fmax=1e9; %maximun frequency of the signal
fs=60*fmax;
ts=1/fs; %time increment
T=10e-9; %total time signal exists
TA=(-T/2:ts:T/2); %time axis
N=numel(TA)
f=1e9; %frequency of the signal
Y=sin(2*pi*f*TA); %sine function
plot(TA,Y);
This expression for FA is incorrect when N is odd (601)
FA=(-N/2:N/2-1)*fs/N; %frequency axis
The correct expression for N odd is
FA = (-(N-1)/2:(N-1)/2)/N*fs;
A general expression that works for N odd or even is
FA = ((0:N-1) - floor(N/2))/N*fs;
FFT=fft(Y); %fourier transform of the signal
figure;
plot(FA,fftshift(abs(FFT)),'-o');
xlim([-2e9 2e9]);
xline(-1e9);
The small-but-nonzero points around the peaks arise because the discrete-time period of the sampled signal is P = 60, but the number of points in the data is 601, which is not an integer multiple of the period.
