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 (
), ....
See also
Apodization Function,
Instrument Function Explore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Uniform Apodization Function Cite this as:
Weisstein, Eric W. "Uniform Apodization Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UniformApodizationFunction.html
Subject classifications
