Spectral Approximation

fk = fk + ((((-1)^k).*(4*k+3)*factorial(2*N))/((2^(2*k+1))*factorial(k+1)*factorial(k))).*exp(1i*k*x);

function prob3

clc

clear

% % % x=[-10:0.01:10];

% % % tau=0;tau2=0;

% % % 

% % % ar=ones(1,30);

% for k=

% % % j=1;

% % % for N=0:1:29

% % %     for k=N+1:1:200

% % %         fk = ((2*k+1)/2)*BESSELJ(k+1/2,2*pi)*sin(0.2*pi+k*pi/2);

% % %         tau = tau + (2/(2*k+1))*abs(fk).^2

% % %     end

% % %     ar(j)=tau;

% % %     j=j+1;

% % % end

N=4;

pnf=0;

x=[-2:0.1:2];

original = sin(2*pi*(x+0.1));

for k=-N/2:1:N/2

    fk = ((2*k+1)/2)*BESSELJ(k+1/2,2*pi)*sin(0.2*pi+k*pi/2);

    pnf = pnf + fk*exp(1i*k.*x)

end

%N=5;

%for k=N+1:1:100

%    fk = ((2*k+1)/2)*BESSELJ(k+1/2,2*pi)*sin(0.2*pi+k*pi/2)

%    tau2 = tau2 + (2/(2*k+1))*abs(fk).^2;

%end

plot(x,log10(original-pnf))

% % % N=[0:1:29];

% % % plot(N,log10(ar),'o')

% p=polyfit(x,tau,2)

% semiogy(p)