`scipy.signal._waveforms:sawtooth`

source: /scipy/signal/_waveforms.py :16

Signature

def sawtooth ( t , width = 1 )

Summary

Return a periodic sawtooth or triangle waveform.

Extended Summary

The sawtooth waveform has a period 2*pi, rises from -1 to 1 on the interval 0 to width*2*pi, then drops from 1 to -1 on the interval width*2*pi to 2*pi. width must be in the interval [0, 1].

Note that this is not band-limited. It produces an infinite number of harmonics, which are aliased back and forth across the frequency spectrum.

Parameters

t : array_like: Time.
width : array_like, optional: Width of the rising ramp as a proportion of the total cycle. Default is 1, producing a rising ramp, while 0 produces a falling ramp. width = 0.5 produces a triangle wave. If an array, causes wave shape to change over time, and must be the same length as t.

Returns

y : ndarray: Output array containing the sawtooth waveform.

Notes

Array API Standard Support

sawtooth has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

A 5 Hz waveform sampled at 500 Hz for 1 second:

import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
t = np.linspace(0, 1, 500)

✓

plt.plot(t, signal.sawtooth(2 * np.pi * 5 * t))

✗

Aliases

scipy.signal.sawtooth