# ExactBlackmanWindow

represents an exact Blackman window function of x.

# Details

• ExactBlackmanWindow is a window function typically used for finite impulse response (FIR) filter design and spectral analysis.
• 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.
• is equal to
• ExactBlackmanWindow automatically threads over lists.

# Examples

open allclose all

## Basic Examples(3)

Shape of a 1D exact Blackman window:

Shape of a 2D exact Blackman window:

Extract the continuous function representing the exact Blackman window:

## Scope(4)

Evaluate numerically:

Translated and dilated exact Blackman window:

2D exact Blackman window with a circular support:

Discrete exact Blackman window of length 15:

Discrete 15×10 2D exact Blackman window:

## Applications(3)

Create a moving average filter of length 11:

Smooth the filter using a exact Blackman 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 exact Blackman window:

Normalize to create a window with unit area:

Fourier transform of the exact Blackman window:

Power spectrum of the exact Blackman window:

Wolfram Research (2012), ExactBlackmanWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.

#### Text

Wolfram Research (2012), ExactBlackmanWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.

#### CMS

Wolfram Language. 2012. "ExactBlackmanWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.

#### APA

Wolfram Language. (2012). ExactBlackmanWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html

#### BibTeX

@misc{reference.wolfram_2024_exactblackmanwindow, author="Wolfram Research", title="{ExactBlackmanWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html}", note=[Accessed: 26-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_exactblackmanwindow, organization={Wolfram Research}, title={ExactBlackmanWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html}, note=[Accessed: 26-May-2024 ]}