Window function
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
A popular window function, the Hann window. Most popular window functions are similar bell-shaped curves.
- Window function and frequency response - Rectangular.svg
Window function and its Fourier transform: Rectangular window
- Window function and its Fourier transform – Triangular (n = 0...N).svg
Triangular window (with L = N + 1)
- Window function and frequency response - Parzen.svg
Parzen window function and frequency response
- Window function and frequency response - Welch.svg
Welch window function and its Fourier transform
- Window function and its Fourier transform – Hann (n = 0...N).svg
Hann window function and its Fourier transform
- Window function and frequency response - Hamming (alpha = 0.53836, n = 0...N).svg
Hamming window, a0 = 0.53836 and a1 = 0.46164. The original Hamming window would have a0 = 0.54 and a1 = 0.46.
- Window function and its Fourier transform – Blackman (n = 0...N).svg
Blackman window; α = 0.16
- Window function and frequency response - Nuttall (continuous first derivative).svg
Nuttall window, continuous first derivative
.svg){kind=link}
.svg){kind=link}