Radon Transform—Square

Author

Eric W. Weisstein
October 16, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegralTransforms/RadonTransformSquare.nb.

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

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

Integral (with a=1)

Integrate[Exp[-I k(y-(τ+p x))],{k,-∞,∞},{y,-a,a},{x,-a,a},Assumptions->(p|τ)∈Integers&&a>0]/(2π)

Factor[ExpandAll[%]]//TraditionalForm

Plot

Plot3D[(1/(2 p))(-Abs[a-a p-τ]+Abs[a+a p-τ]-Abs[a-a p+τ]+Abs[a+a p+τ]) /. a->1,{τ,-5,5},{p,-5,5},PlotPoints->50,Boxed->False,PlotRange->{0.,2.},AxesLabel->TraditionalForm/@{p,τ,R[p,τ]}]