sawtooth

R2026b

Sawtooth or triangle wave

Syntax

x = sawtooth(t)

x = sawtooth(t,xmax)

Description

x = sawtooth(t) generates a sawtooth wave with period 2π for the elements of the time array t. sawtooth is similar to the sine function but creates a sawtooth wave with peaks of –1 and 1. The sawtooth wave is defined to be –1 at multiples of 2π and to increase linearly with time with a slope of 1/π at all other times.

x = sawtooth(t,xmax) generates a modified triangle wave with the maximum location at each period controlled by xmax. Set xmax to 0.5 to generate a standard triangle wave.

Examples

50 Hz Sawtooth Wave

Generate 10 periods of a sawtooth wave with a fundamental frequency of 50 Hz. The sample rate is 1 kHz.

T = 10*(1/50);

fs = 1000;
t = 0:1/fs:T-1/fs;

x = sawtooth(2*pi*50*t);

plot(t,x)
grid on

Plot the power spectrum of the wave.

pspectrum(x,fs,'Leakage',0.91)

50 Hz Triangle Wave

Generate 10 periods of a triangle wave with a fundamental frequency of 50 Hz. The sample rate is 1 kHz.

T = 10*(1/50);

fs = 1000;
t = 0:1/fs:T-1/fs;

x = sawtooth(2*pi*50*t,1/2);

plot(t,x)
grid on

Plot the power spectrum of the wave.

pspectrum(x,fs,'Leakage',0.91)

Input Arguments

t — Time array

vector | matrix | N-D array

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

Note

Depending on the values specified in t, the wave might not reach the exact peaks of -1 and 1.

Data Types: double

xmax — Wave maximum location

1 (default) | scalar between 0 and 1

Wave maximum location, specified as a scalar between 0 and 1. xmax determines the point between 0 and 2π at which the wave reaches its maximum. The function increases from –1 to 1 on the interval 0 to 2π × xmax, then decreases linearly from 1 to –1 on the interval 2π × xmax to 2π. The shape then repeats with a period of 2π.

Example: xmax = 0.5 specifies a standard triangle wave, symmetric about time π.

Data Types: double

Output Arguments

x — Sawtooth wave

vector | matrix | N-D array

Sawtooth 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™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The sawtooth function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a

R2026b: Use thread-based environments

You can use sawtooth in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.