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 w_M/2 = 1. And when N is even, the peak values are w_N/2-1 = w_N/2 < 1.

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

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