Window function

Simplest possible window function: rectangular. Notice the loss of signal at certain frequencies (right)

Example of a window function: Using a limited Gauss curve will produce "spikes"

In mathematics, a window function is a special function that can be applied to a signal, as it occurs in digital signal processing. A window function has a value of zero outside the domain which is of interest, and a non-zero value inside this domain. When multiplied with the signal (function), the result will be zero outside the domain of interest, and non-zero inside it - it will only leave the "window". The simplest possible window function is rectangular: It is 1 inside the domain of interest, and zero everywhere else. It is named Dirichlet window (after Peter Gustav Lejeune Dirichlet). Many window functions are symmetric around the center (which is often in the middle of the interval). They will amplify or weaken the signal in certain positions,

Window Function Media

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  A popular window function, the Hann window. Most popular window functions are similar bell-shaped curves.

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  Window function and its Fourier transform: Rectangular window

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  Triangular window (with L = N + 1)

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  Parzen window function and frequency response

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  Welch window function and its Fourier transform

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  The first figure is ½ cycle of a sine function, called a sine window function. Window functions are sometimes depicted centered around n=0, in which case this becomes a cosine function. Therefore, it is sometimes also referred to as a "cosine window", which is easily confused with the unrelated "family of cosine windows".

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  Hann window function and its Fourier transform

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  Hamming window, a0 = 0.53836 and a1 = 0.46164. The original Hamming window would have a0 = 0.54 and a1 = 0.46.

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  Blackman window; α = 0.16