Question

3. Determine the complex Fourier series to represent the function f(t) = 2t in the range T to + 4. Show that the complex Fourier series in problem 3 above is equivalent to: f (t) = 4( sin t – įsin 2t + eşsin 3t - sin 4t + ... III.

Answer 1

3 ditelmine the represent the Range - complex fouuel series to function f(t) = at in to ta. the series 3 above showe that the complex fowice to problem is equivalent to # (t) = 4 (sint- sinat + sinat --) 970) can Be represented as ao + bn sinuet t an Cosnut. #64) T= -ñ to a ao = 1 f(e) df T=an т 2T ㅗ at.dt Sot 20 A LX2 2K ben #(4) sinnwt.dt - . 2 T 1 w=, ne bas [w= alt at sint.de a

* 2x2 Fosint ttcast teost] 082 ZA stomilary, ba=-2, -2 ba = 9 ধু and 3 SO an R T 112 f(t) Cosnwt at -T/2 at. Cosut. dt. 91 = 2 id sint tcost Casime 2: lin So a similary we can say da= 91=0=an. fis. of f(t) 4 (sint-b I sinat tisinat Hence proved 1