Kaiser Window - Kaiser-Bessel Derived (KBD) Window

Kaiser-Bessel Derived (KBD) Window

A related window function is the Kaiser-Bessel derived (KBD) window, which is designed to be suitable for use with the modified discrete cosine transform (MDCT). The KBD window function is defined in terms of the Kaiser window of length M+1, by the formula:

$d_n = \left\{ \begin{matrix} \sqrt{\frac{\sum_{j=0}^{n} w_j} {\sum_{j=0}^{M} w_j}} & \mbox{if } 0 \leq n < M \\ \\ \sqrt{\frac{\sum_{j=0}^{2M-1-n} w_j} {\sum_{j=0}^{M} w_j}} & \mbox{if } M \leq n < 2M \\ \\ 0 & \mbox{otherwise} \\ \end{matrix} \right.$

This defines a window of length 2M, where by construction d_n satisfies the Princen-Bradley condition for the MDCT (using the fact that w_M−n = w_n): d_n2 + d_{n + M}2 = 1 (interpreting n and n + M modulo 2M). The KBD window is also symmetric in the proper manner for the MDCT: d_n = d_2M−1−n.

Read more about this topic: Kaiser Window

Famous quotes containing the words derived and/or window:

“These are our grievances which we have thus laid before his majesty with that freedom of language and sentiment which becomes a free people, claiming their rights as derived from the laws of nature, and not as the gift of their chief magistrate.”
—Thomas Jefferson (1743–1826)

“The knocking out of a pipe can be made almost as important as the smoking of it, especially if there are nervous people in the room. A good, smart knock of a pipe against a tin wastebasket and you will have a neurasthenic out of his chair and into the window sash in no time.”
—Robert Benchley (1889–1945)