Electrical FE /EIT Exam Prep - Communications 3: Dirac Delta Function Integral

[@irenamilasevski4451]

Andrew, thank you very much for your videos. Can you please explain, why here t=t0, do not understand this step. Thank you in advance!

[@moisenistrian9566]

In the sifting property that he outlined, it states that the integral of the product of a function x(t) and a shifted dirac delta function simply evaluates to the value of the function x(t) at the location where the dirac delta is non-zero, which is at the shifted location of t=t0. Therefore the integral has only one non-zero value (x(to)), and that is at the location where the delta function is non-zero (t=t0)

[@andrewsaunders5945]

I dont understand how on the last step when you have omega*pi/3 to 2*pies/3? im confused because i thought omega = 2*pie* frequency. a little more explanation would be helpful.

[@EngineeringEducation]

Hi Andrew, w = 2 is given at the beginning of the problem. Here, the integral is over time t (and not w) therefore omega is a constant. We plugged in 2 for omega and solved. Does this help clarify?

[@andrewsaunders5945]

Ah yes. thanks for the help.