frequency leakage

f = 4.5;
t = linspace(-0.5,0.5,401);
yf = cos(2*pi*f*t);
plot(t,yf);

k=1:9;
c = 0.5*(sinc(f-k)+sinc(f+k));
t = linspace(-0.5,0.5,401);
y = ones(size(t))*sinc(f);
for m = k
    y = y + 2*c(m)*cos(2*pi*m*t);
end
plot(t,yf,t,y,'k','LineWidth',2)

idx = [0 k];
cx = [ sinc(f) c];
stem(idx,abs(cx))