewhat.

Figure 3.24: Kaiser window and transform for $\alpha =1,2,3$ .

Figure 3.25 shows a plot of the Kaiser window for various values of $\beta = [0,2,4,6,8,10]$ . Note that for $\beta=0$ , the Kaiser window reduces to the rectangular window.

Figure 3.25: The Kaiser window for various values of the time-bandwidth parameter $\beta$ .

Figure 3.26 shows a plot of the Kaiser window transforms for $\beta = [0,2,4,6]$ . For $\beta=0$ (top plot), we see the dB magnitude of the aliased sinc function. As $\beta$ increases the main-lobe widens and the side lobes go lower, reaching almost 50 dB down for $\beta=6$ .

Figure 3.26: Kaiser window transform magnitude for various $\beta$ .

Figure 3.27 shows the effect of increasing window length for the Kaiser window. The window lengths are $M = [20,30,40,50]$ from the top to the bottom plot. As with all windows, increasing the length decreases the main-lobe width, while the side-lobe level remains essentially unchanged.

Figure 3.27: Kaiser window transform magnitudes for various window lengths.

Figure 3.28 shows a plot of the Kaiser window side-lobe level for various values of $\alpha = [0,0.5,1,1.5,\ldots,4]$ . For $\beta=0$ , the Kaiser window reduces to the rectangular window, and we expect the side-lobe level to be about 13 dB below the main lobe (upper-lefthand corner of Fig.3.28). As $\alpha =\beta /\pi$ increases, the dB side-lobe level reduces approximately linearly with main-lobe width increase (approximately a 25 dB drop in side-lobe level for each main-lobe width increase by one sinc-main-lobe).

Figure 3.28: Kaiser window side-lobe level for various values of $\alpha =\beta /\pi$ .