Uniform Apodization Function

An apodization function

(1)

having instrument function

(2)

The peak of  is . The full width at half maximum of  can found by setting  to obtain

(3)

and solving for , yielding

(4)

Therefore, with ,

(5)

The extrema are given by taking the derivative of , substituting , and setting equal to 0

(6)

Solving this numerically gives sidelobes at 0.715148 (), 1.22951 (0.256749), 1.73544 (), ....

REFERENCES:

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 554-556, 1992.