## Bartlett Function

 (1)

which is a generalization of the one-argument Triangle Function. Its Full Width at Half Maximum is . It has Instrument Function

 (2)

Letting in the first part therefore gives
 (3)

Rewriting (2) using (3) gives
 (4)

Integrating the first part and using the integral
 (5)

for the second part gives

 (6)

where is the Sinc Function. The peak (in units of ) is 1. The function is always positive, so there are no Negative sidelobes. The extrema are given by letting and solving
 (7)

 (8)

 (9)

 (10)

Solving this numerically gives for the first maximum, and the peak Positive sidelobe is 0.047190. The full width at half maximum is given by setting and solving
 (11)

for , yielding
 (12)

Therefore, with ,
 (13)

See also Apodization Function, Parzen Apodization Function, Triangle Function

References

Bartlett, M. S. Periodogram Analysis and Continuous Spectra.'' Biometrika 37, 1-16, 1950.

© 1996-9 Eric W. Weisstein
1999-05-26