Page 244 - Engineering Mathematics Workbook_Final

Fourier Series

) 0, be a function
15. Let g  : 0, → ) 18. The Fourier cosine series for an even
defined by ( ) x = x −   x , where [x] function f(x) is given by
g

represents the integer part of x. (That f ( ) x = a + 0  a n cosn ( ) x . The
is, it is the largest integer which is n= 1
2
less than or equal to x). The value of value of the coefficient a for the
( )

f x =
2
the constant term in the Fourier series function ( ) cos x in 0, is
expansion of g(x). is _______
(a) -0.5 (b) 0.0
[GATE-2014-EE-SET 1]
(c) 0.5 (d) 1.0
16. Fourier series of any periodic signa
x(t) can be obtained if [GATE-2018 (ME-AFTERNOON
SESSION)]
T
1.  x ( ) t dt  
0 19. In the Fourier series expansion of
2
f ( ) x = x in  − ,  the sum of
2. Finite number of
discontinuities within finite time absolute values of the Fourier
interval t coefficients of f is _____.

3. Infinite number of  2  2
discontinuities (a) (b)
6 3
Select the correct answer using the
codes given below: 2 2
2
(c) (d) 
(a) 1, 2 and 3 (b) 1 and 3 only 3

(c) 1 and 2 only (d) 2 and 3 only 20. The Fourier series of the periodic
function
[ESE 2017 (EE)]

−
f ( ) x = x , 1 x  1, ( f x + ) 2 = f ( ) x
17. The Fourier series expansion of the 1  cos (2n − ) 1  x
( )
x
saw-toothed waveform f x = in is given by 2 −  4 2 2 .
( − ,  ) of period 2 gives the n= 1 (2n − ) 1 
1 1 1 Using the above, the sum of
series, 1− + − + ...... ? 1 1
=
3 5 4 1+ + + ..... is ______
3 2 5 2
  2
(a) (b)  2 3 2
2 4 (a) (b)
4 8
 2 
(c) (d) 2 2
2 4 (c)  (d) 
8 2
[ESE 2017 (EE)]

242