hello
first a comment : not sure why your frequencies are all normalized by fs...i changed that in my code below
you need to perform a fft to see the frequencies of your signal
notice that you need a frequency resolution of 0.01 Hz to separate the components of xp2
the length of the signal is computed with that freq resolution of 0.01 Hz in mind
FFT plot
clc
clearvars
fs = 200; % sampling freq in Hz (so Nyquist freq = 100 Hz > your signal highest frequency)
dt = 1/fs; % seconds
df = 0.01; % freq resolution (Hz)
samples = ceil(fs/df); % make sure the signal is long enough to get the required freq resolution (fft freq points are separated by df = fs/nfft , here nfft = samples)
t=(0:samples-1)*dt;
xp1=sin(2*pi*(50)*t);
xp2=sin(2*pi*(49.98)*t)+sin(2*pi*(50.01)*t)+sin(2*pi*(49.99)*t)+sin(2*pi*(50.01)*t);
% FFT plot
[f1,fft_spectrum1] = do_fft(t,xp1);
[f2,fft_spectrum2] = do_fft(t,xp2);
figure(1)
plot(f1,fft_spectrum1,'*--',f2,fft_spectrum2,'*--')
title('FFT Spectrum')
ylabel('|X(f)|')
xlabel('Frequency[hz]')
legend('xp1','xp2');
xlim([49.9 50.1]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [freq_vector,fft_spectrum] = do_fft(time,data)
time = time(:);
data = data(:);
dt = mean(diff(time));
Fs = 1/dt;
nfft = length(data); % maximise freq resolution => nfft equals signal length
%% use windowing or not at your conveniance
% no window
fft_spectrum = abs(fft(data))*2/nfft;
% % hanning window
% window = hanning(nfft);
% window = window(:);
% fft_spectrum = abs(fft(data.*window))*4/nfft;
% one sidded fft spectrum % Select first half
if rem(nfft,2) % nfft odd
select = (1:(nfft+1)/2)';
else
select = (1:nfft/2+1)';
end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end
