Blackman Function

$\begin{figure}\begin{center}\BoxedEPSF{Blackman.epsf scaled 800}\end{center}\end{figure}$

An Apodization Function given by

$\begin{displaymath} A(x)=0.42+0.5\cos\left({\pi x\over a}\right)+0.08\cos\left({2\pi x\over a}\right). \end{displaymath}$

(1)

Its Full Width at Half Maximum is

. The Apparatus Function is

$\begin{displaymath} I(k)={a(0.84-0.36a^2k^2-2.17\times 10^{-19}a^4k^4)\sin(2\pi ak)\over (1-a^2k^2)(1-4a^2k^2)}. \end{displaymath}$

(2)

The Coefficients are approximations to

$\displaystyle a_0$	$\textstyle =$	$\displaystyle {3969\over 9304}$	(3)
$\displaystyle a_1$	$\textstyle =$	$\displaystyle {1155\over 4652}$	(4)
$\displaystyle a_2$	$\textstyle =$	$\displaystyle {715\over 18608},$	(5)

which would have produced zeros of

and

See also Apodization Function

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.