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

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 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

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