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# Gaussian

class Gaussian(duration: Union[int, qiskit.circuit.parameterexpression.ParameterExpression], amp: Union[complex, float, qiskit.circuit.parameterexpression.ParameterExpression], sigma: Union[float, qiskit.circuit.parameterexpression.ParameterExpression], angle: Optional[Union[float, qiskit.circuit.parameterexpression.ParameterExpression]] = None, name: Optional[str] = None, limit_amplitude: Optional[bool] = None)

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Bases: object

A lifted and truncated pulse envelope shaped according to the Gaussian function whose mean is centered at the center of the pulse (duration / 2):

$\begin{split}f'(x) &= \exp\Bigl( -\frac12 \frac{{(x - \text{duration}/2)}^2}{\text{sigma}^2} \Bigr)\\ f(x) &= \text{A} \times \frac{f'(x) - f'(-1)}{1-f'(-1)}, \quad 0 \le x < \text{duration}\end{split}$

where $f'(x)$ is the gaussian waveform without lifting or amplitude scaling, and $\text{A} = \text{amp} \times \exp\left(i\times\text{angle}\right)$.

Create new pulse instance.

Parameters

• duration – Pulse length in terms of the sampling period dt.
• amp – The magnitude of the amplitude of the Gaussian envelope. Complex amp support will be deprecated.
• sigma – A measure of how wide or narrow the Gaussian peak is; described mathematically in the class docstring.
• angle – The angle of the complex amplitude of the Gaussian envelope. Default value 0.
• name – Display name for this pulse envelope.
• limit_amplitude – 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.

## Attributes

### alias

Default value: 'Gaussian'