An Apodization Function, also called the Hann Function, frequently used to reduce Aliasing in
Fourier Transforms. The illustrations above show the Hanning function, its Instrument
Function, and a blowup of the Instrument Function sidelobes. The Hanning function is given by
|
(1) |
The Instrument Function for Hanning apodization can also be written
|
(2) |
Its Full Width at Half Maximum is . It has Apparatus Function
The first integral is
|
(4) |
The second integral can be rewritten
Combining (4) and (5) gives
|
(6) |
To find the extrema, define
and rewrite (6) as
|
(7) |
Then solve
|
(8) |
to find the extrema. The roots are and 10.7061, giving a peak Negative sidelobe of and a peak
Positive sidelobe (in units of ) of 0.00843441. The peak in units of is 1, and the full-width at half maximum is
given by setting (7) equal to 1/2 and solving for , yielding
|
(9) |
Therefore, with , the Full Width at Half Maximum is
|
(10) |
See also Apodization Function, Hamming Function
© 1996-9 Eric W. Weisstein
1999-05-25