Can someone explain to me how do they use the sampling property to end up having the fourier transform being one. In my attempt to get the answer, am in the correct direction ?
Attachments

86.9 KB Views: 42
No, you made an invalid step there. The delta function is not one over the whole range of integration. Ask yourself where the delta function is zero and where is it nonzero. Then ask yourself what the value of exp(jwt) is in the places where the delta function is not zero.Can someone explain to me how do they use the sampling property to end up having the fourier transform being one. In my attempt to get the answer, am in the correct direction ?
The dirac function is one when x=0 of which the exponential function is also one when x=0. Thanks for the help.No, you made an invalid step there. The delta function is not one over the whole range of integration. Ask yourself where the delta function is zero and where is it nonzero. Then ask yourself what the value of exp(jwt) is in the places where the delta function is not zero.
That's not quite correct, but you are homing in on the correct viewpoint. Remember that the Dirac delta function is not one at zero, but goes to infinity. It is the area under the delta function that is one, as shown by your integral equation for the sifting property.The dirac function is one when x=0 of which the exponential function is also one when x=0. Thanks for the help.
by Aaron Carman
by Jake Hertz
by Duane Benson
by Duane Benson