Question

Fourier transform of a rectangular pulse is a: Tan function Cosine function Sinc function Sine function Question 28 1 pts Every periodic function can be expressed as a linear combination of: Sine and cosine functions Sine functions Logarithmic functions None of the above

Answer 1

Fourier transform of a rectangular pulse is a sinc function xt) ::x) = sheet (9) i Fouries thansform of above one is, O -Ta Ті, + la X(W) - Sat) e dut et So edut, at -7% T/ xW) = 5jwt 1 -d10(E) EE) 9.. te مال - -T/g jwT/2 -jwT/2 e e 2 & sinut x(W) = 7 sin(WI) T. sinc(wI). WT |- *W = T. sinc (1) 8. Every periodic function can be expressed as a linear combination of ine and cosine functions This can be achieved by using fowrien series concept for eveny perciodic function:

Let a function f(t) is a periodic function with period t. :: (t+1) = fu). Then it can be represented as, f(t) = ao + { (an cosnoot + bn sinnwot) n-1 T #se ao Average value of f(t) = Here, ↑ ( fel.at 0 Wo = QT T T an = a s PC). Cos nust. dt 0 bn عواد s fle). sin nwt. dt.