Kaiser window

It is a one-parameter family of window functions used in finite impulse response filter design and spectral analysis.

(see A list of window functions) In the Fourier transform, the first null after the main lobe occurs at

For large α, the shape of the Kaiser window (in both time and frequency domain) tends to a Gaussian curve.

The Kaiser window is nearly optimal in the sense of its peak's concentration around frequency

The KBD window function is defined in terms of the Kaiser window of length N+1, by the formula: This defines a window of length 2N, where by construction dn satisfies the Princen-Bradley condition for the MDCT (using the fact that wN−n = wn): dn2 + (dn+N)2 = 1 (interpreting n and n + N modulo 2N).

The KBD window is also symmetric in the proper manner for the MDCT: dn = d2N−1−n.