Minimum Frequency Separation vs. Window Length

The requirements on window length for resolving closely tuned sinusoids was discussed in §4.7. This section considers this issue for the Kaiser window. Table 3.1 lists the $\alpha$ parameter required for a Kaiser window to resolve equal-amplitude sinusoids with a frequency spacing of $\Delta\omega$ rad/sample [1, Table 8-9]. Recall from §3.8 that $\alpha$ can be interpreted as half of the time-bandwidth of the window (in cycles).

Table: Kaiser $\alpha$ parameter for various frequency resolutions, assuming an FFT zero-padding factor of at least 3.5.

$\alpha$	$\Delta\omega$
1.5	$2.1$
2.0	$2.5$
2.5	$2.9$
3.0	$3.4$