square

Create a vector of 100 equally spaced numbers from $$0$$ to $$3\pi$$. Generate a square wave with a period of $$2\pi$$.

t = linspace(0,3*pi)';
x = square(t);

Plot the square wave and overlay a sine. Normalize the x-axis by $$\pi$$. The generated square wave has a value of $$1$$ for intervals [$\mathit{n}\pi ,\left(\mathit{n}+1\right)\pi$) with even $\mathit{n}$ and a value of $$-1$$ for intervals [$\mathit{n}\pi ,\left(\mathit{n}+1\right)\pi$) with odd $\mathit{n}$. The wave never has a value of $$0$$.

plot(t/pi,x,'.-',t/pi,sin(t))
xlabel('t / \pi')
grid on

Repeat the calculation, but now evaluate square(2*t) at 121 equally spaced numbers between $$-\pi$$ and $$2\pi$$. Change the amplitude to $$1.15$$. Plot the wave and overlay a sine with the same parameters. This new wave is negative at $$t=0$$ and positive at the endpoints, $$-\pi$$ and $$2\pi$$.

t = linspace(-pi,2*pi,121);
x = 1.15*square(2*t);

plot(t/pi,x,'.-',t/pi,1.15*sin(2*t))
xlabel('t / \pi')
grid on

Generate a 30 Hz square wave sampled at 1 kHz for 70 ms. Specify a duty cycle of 37%. Add white Gaussian noise with a variance of 1/100.

t = 0:1/1e3:0.07;
y = square(2*pi*30*t,37)+randn(size(t))/10;

Compute the duty cycle of the wave. Plot the waveform and annotate the duty cycle.

dutycycle(y,t)

ans = 
0.3639