“Bartlett Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Bartlett Function

释义

Bartlett Function

The Apodization 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

where

is the Sinc Function. The peak (in units of

) is 1. The function

is always positive, sothere 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. Thefull 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.

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