GaussianWindow
represents a Gaussian window function of x.
GaussianWindow[x,σ]
uses standard deviation σ.
Details
- GaussianWindow is a window function typically used for antialiasing and resampling.
- Window functions are used in applications where data is processed in short segments and have a smoothing effect by gradually tapering data values to zero at the ends of each segment.
- GaussianWindow[x,α] is equal to .
- GaussianWindow[x] is equivalent to GaussianWindow[x,3/10].
- GaussianWindow automatically threads over lists.
Examples
open allclose allBasic Examples (3)
Scope (6)
Applications (3)
Create a moving average filter of length 11:
Smooth the filter using a Gaussian window:
Log-magnitude plot of the frequency spectrum of the filters:
Use a window specification to calculate sample PowerSpectralDensity:
Compare to spectral density calculated without a windowing function:
The plot shows that window smooths the spectral density:
Compare to the theoretical spectral density of the process:
Properties & Relations (8)
GaussianWindow[x,∞] is equivalent to a Dirichlet window:
The area under the Gaussian window:
Normalize to create a window with unit area:
Fourier transform of the Gaussian window:
Power spectrum of the Gaussian window:
Fourier transform of the parametrized Gaussian window:
Variation of the magnitude spectrum as a function of the parameter σ:
Discrete-time Fourier transform of the discrete Gaussian window of length 11:
Power spectra for three different window lengths:
Power spectra for three different values of the shape parameter σ:
Possible Issues (1)
2D sampling of Gaussian window will use a different standard deviation for each row of samples when passed as a symbol to Array:
Text
Wolfram Research (2012), GaussianWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/GaussianWindow.html.
CMS
Wolfram Language. 2012. "GaussianWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GaussianWindow.html.
APA
Wolfram Language. (2012). GaussianWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GaussianWindow.html