So, I'm trying to prove [tex] \Delta\nu\Delta\tau\approx0.44 [/tex](adsbygoogle = window.adsbygoogle || []).push({});

where;

[tex] \Delta\nu [/tex] is the FWHM in freq domain for a gaussian pulse and

[tex] \Delta\tau [/tex] is FWHM in time domain for a gaussian pulse.

I do the problem by taking a standard gaussian exponential and finding the FWHM in both the time and frequency domain.

BUT, my answer is always EXACTLY a factor of 2 off. Ie. I get [tex] \approx0.88 [/tex].

No matter what form of a gaussian I use it is a factor of 2 off. 0.44 is the right answer (its quoted in many books).

Anyone familiar with this derivation?

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# Time-Bandwidth Product (Ideal Mode-Locking)

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