signalfft

Fs = 10000;           % Sampling frequency
T = 1/Fs;             % Sampling period
L = 10000;            % Length of signal
t = (0:L-1)*T;        % Time vector

simples = zeros(size(t,2),3);
simples(:,1) = 0.7*sin(2*pi*50*t);
simples(:,2) = sin(2*pi*120*t);
simples(:,3) = 2*sin(2*pi*250*t);

S = (simples(:,1) + simples(:,2) + simples(:,3)).';     %Source signal

plot(1000*t(1:250),simples(1:250))
title('Source Signal')
xlabel('t (milliseconds)')
ylabel('S(t)')

X = S + 2*randn(size(t));       %Source signla + Noise

plot(1000*t(1:500),simples(1:500,:))
title('Signal + Noise')
xlabel('t (milliseconds)')
ylabel('X(t)')

Y = fft(X);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

f = Fs*(0:(L/2))/L;
plot(f(1:500),P1(1:500))
title('Single-Sided Amplitude Spectrum of X(t)')
xlabel('f (Hz)')
ylabel('|P1(f)|')