Page 241 - Engineering Mathematics Workbook_Final

Fourier Series


1. A function with a period  is shown (d)  4 (1 sin n

)
+
below. The Fourier series for the n= 1 2 n 2
function is given by
[GATE-2003]
3. The period of the signal
  
x t = ( ) 8sin 0.8 t  +       is
 4 

(a) 0.4 s (b) 0.8 s

(c) 1.25 s (d) 2.5 s

[GATE-2010]
1  2   n  
(a) ( ) x = +  sin     cosnx
f
2 n= 1 n  2  4. The Fourier series of the function,

f x = −   x  0
( ) 0 ,

(b) ( ) x =  2 sin    n      cosnx =  x , 0 x  −  
f
n= 1 n  2 

1  2   n   in the interval  − ,  is
(c) ( ) x = +  sin     sin nx
f
2 n= 1 n  2   2 cos x cos3x 


f ( ) x = 4   +   1 2 + 3 2 + .... +



(d) ( ) x =  2 sin    n      sin nx  
f
n= 1 n  2   sin x sin 2x sin3x 

  + + + ......

[GATE-2000 (CE)]   1 2 3  
2. The Fourier series expansion of a The convergence of the above
symmetric and even function, ( ) x Fourier series at x = 0 gives
f
where  1  2
(a)  =
 1 2 / , −   0 n= 1 n 2 6

+

x
x

f ( ) x = 
 1 2 / , 0    − n− 1  2

−
x 
x

(b)  ( ) 1 2 = 12
n

)
+
(a)  4 2 (1 cosn n= 1
2
n= 1 n  1  2
(c)  (2n − ) 1 = 8

(b)  4 (1 cosn− ) n= 1
n= 1 2 n 2  ( ) 1− n+ 1 

(c)  4 2 (1 sin n− ) (d)  (2n − ) 1 = 4
n=
1
2
n= 1 n
[GATE-2016-CE-SET-2; 1 MARK]

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