TableFS1 - FOURIER SERIES REPRESENTATION OF COMMON SIGNALS...

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FOURIER SERIES REPRESENTATION OF COMMON SIGNALS Rectangular Pulse Train -2T0 -T0 0 T0 2T0 0 h t x(t) τ = pulse width ( −τ /2 to τ /2) d = duty cycle = τ /T 0 . ω 0 = fundamental frequency = 2 π /T 0 sinc(x) = sin( π x)/( π x) 0 ,0 sinc( ) sinc( ) sin( ) n hd n h Xn d h d n d nd T hn n τ π = === () ( ) 0 1 2s i n c () c o s n x th d h d n d n t ω = =+ 00 1 cos nn n xt c c n t θ = + 0 0 ,2 s in c ( ) 0 ,2 s i n c ( ) , 0, hd nd h c hd c hd nd otherwise T < == = = If τ = T 0 /2, d = 1/2, and the equations given above becomes 2 n sinc n sin 22 2 n h n h X n = ⎛⎞ ⎜⎟ ⎝⎠ 0 1 n sinc cos n h x n t = 1
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() ( ) 00 1 cos nn n xt c c n t ω θ = =+ + 0 n ,s i n c 0 n i n c , 2 22 0, h h cc h otherwise π ⎛⎞ < ⎜⎟ == = ⎝⎠ Let y(t) = x(t T 0 /2). Then, () 0 0 2 2 n ,0 2 cos n 1s i n 2 T jn T jn n n h n YX e X e X n hn n = = = Rectangular Pulse Train with Time Shifting t o = τ /2.
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TableFS1 - FOURIER SERIES REPRESENTATION OF COMMON SIGNALS...

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