Bartlett Function

Author

Eric W. Weisstein
October 7, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/BartlettFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BartlettFunction.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Apodization Function

Bartlett[x,a]

Maximum

Limit[Bartlett[x,a],x->0]

Instrument Function

InstrumentFunction[Bartlett[x,a],{x,a},k,Assumptions->k>0&&a>0]

i[k_]:=(((Sin[a k π])^2)/(a (k^2) (π^2)))

Plot

ApodizationPlot[{Bartlett[x,a],(((Sin[a k π])^2)/(a (k^2) (π^2)))},{x,k},a]

FWHM

Apodization Function

FWHM[Bartlett[x,a],x]

Instrument Function

Solve[(Sin[x]/x)^2==1/2,x]

2NFWHM[i[k]/a/.a->x/k,x]/L

Sidelobes

FullSimplify[Together[D[i[k],k]/.a->r/k]]

f[x_]:=-1+Cos[2 π x]+π x Sin[2 π x]

roots=x/.PlotRoot[f[x],{x,0,5},
PlotStyle->Red]

extrema=Chop[{#,i[#]/.a->1}&/@roots]

Plot[Evaluate[i[k]/.a->1],{k,0,5},PlotStyle->Red,
Epilog->{PointSize[.02],Red,Point/@extrema}]