Hanning window

Windows are functions defined over a finite range that are used in digital signal processing. The window functions achieve their maximum value at the middle point of their finite range, and decay symmetrically away from it, both to the start and end of the range. Windows are used to weigh more strongly the data values at the center of the finite range, to the detriment of the values at the extremes of the range. A window is applied a finite set of data by calculating a set of window values of the same length as the data, and then multiplying the each data value by the corresponding window value.

The Hanning window, is a particular type of window, as described above. A Hanning window of length $N$ is defined by:

$h(k) = \frac{1}{2} \left( 1 - \cos(2 \pi k / N) \right)$

In the Hanning window, the center value is 1 (no change to the data), while the end values are zero.

The most common use of the Hanning window and other windows of its kind is to preprocess data before applying a fast fourier transform. This is necessity to avoid aliasing artifacts that occur if the start and end points of the data do not match. The aliasing occurs because the fast fourier transform assumes the data is periodical, i.e. it assumes the segment of data presented repeats end to end infinitely many times.

Categories: Digital signal processing