fs=5120;% sampling frequency
ts=1/fs;% sampling interval
N=1024;% number of samples
t=0:ts:(N-1)*ts;% symbol duration
df=fs/N;% frequency resolution = 5
sigma=0.01;
for i=1:64
    f(i)=5*i;% hopping set, that is, hopping frequencies (f1=5Hz,f2=10Hz,...,f64=320Hz)
    s(i,:)=cos(2*pi*f(i)*t+rand*2*pi);% each row of the matrix 's' is a tone with different frequency
end
% plot(t,s(1,:),t,s(2,:),t,s(6,:))
r=s(1,:)+s(6,:)+s(20,:)+sigma*randn(1,N);
R=fft(r,N)/fs;% FFT detection
RR=(abs(R)).^2;% energy at each frequency
RRR=fftshift(RR);
% freq=[0:df:fs-df]-fs/2;% frequency axis
% figure(1)
% stem(freq,RR,'.')
% axis([-inf inf 0 0.12]);
% figure(2)
% freq_half=[0:df:fs/2-df];
% stem(freq_half,RR(1:length(RR)/2),'.')
% axis([-inf inf 0 0.12]);
% figure(3)
% stem(freq,RRR,'.')
% axis([-inf inf 0 0.12]);

figure(1)
stem(RR,'.')
figure(2)
stem(RR,'.')
figure(3)
stem(RRR,'.')