FOURIER SERIES






PREPARD BY:130200111031 TO 130200111040
GUIDED BY:VIHOL SIR
DEPARTMENT:ELECTRONICS AND COMMUNICATION
CONTENTS
SR NO.
CONTENTS
SLIDE NO.
1
PERIODIC FUNCTION
3-5
2
FOURIER SERIES
6-10
3
HALF RANGE SERIES OF SINE AND COSINE
11-13
4
FOURIER INTEGRAL AND SINE COSINE SERIES
14-17
5
REFRENCE
18
PERIODIC
FUNCTION
f  
0

T
Here period of the waveform T so we can
say that,
f(θ+T)=f(θ)
PERIODIC FUNCTION
A function is called periodic function is defined
all real x & if there is positive number P such
that,
f(x + P) = f(x)
Ex 1) for function f(x)=cos x and f(x)=sin x they
are periodic function and its period 2π.
Ex 2) f(x)=constant function period of that
function every positive number.

FOURIER SERIES
FOURIER SERIES
a0 
f ( x)    (an cos nx  bn sin nx).
2 n1
Any
function
f(x) define in
the interval of
c ≤ x ≤ c+2π
can be
expressed in
the series,
Where a0 an
bn they are
Fourier
coefficient
TO DETERMINE A0, AN, BN, FOLLOWING
INTEGRALS AN PROPERTIES HAVE TO BE USED
TO FIND A0 ,AN ,BN
CHANGE OF INTERVAL

The Fourier series of f(x) in interval c ≤ x ≤ c+2l
HALF RANGE
FOURIER SERIES OF
SINE AND COSINE
HALF RANGE FOURIER SERIES

Cosine series

Sine series
F(X) IN INTERVAL C ≤ X ≤ C+2L HALF RANGE
FOURIER SERIES

Cosine series

Sine series
FOURIER
INTEGRAL
FOURIER INTEGRAL

The representation of f(x) by a Fourier integral
is,
FOURIER COSINE INTEGRAL

If f(x) is an even function then B(w) is zero,

Than Fourier integral reduces is to the Fourier
cosine integral
FOURIER SINE INTEGRAL

Similarly f(x) is odd function than A(w) is zero,

Than Fourier integral reduces is to the Fourier
sine integral
REFRENCES
www.google.com
 Advanced Engineering Mathematics 10th
Edition
