info prev up next book cdrom email home

Blackman Function

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

An Apodization Function given by

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 $0.810957a$. The Apparatus Function is

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 $I(k)$ at $k=(7/4)a$ and $k=(9/4)a$.

See also Apodization Function


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.

© 1996-9 Eric W. Weisstein