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Blackman Function


Blackman

An apodization function given by

 A(x)=(21)/(50)+1/2cos((pix)/a)+2/(25)cos((2pix)/a),
(1)

which has full width at half maximum of 0.810957a. This function is defined so that the coefficients are approximations in the general expansion

 A(x)=a_0+2sum_(n=1)^inftya_ncos((npix)/b),
(2)

to

a_0=(3969)/(9304) approx 0.42659
(3)
a_1=(1155)/(4652) approx 0.24828
(4)
a_2=(715)/(18608) approx 0.038424,
(5)

which produce zeros of I(k) at ka=7/4 and ka=9/4.

The corresponding instrument function is

 I(k)=(a(0.84-0.36a^2k^2)sinc(2piak))/((1-a^2k^2)(1-4a^2k^2)),
(6)

where sinc(x) is the sinc function. It is full width at half maximum is 2.2988/L.


See also

Apodization Function

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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.

Referenced on Wolfram|Alpha

Blackman Function

Cite this as:

Weisstein, Eric W. "Blackman Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BlackmanFunction.html

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