Question

6. using the property F{f1 + f2} = F{fi} F{12} Calculate the Fourier transform of a triangular pulse. See Prob. 1

Number one posted as a reference. Only need problem 6 answered. Thanks

Answer 1

Given ୧୪ property FCF* f2) = F(fi) x F (fa) Fouried tdarsfoom of triangular pulse. As we know the convolution of two rectangular pulse gives triangulas ware confides two rectangulay pulses poft) - P g (t) A DE 9 . Tot -To 1 Tot Now find convolution of f(t), g(t) (8 + 9) 4 = ses 7 ct=y) du

tt To I - TO A.Adu - gło to (849)“) = Y A - A du, olt<Q To t-to .:(fog)(t) = 12 (4+2 to) , -210<tco A² (2To-t) oct<9TO Iti 79 To signal which is triangular g(fxg) (2 m2 To -310 STO Now in given problem 9V 1. To = A= V vm

Given rectangulas signal a hez) van - TE A= : convolution of he) with it self gives (hen) = p m (tf ), ctco (8-4), Octavia lo Ft

ๆ lolo - convolution of two rectangulas signall give triangulay signal (het) & h(t)) = triangulay signal from given propesty F Chah) = F(G) x F(h) Here F(h) is fousies transform of signal hit). FC hxb) = (Ech)? | het)= rectangulay pulse htha triangulay pulse

fourier transform of (triangular) = fale Forectangular)) ? IF( triangulay. Pulfe) = (F(2) 2 of we know that fourier thanx form rectangulay sigual F (rectorgulay) = (FCA) for rectangular sigral : *+ t -T12 7/2 signal forsies transform of above F(x+y) = Af Sincang :: 5(84)) = 2. Sin (176) .: F(trangulay) = ( 2A sin (WI) je

But given rectangulay signal : fourig transform of real triangulas signal 92 presiones To somente U forurier transform of trianguloy signal F(triangulay) - 8 km ow (08) Vom (sa (wo)? F(triangulay) =