1. FOURIER SERIES PREPARD BY:- 130200111031 TO 130200111040 GUIDED BY:-
VIHOL SIR
DEPARTMENT:-
ELECTRONICS AND COMMUNICATION

2. 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

3. Periodic function

4. Here period of the waveform T so we can say that,
f(θ+T)=f(θ)

5. 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.

6. Fourier series

7. FOURIER SERIES
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

8. To determine a0, an, bn, following integrals an properties have to be used

9. To find a0 ,an ,bn

10. Change of interval
The Fourier series of f(x) in interval c ≤ x ≤ c+2l

11. Half range FOURIER SERIES OF SINE AND COSINE

12. Half range Fourier series
Cosine series
Sine series

13. f(x) in interval c ≤ x ≤ c+2l half range Fourier series
Cosine series
Sine series

14. Fourier integral

15. Fourier integral
The representation of f(x) by a Fourier integral is,

16. 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

17. Fourier sine integral
Similarly f(x) is odd function than A(w) is zero,
Than Fourier integral reduces is to the Fourier sine integral

18. REFRENCES
Advanced Engineering Mathematics 10th Edition

19. THANK YOU