symop.modes.transfer.gaussian.lowpass¶

Gaussian low-pass transfer function.

This module defines a Gaussian low-pass amplitude transfer.

The transfer is given by

\[H(\omega) = \exp\left[ -\frac{1}{2} \left( \frac{\omega - \omega_0}{\sigma_\omega} \right)^2 \right].\]

It transmits frequencies near \(\omega_0\) and suppresses components away from the center with bandwidth \(\sigma_\omega\).

Within the Gaussian-closed formalism, this transfer admits an analytic representation and can be applied in closed form to Gaussian envelopes.

Classes

Gaussian low-pass amplitude transfer.

class GaussianLowpass(w0: float, sigma_w: float) → None¶

Gaussian low-pass amplitude transfer.

\[H(\omega) = \exp\left[ -\frac{1}{2} \left( \frac{\omega-\omega_0}{\sigma_\omega} \right)^2 \right].\]

Parameters:

Convert this transfer into a Gaussian expansion.

Returns:

Expansion consisting of a single Gaussian atom:

\[H(\omega) = \exp\left[ -\frac{1}{2} \left( \frac{\omega-\omega_0}{\sigma_\omega} \right)^2 \right].\]

Return type:

GaussianTransferExpansion

Notes

This representation enables closed-form propagation of Gaussian envelopes and Gaussian mixtures.