18bme0095_vl2018195000637_ast07

EXPERIMENT 1A TITLE: FOURIER SERIES AIM: TO FIND THE FOURIER SERIES clc; clear all; syms x; f=input('enter the function f(x):'); I=input('enter the interval [a,b]:'); a=I(1);b=I(2); m=input('enter number of harmonics:') L=(b-a)/2; a0=(1/L)*int(f,a,b); Fx=a0/2; for n=1:m figure; an(n)=(1/L)*int(f*cos(n*pi*x/L),a,b); bn(n)=(1/L)*int(f*sin(n*pi*x/L),a,b); Fx=Fx+an(n)*cos(n*pi*x/L)+bn(n)*sin(n*pi*x/L); Fx=vpa(Fx,4); ezplot(Fx,[a,b]) hold on ezplot(f,[a,b]) end title('Fourier series',num2str(n),'Hormonics') legend('Fourier series','given function')

INPUT: enter the function f(x):x-x^2 enter the interval [a,b]:[-pi,pi] enter number of harmonics:3

m=

3

FIGURE 1:

FIGURE 2:

ANALYTIC SOLUTION

enter the function f(x):x-x^2 enter the interval [a,b]:[-pi,pi] enter number of harmonics:3

m=

3

Fx =

(5734161139222659*pi*cos(x))/4503599627370496 + (5734161139222659*pi*sin(x))/9007199254740992 - (1911387046407553*pi^3)/18014398509481984

Fx =

4.0*cos(x) + 2.0*sin(x) - (5734161139222659*pi*cos(2*x))/18014398509481984 (5734161139222659*pi*sin(2*x))/18014398509481984 - 3.289868133710115216672420501709

Fx =

4.0*cos(x) - 1.0*sin(2.0*x) - 1.0*cos(2.0*x) + 2.0*sin(x) + (1911387046407553*pi*cos(3*x))/13510798882111488 + (1911387046407553*pi*sin(3*x))/9007199254740992 - 3.289868133710115216672420501709