Kaiser Window

Jim Kaiser discovered a simple approximation to the DPSS window based
upon Bessel functions [115], generally known as the Kaiser
window (or *Kaiser-Bessel window*).

**Definition:**

(4.39) |

**Window transform:**

The Fourier transform of the Kaiser window
(where
is
treated as continuous) is given by^{4.11}

(4.40) |

where is the zero-order modified Bessel function of the first kind:

- Reduces to rectangular window for
- Asymptotic roll-off is 6 dB/octave
- First null in window transform is at
- Time-bandwidth product radians if bandwidths are measured from 0 to positive band-limit
- Full time-bandwidth product radians when frequency bandwidth is defined as main-lobe width out to first null
- Sometimes the Kaiser window is parametrized by
, where
(4.42)

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University