Bartlett Function


The apodization function


which is a generalization of the one-argument triangle function. Its full width at half maximum is a.

It has instrument function


where sinc(x) is the sinc function. The peak of I(k) is a, and the full width at half maximum is given by setting x=pika and numerically solving


for x_(1/2), yielding


Therefore, with L=2a,


The function I(k) is always positive, so there are no negative sidelobes. The extrema are given by differentiating I(k) with respect to k, defining r=ka, and setting equal to 0,


Solving this numerically gives minima of 0 at r=1, 2, 3, ..., and sidelobes of 0.047190, 0.01648, 0.00834029, ... at r=1.4303, 2.45892, 3.47089, ....

See also

Apodization Function, Instrument Function, Parzen Apodization Function, Triangle Function

Explore with Wolfram|Alpha


Bartlett, M. S. "Periodogram Analysis and Continuous Spectra." Biometrika 37, 1-16, 1950.Blackman, R. B. and Tukey, J. W. The Measurement of Power Spectra, From the Point of View of Communications Engineering. New York: Dover, pp. 98-99, 1959.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 554-556, 1992.

Referenced on Wolfram|Alpha

Bartlett Function

Cite this as:

Weisstein, Eric W. "Bartlett Function." From MathWorld--A Wolfram Web Resource.

Subject classifications