Hamming Function

An Apodization Function chosen to minimize the height of the highest sidelobe. The Hamming function is given by

 (1)

Its Full Width at Half Maximum is . The corresponding Instrument Function is
 (2)

This Apodization Function is close to the one produced by the requirement that the Apparatus Function goes to 0 at . From Apodization Function, a general symmetric apodization function can be written as a Fourier Series
 (3)

where the Coefficients satisfy
 (4)

The corresponding apparatus function is

 (5)

To obtain an Apodization Function with zero at , use
 (6)

so
 (7)

 (8)

 (9)

 (10) (11)

The FWHM is 1.81522, the peak is 1.08, the peak Negative and Positive sidelobes (in units of the peak) are and 0.00734934, respectively.

Blackman, R. B. and Tukey, J. W. Particular Pairs of Windows.'' In The Measurement of Power Spectra, From the Point of View of Communications Engineering. New York: Dover, pp. 98-99, 1959.