square

Square wave

Syntax

x = square(t)

x = square(t,duty)

Description

x = square(t) generates a square wave with period 2π for the elements of the time array t. square is similar to the sine function but creates a square wave with values of –1 and 1.

x = square(t,duty) generates a square wave with specified duty cycle duty. The duty cycle is the percent of the signal period in which the square wave is positive.

Examples

Generate Square Waves

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

$$x\left(t\right)=\{\begin{array}{ll}{\left(-1\right)}^{t/\pi },& t=k\pi \forall k\in \mathbb{Z}\\ \text{sign}\left(\sin \left(t\right)\right),& t\ne k\pi \forall k\in \mathbb{Z}\end{array}$$

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

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

scatter(t,x,".")
hold on
scatter(t,sin(t),".")
hold off
xlabel("t")
xticks((0:3)*pi)
xticklabels(["0" "\pi" "2\pi" "3\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 $$2\pi$$. The period is now $$\pi$$ because the time values increase twice as fast as before, so the period is half as before.

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

scatter(t,x,".")
hold on
scatter(t,1.15*sin(2*t),".")
hold off
xlabel("t")
xticks((-1:2)*pi)
xticklabels(["-\pi" "0" "\pi" "2\pi"])
grid on

Generate Square Waves with Periods and Frequencies

Since R2026a

This example shows how to create square waves with any oscillating period or frequency.

Generate a square wave with the default period of $2\pi$ seconds during 10 seconds.

$$x\left(t\right)=\{\begin{array}{ll}{\left(-1\right)}^{t/\pi },& t=k\pi \forall k\in \mathbb{Z}\\ \text{sign}\left(\sin \left(t\right)\right),& t\ne k\pi \forall k\in \mathbb{Z}\end{array}$$

Fs = 1000;
tEnd = 10-1/Fs;
t = 1/Fs:1/Fs:tEnd;

x1 = square(t);

Generate a square wave that oscillates with a period $T$ of 2.5 seconds.

$$x_T\left(t\right)=x\left(\frac{2\pi }{T}t\right)$$

T = 2.5;
x2 = square(2*pi/T*t);

Generate a square wave that oscillates at a frequency $F$ of 2 Hz.

$$x_F\left(t\right)=x\left(2\pi \text{Ft}\right)$$

F = 2;
x3 = square(2*pi*F*t);

Compare the square waves. The waves oscillate at the specified period or frequency specification. x1, x2, and x3 oscillates every 6.28, 2.5, and 0.5 seconds, respectively.

strips([x1 x2 x3],tEnd,Fs)
xlabel("Time (seconds)")
yticklabels(["x3" "x2" "x1"])

Duty Cycle of Square Wave

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

Input Arguments

t — Time array

vector | matrix | N-D array

Time array, specified as a vector, matrix, or N-D array. square operates along the first array dimension of t with size greater than 1.

Data Types: single | double

duty — Duty cycle

50 (default) | real scalar from 0 to 100

Duty cycle, specified as a real scalar from 0 to 100.

Data Types: single | double

Output Arguments

x — Square wave

vector | matrix | N-D array

Square wave, returned as a vector, matrix, or N-D array.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced before R2006a

R2024a: square supports GPU code generation

The square function supports code generation for graphical processing units (GPUs). You must have MATLAB^® Coder™ and GPU Coder™ to generate CUDA^® code.