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scijs-window-functions

scijs-window-functions

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Window functions for digital signal processing

Introduction

Among other uses, window functions help control spectral leakage when doing Fourier Analysis. This collection of window functions is copied directly from Wikipedia. Caveat emptor.

Usage

To require all window functions, include the top-level scijs-window-functions module:

var wfuncs = require('scijs-window-functions')
 
var value = wfuncs.blackmanHarris( 50, 101 )

You can also require a single window function:

var blackmanHarris = require('scijs-wind-wfunctions/blackman-harris')
 
var value = blackmanHarris( 50, 101 )

To calculate the value of a window function, pass the sample number and total number of samples to one of the window functions listed below, along with any additional parameters it may require. The plots below are calculated from the npm module and plotted with Fourier transform to illustrate the spectral leakage. See the Wikipedia page on window functions for more details.

bartlettHann( i, N ):

Bartlett-Hann Window Equation 1

Bartlett-Hann Window Equation 2

Bartlett-Hann

bartlett( i, N ):

Bartlett

blackman( i, N ):

Blackman Window Equation 1

Blackman Window Equation 2

Blackman

blackmanHarris( i, N ):

Blackman-Harris Window Equation 1

Blackman-Harris Window Equation 2

Blackman-Harris

blackmanNuttall( i, N ):

Blackman-Nuttall Window Equation 1

Blackman-Nuttall Window Equation 2

Blackman-nuttall

cosine( i, N ):

Cosine Window Equation 1

Cosine

exactBlackman( i, N ):

Exact Blackman

The same as the Blackman window, except a0 = 0.42659 a1 = 0.49656, and a2 = 0.076849. These place zeros at the third and fourth sidelobes.

flatTop( i, N ):

Flat top Window Equation 1

Flat top Window Equation 2

Flat Top

gaussian( i, N, sigma ):

Sigma controls the width of the window.

Gaussian Window Equation 1

Gaussian Window Equation 2

Gaussian

hamming( i, N ):

Hamming Window Equation 1

Hamming Window Equation 2

Hamming

hann( i, N ):

Hann Window Equation

Hann

lanczos( i, N ):

Lanczos Window Equation

Lanczos

nuttall( i, N ):

Nuttall Window Equation 1

Nuttall Window Equation 2

Nuttall

rectangular( i, N ):

Rectangular Window Equation

Rectangular

triangular( i, N ):

Triangular Window Equation

Triangular

tukey( i, N, alpha ):

A tapered cosine window. Alpha controls the relative width of the flat section. Alpha=0 is rectangular, alpha=1 is Hann. Tukey Window Equation

Tukey

welch( i, N ):

Welch Window Equation

Welch

Testing

The tests ensure the window functions aren't returning NaN, but it's hard to have confidence in the accuracy with tests. Instead, I opted to focus on visual testing via plots and Fourier Transforms. To generate the plots, run

$ npm run generate-plots

It pipes them through matplotlib. Don't worry. I realize the irony.

Credits

Window function definitions and equation images from Wikipedia: Window Function.

(c) 2015 Ricky Reusser. MIT License