Matlab code demonstrating use of fft (Fast Fourier Transform)

Question

I posted the following Matlab script in response to a question on Signal Processing. Here is the questions with my answer.

I am looking for comments on how to make this code more instructive for the questioner. Any other code review comments are also welcomed.

fs = 2^10; %sample frequency in Hz
T = 1/fs; %sample period in s
L = 2^20; %signal length
t = (0:L-1) * T; %time vector
A1 = 0.2; %amplitude of x1 (first signal)
A2 = 1.0; %amplitude of x2 (second signal)
f1 = 1; %frequency of x1
f2 = 50; %frequency of x2
x1 = A1*sin(2*pi*f1 * t); %sinusoid 1
x2 = A2*sin(2*pi*f2 * t); %sinusoid 2
y = x1 + x2;
%Plot signal
figure;
set(gcf,'Color','w'); %Make the figure background white
plot(fs*t(1:100), y(1:100));
set(gca,'Box','off'); %Axes on left and bottom only
str = sprintf('Signal with %dHz and %dHz components',f1,f2);
title(str);
xlabel('time (milliseconds)');
ylabel('Amplitude');
%Calculate spectrum
Y = fft(y)/L;
ampY = 2*abs(Y(1:L/2+1));
f = fs/2*linspace(0,1,L/2+1);
i = L/fs * (max(f1,f2)) + 1; %show only part of the spectrum
%Plot spectrum.
figure;
set(gcf,'Color','w'); %Make the figure background white
plot(f(1:i), ampY(1:i));
set(gca,'Box','off'); %Axes on left and bottom only
title('Single-Sided Amplitude Spectrum of y(t)');
xlabel('Frequency (Hz)');
ylabel('|Y(f)|');

• user22171: Y = fft(y)/L Why do you divide by L?

Answer 1

Your time vector definition is defined a bit strange, I would go for the more standardized form of

startpoint:stepsize:endpoint

endpoint = T*(L-1) % is this correct?
0:T:endpoint

Besides this you could perhaps add some comments in the calculate spectrum section, but for the rest it looks quite clear.