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Date: 24-1-2020
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An apodization function chosen to minimize the height of the highest sidelobe (Hamming and Tukey 1949, Blackman and Tukey 1959). The Hamming function is given by
(1) |
and 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 instrument function goes to 0 at . The FWHM is , the peak is 1.08, and the peak negative and positive sidelobes (in units of the peak) are and 0.00734934, respectively.
From the apodization function, a general symmetric apodization function can be written as a Fourier series
(3) |
where the coefficients satisfy
(4) |
The corresponding instrument function is
(5) |
To obtain an apodization function with zero at , use
(6) |
so
(7) |
(8) |
(9) |
(10) |
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(11) |
REFERENCES:
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.
Hamming, R. W. and Tukey, J. W. "Measuring Noise Color." Unpublished memorandum, 1949.
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