qiskit.pulse.library.Sawtooth

Sawtooth(duration, amp, phase, freq=None, angle=0.0, name=None, limit_amplitude=None)

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 (Union[int, ParameterExpression]) – Pulse length in terms of the sampling period dt.

• amp (Union[float, ParameterExpression]) – The magnitude of the amplitude of the sawtooth wave. Wave range is [-amp,`amp`].

• phase (Union[float, ParameterExpression]) – The phase of the sawtooth wave (note that this is not equivalent to the angle of the complex amplitude)

• freq (Optional[Union[float, ParameterExpression]]) – 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 (Optional[Union[float, ParameterExpression]]) – The angle in radians of the complex phase factor uniformly scaling the pulse. Default value 0.

• name (Optional[str]) – Display name for this pulse envelope.

• limit_amplitude (Optional[bool]) – 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