00:01
Now, in this question, basically, we look at, we ask to determine the exponential free series, representations of each of the foreign signals, right? let's look at the first signals.
00:13
The xt is given by exponential j10 -t, right? obviously, this is already the exponential free theory.
00:21
We don't have to do anything, right? so this is it.
00:24
And the second is xt equals sine and two.
00:30
T plus cosine 12t, right? and this we can read it as sine 2d can be written as 2i, explanation of g 2t minus explanation of g 2t, right? and then cosine 12t can be written as 1 over 2 times explanation of g 12t plus explanation minus g 12t, right? so that's the f series.
00:55
And c we look at xt equals cosine, i equals cosine, two, 7 pi t and plus sign 11 pi t right and of course this can be written as two two times this actually is just some exponential of j a times 7 pi t plus explanation minus j a times 7 pi t right and plus the sign part can be written as 1 over 2 i just exponential ga times 11 pi t minus explanational minus ga times 11 part t right and then the final part is x t equals sine 4 t plus cosine square two t and this can be written as sine 4t and plus cosine square two t can be can be actually rewritten as cosine 2 t plus 1 over 2 2 right so this becomes half, that means the constant half i take it to front...