Page 243 - Engineering Mathematics Workbook_Final

Fourier Series

(a) 2 (b) 4 The same function x(t) can also be
considered as a periodic function with
(c) 0 (d) -2
period T = 40. Let b be the Fourier
1
k
[ECE 2017 (COMMON PAPER)] series coefficient when period is
1
 −  ,if −   x  0 taken as T . If   a = 16, then
k=−
k

11. Let ( ) x =  
f
  , if 0  x    k=− b is equal to

k
be a periodic function of period 2 . (a) 256 (b) 64
The coefficient of sin 5x in the (c) 16 (d) 4
Fourier series expansion of f(x) in the
interval  − ,  is [GATE-2018 (EC)]

4 5 14. The Fourier series of the function,
(a) (b)
( ) 0,   
5 4 f x = − x 0
4 3 =  x , 0 x  −   in the interval
(c) (d)
3 4
 − ,  is
[ESE-2018 (COMMON PAPER)]

 2 cos x cos3x  

12. The Fourier cosine series for an even f ( ) x = 4 +     1 2 + 3 2 + ........   
function f(x) is given by  sin x sin2x sin3x 

+   + + + ...... .


f ( ) x = a + 0  a n cosn ( ) x   1 2 3  
n= 1 The convergence of the above Fourier

The value of the coefficient a for the series at x = 0 gives
2

function ( ) x = cos 2 ( ) x in 0, is  1  2
f
(a)  2 =
(a) -0.5 (b) 0.0 n= 1n 6

(c) 0.5 (d) 1.0  ( ) 1− n− 1  2
(b)  2 =
[GATE-2018 (ME-Afternoon Session)] n= 1 n 12


13. Let x(t) be a periodic function with (c)  1 =  2
period T = 10. The Fourier series n= 1 (2n − ) 1 8
coefficients for this series are denoted
by a , that is  ( ) 1− n− 1 
k
(d)  1 = 4
1 2n −
n=

x ( ) t =  a e jk 2 t [GATE-2016-CE-SET 2]
T
k
k=−

241