Kaiser Window

The Kaiser window is a one-parameter family of window functions used for digital signal processing, and is defined by the formula :

w_n = \left\{ \begin{matrix} \frac{I_0\left(\pi \alpha \sqrt{1 - \left(\frac{2n}{M}-1\right)^2}\right)} {I_0(\pi \alpha)}, & 0 \leq n \leq M \\ \\ 0 & \mbox{otherwise} \\ \end{matrix} \right.

where:

  • I0 is the zeroth order Modified Bessel function of the first kind.
  • α is an arbitrary real number that determines the shape of the window. In the frequency domain, it determines the trade-off between main-lobe width and side lobe level, which is a central decision in window design.
  • M is an integer, and the length of the sequence is N=M+1.

When N is an odd number, the peak value of the window is wM/2 = 1. And when N is even, the peak values are wN/2-1 = wN/2 < 1.

Read more about Kaiser Window:  Frequency Response, Kaiser-Bessel Derived (KBD) Window

Famous quotes containing the words kaiser and/or window:

    “Modern tourist guides have helped raised tourist expectations. And they have provided the natives—from Kaiser Wilhelm down to the villagers of Chichacestenango—with a detailed and itemized list of what is expected of them and when. These are the up-to- date scripts for actors on the tourists’ stage.”
    —Daniel J. Boorstin (b. 1914)

    “A big leather-bound volume makes an ideal razorstrap. A thin book is useful to stick under a table with a broken caster to steady it. A large, flat atlas can be used to cover a window with a broken pane. And a thick, old-fashioned heavy book with a clasp is the finest thing in the world to throw at a noisy cat.”
    —Mark Twain [Samuel Langhorne Clemens] (1835–1910)