LanczosWindow

LanczosWindow[x]

represents a Lanczos window function of x.

Details

Examples

open allclose all

Basic Examples  (3)

Shape of a 1D Lanczos window:

Shape of a 2D Lanczos window:

Extract the continuous function representing the Lanczos window:

Scope  (4)

Translated and dilated Lanczos window:

2D Lanczos window with a circular support:

Evaluate numerically:

Discrete Lanczos window of length 15:

Discrete 15×10 2D Lanczos window:

Applications  (3)

Create a moving average filter of length 11:

Smooth the filter using a Lanczos window:

Log-magnitude plot of the frequency spectrum of the filters:

Use a window specification to calculate sample PowerSpectralDensity:

Calculate the spectrum:

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:

Use a window specification for time series estimation:

Specify window for spectral estimator:

Properties & Relations  (2)

The area under the Lanczos window:

Normalize to create a window with unit area:

Fourier transform of the Lanczos window:

Power spectrum of the Lanczos window:

Introduced in 2012
 (9.0)