00:01
So in this question we're told that f of omega is the fourier transform of f of x.
00:07
So this is the integral from minus infinity to infinity, f of x, e to the minus i, omega x, dx.
00:15
And g of omega is the fourier transform of g, minus infinity to infinity, g of x, e to the minus i, omega x, dx.
00:26
Now let's say that g of x is f of x plus a.
00:34
Then g of omega is the integral from minus infinity to infinity, f of x plus a, e to minus i, omega x, d x.
00:44
Now let's write y is x plus a, so that dy is d x, and x is y minus a.
00:57
Then g of omega is the integral from minus infinity to infinity, f of y, e to the minus i, y minus a, dy, which is e to the i omega a, integral from minus infinity to infinity, f of y, e to minus i omega y, y, d y, which is e to the i omega a f of omega...