# MATLAB Plot of FT(Cos) Displays Weird Impulse

It is known that: $$\mathcal{F}\{\cos(2\pi t)\}=\frac{\delta(f-1)+\delta(f+1)}{2}$$ However, on MATLAB, I used F=fftshift(fft(x))/N; to obtain the FT of $$\cos(2\pi t)$$ and I obtained the following:

My question is why does each $$\delta$$ appear to be made up of two thin close parallel lines. Note that I have used $$1024$$ sample points and constructed $$f$$ a vector from $$-51.2$$Hz to $$51.2$$Hz and $$t$$ a vector from $$-5$$ to $$5$$.