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Hamming Function

المؤلف:  Hamming, R. W. and Tukey, J. W.

المصدر:  "Measuring Noise Color." Unpublished memorandum, 1949.

الجزء والصفحة:  ...

18-4-2020

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Hamming Function

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

{a_0sinc(2pikb)+sum_(n=1)^infty[sinc(2pikb+npi)+sinc(2pikb-npi)]}. " src="https://mathworld.wolfram.com/images/equations/HammingFunction/NumberedEquation5.gif" style="height:45px; width:431px" />

(5)

To obtain an apodization function with zero at , use

(6)

so

(7)

(8)

(9)

			(10)
			(11)

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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 Unpublished memorandum, 1949.