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19 Nov 2019
please show work Imagine a Gaussian pulse, exp[ - (t/ delta t)2/2), where At is its approximate pulse length in time. Find its spectrum. Show that, as the pulse increases in length( delta t rightarrow infinity ), its spectrum becomes infinite at omega = 0 and also infinitely narrow. This function (whose area actually remains constant) is known as a "Dirac delta function," and it plays a very important role in physics.
please show work
Imagine a Gaussian pulse, exp[ - (t/ delta t)2/2), where At is its approximate pulse length in time. Find its spectrum. Show that, as the pulse increases in length( delta t rightarrow infinity ), its spectrum becomes infinite at omega = 0 and also infinitely narrow. This function (whose area actually remains constant) is known as a "Dirac delta function," and it plays a very important role in physics.