An Apodization Function

(1) 
having Instrument Function
The peak (in units of ) is 2. The extrema are given by letting
and solving

(3) 

(4) 

(5) 
Solving this numerically gives ,
,
, ...for the first few solutions. The
second of these is the peak Positive sidelobe, and the third is the peak Negative sidelobe. As a fraction of the peak,
they are 0.128375 and . The Full Width at Half Maximum is found by setting

(6) 
and solving for , yielding

(7) 
Therefore, with ,

(8) 
See also Apodization Function
© 19969 Eric W. Weisstein
19990526