I am SHARING you a question from the communication system. please donot attempt the question if you cant solve according to the instructions. please don't waste my question and I will share you the solution also.

instructions

1) write down the step as 1,2,3 and so on

2) while writing any equation tell that how and why you write this equation or function

3) while writing any step write in words that what you have done in this step

4) make sure that your answer is correct

question:

Find the Fourier transform of the half - cosine pulse shown in the figure P2.1a

solution:

g(t) g A t 0 - T 2 T 2 (a) 2.1 (a) 810) Acos(257) [] We can rewrite the half-cosine as: Acos( 211 ) - rect( Using the property of multiplication in the time-domain: G=G*G. 3184 -1)+815 +1) Arsin() f Writing out the convolution: GU- 5 A ( 0 7 | 8418+)+84-4 -1]da A sin((/+S)T) sin(74-8.)T) + - 2. A cos TfT) cos(3/7) 2.1 27 27 (b)By using the time-shifting property: T 81-1) exp(-28 ft.) GD) A COSLE /T) cos(a) 2.1 expl-jx [T) g(t) g A t 0 - T 2 T 2 (a) 2.1 (a) 810) Acos(257) [] We can rewrite the half-cosine as: Acos( 211 ) - rect( Using the property of multiplication in the time-domain: G=G*G. 3184 -1)+815 +1) Arsin() f Writing out the convolution: GU- 5 A ( 0 7 | 8418+)+84-4 -1]da A sin((/+S)T) sin(74-8.)T) + - 2. A cos TfT) cos(3/7) 2.1 27 27 (b)By using the time-shifting property: T 81-1) exp(-28 ft.) GD) A COSLE /T) cos(a) 2.1 expl-jx [T)