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
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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 Web Resource. https://mathworld.wolfram.com/UniformApodizationFunction.html
Subject classifications
