sawtooth — Generate a periodic sawtooth waveform with optional peak position.

y = sawtooth(t) generates a sawtooth wave with period 2*pi at the sample times in t, ranging in [-1, 1]. y = sawtooth(t, xmax) controls the peak position with xmax in [0, 1]: xmax = 1 (the default) produces a rising sawtooth, xmax = 0 produces a falling sawtooth, and intermediate values such as xmax = 0.5 produce a triangle wave whose peak is at the centre of each period.

How sawtooth works

• Operates element-wise on scalars, vectors, matrices, and N-D tensors; preserves input shape.
• Reduces input modulo 2*pi so the waveform is periodic across negative and positive sample times.
• Returns -1 at the start of each period and approaches +1 just before the period boundary wraps when xmax = 1.
• Returns a piecewise-linear triangle wave when xmax = 0.5, peaking at 1 at the centre of each period.
• Returns a pure falling ramp when xmax = 0 and a pure rising ramp when xmax = 1.
• Integer and logical inputs are promoted to double precision before evaluation.
• Non-finite sample times (NaN, +Inf, -Inf) propagate as NaN element-wise, matching MATLAB.
• Complex and text inputs are rejected with a builtin-scoped error.
• Rejects xmax values outside [0, 1] and non-scalar xmax arguments.

Examples

Default rising sawtooth over two periods

t = 0:pi/2:4*pi;
y = sawtooth(t)

Expected output:

y = [-1 -0.5 0 0.5 -1 -0.5 0 0.5 -1]

Triangle wave via xmax = 0.5

t = linspace(0, 2*pi, 5);
y = sawtooth(t, 0.5)

Expected output:

y = [-1 0 1 0 -1]

Pure falling sawtooth via xmax = 0

y = sawtooth([0 pi 2*pi], 0)

Expected output:

y = [1 0 1]

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how sawtooth works, line by line, in Rust.

• View sawtooth.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

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