00:01
For this problem, we want to calculate some fourier transforms.
00:06
The definition of the fourier transform looks like this, and we're going to integrate over times from minus infinity to plus infinity.
00:16
So for number 25, we have a simple, just from minus a to a in time, goes up to capital a.
00:30
So we integrate that.
00:32
It's really just a constant function in between, minus a and a and it's zero outside of that.
00:38
So our integral looks like this.
00:41
There's our result.
00:44
To draw it, the dotted lines represent one over omega or minus one over omega.
00:50
They define the envelope of the sign function.
00:54
And so we get this.
00:55
And of course, at omega equals zero, the sign is equal to one...