Fs = 120; % Sampling frequency, 50 Hz
t = 0:1/Fs:1; % Time vector from 0 to 1 second
% Create the signal according to the given intervals
step = zeros(size(t));
step(t >= 0 & t < 0.05) = 1;
step(t >= 0.05 & t < 0.021) = -1;
step(t >= 0.021 & t < 0.041) = 1;
step(t >= 0.041 & t < 0.061) = -1;
step(t >= 0.061 & t < 0.1) = -1;
step(t >= 0.1 & t < 0.2) = 1;
step(t >= 0.2 & t < 0.3) = -1;
step(t >= 0.3 & t < 0.35) = 1;
step(t >= 0.35 & t < 0.38) = 1;
step(t >= 0.38& t < 0.4) = 1;
step(t >= 0.4 & t < 0.5) = -1;
step(t >= 0.5 & t < 0.55) = -1;
step(t >= 0.55 & t < 0.6) = -1;
step(t >= 0.6 & t < 0.8) = -1;
step(t >= 0.8 & t < 0.85) = 1;
step(t >= 0.85 & t < 0.9) = 1;
step(t >= 0.9 & t <= 1) = 1;
% Plot the signal in the time domain using stairs
figure;
subplot(3,2,1)
stairs(t, step);
ylim([-1.5 1.5])
xlabel('Time (s)');
ylabel('Amplitude');
title('Signal in Continuous Time Domain');
% Compute the FFT of the signal
n = length(t);
f = Fs*(0:(n/2))/n; % Frequency vector
Y = fft(step)/n; % Normalized FFT
Y = Y(1:n/2+1); % Single-sided spectrum
% Plot the stem-like FFT of the signal
%figure;
subplot(3,2,2)
stem(f, abs(Y));
xlabel('Frequency (Hz)');
ylabel('Magnitude');
title('FFT of Signal');
This is (as I'm sure you've noticed) a very inefficient way to generate a varying frequency square wave -- it's essentially a hopeless task from just the info you've provided; you need a definition of what the frequency signal actually is for each example which one would presume is in the text or homework problem definition besides just the figure...
