---
title: Sawtooth (v1.1)
description: API reference for qiskit.pulse.library.Sawtooth in qiskit v1.1
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/1.1/qiskit.pulse.library.Sawtooth_class.rst
---

# qiskit.pulse.library.Sawtooth

`qiskit.pulse.library.Sawtooth(duration, amp, phase, freq=None, angle=0.0, name=None, limit_amplitude=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/pulse/library/symbolic_pulses.py#L1620-L1685)

A sawtooth pulse.

The envelope of the pulse is given by:

$$
f(x) = 2\text{A}\left[g\left(x\right)-
\lfloor g\left(x\right)+\frac{1}{2}\rfloor\right]
$$

where $\text{A} = \text{amp} \times\exp\left(i\times\text{angle}\right)$, $g\left(x\right)=x\times\text{freq}+\frac{\text{phase}}{2\pi}$, and $\lfloor ...\rfloor$ is the floor operation.

**Parameters**

- **duration** ([*int*](https://docs.python.org/3/library/functions.html#int)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression")) – Pulse length in terms of the sampling period dt.
- **amp** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression")) – The magnitude of the amplitude of the sawtooth wave. Wave range is \[-amp,\`amp\`].
- **phase** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression")) – The phase of the sawtooth wave (note that this is not equivalent to the angle of the complex amplitude)
- **freq** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression") *| None*) – The frequency of the sawtooth wave, in terms of 1 over sampling period. If not provided defaults to a single cycle (i.e :math:’frac\{1}\{text\{duration}}’). The frequency is limited to the range $\left(0,0.5\right]$ (the Nyquist frequency).
- **angle** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression") *| None*) – The angle in radians of the complex phase factor uniformly scaling the pulse. Default value 0.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *| None*) – Display name for this pulse envelope.
- **limit\_amplitude** ([*bool*](https://docs.python.org/3/library/functions.html#bool) *| None*) – If `True`, then limit the amplitude of the waveform to 1. The default is `True` and the amplitude is constrained to 1.

**Returns**

ScalableSymbolicPulse instance.

**Return type**

ScalableSymbolicPulse