Page 242 - Engineering Mathematics Workbook_Final

Fourier Series

) 0, be a function
5. Let  : 0, → ) Select the correct answer using the
g
defined by ( ) x = x −   x , where [x] codes given below:
g
represents the integer part of x. (That (a) 1, 2 and 3 (b) 1 and 3 only
is, it is the largest integer which is

less than or equal to x). The value of (c) 1 and 2 only (d) 2 and 3 only
the constant term in the Fourier series [ESE-2017 (EE)]
expansion of g(x) is ___________
8. Given the Fourier series in ( − , )
[GATE-2014-EE-SET-1]
for ( ) x = x cos x, the value of a will
f
0
6. A periodic signal x(t) has a be
trigonometric Fourier series
expansion (a) − 2  (b) 0
2
3
0 
x ( ) t = a +  (a n cosn t b n sin n + 0 ) t 2

−
0
n= 1 ( ) 1 2n
(c) 2 (d) n −
2
If ( ) t = x ( ) t − = − ( x t − / 0 ) . We 1
x
can conclude that [ESE-2017 (EE)]
(a) a are zero for all n and b are 9. The Fourier series expansion of the
n
n
f
x
zero for n even saw-toothed waveform ( ) x = in
( − , ) of period 2 gives the series,
(b) a are zero for all n and b are 1 1 1
n
n
=
zero for n odd 1− + − + ....... ?
3 5
4
(c) a are zero for n even and b are   2
n
n
zero for n odd (a) 2 (b) 4
(d) a are zero for n odd and b are  2 
n
n
zero for n even (c) 16 (d) 4

[GATE-2017 EC SESSION-1] [ESE-2017 (EE)]

7. Fourier series of any periodic signal 10. For the function
x(t) can be obtained if
 − 2, −   0

x

f ( ) x = 

T

I.  x ( ) t dt    2, 0  x 
0
The value of a in the Fourier series
II. Finite number of discontinuities n
within finite time interval t expansion of f(x) is

III. Infinite number of discontinuities

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