Exponential Windows

The shape of an exponential window is that of a decaying exponential. It can be mathematically expressed as

for n = 0, 1, 2……N-1,

where f is the final value. The initial value of the window is 1, and it gradually decays towards 0. The final value of the exponential can be adjusted to between 0 and 1. The exponential window for N = 32, with the final value specified as 0.1, is shown in the following illustration.

The exponential window is useful in analyzing transients, signals that exist only for a short time duration, whose duration is longer than the length of the window. You can apply the exponential window to signals that decay exponentially, such as the response of structures with light damping that are excited by an impact, for example, a hammer.