symop.modes.transfer.gaussian.highpass

Gaussian high-pass transfer function.

This module defines a soft Gaussian high-pass amplitude transfer.

The transfer is constructed as the complement of a Gaussian low-pass,

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

which produces a smooth high-pass characteristic rather than a sharp physical cutoff.

Within the Gaussian-closed formalism, this transfer admits an analytic representation as a constant term plus a single Gaussian atom, so it can be applied in closed form to Gaussian envelopes and Gaussian mixtures.

Classes

GaussianHighpass(w0, sigma_w)

Soft Gaussian high-pass amplitude transfer.

class GaussianHighpass(w0: float, sigma_w: float) → None

Bases: GaussianClosedTransferBase

Soft Gaussian high-pass amplitude transfer.

The transfer is defined by

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

Parameters:

• w0 (float) – Center angular frequency \(\omega_0\).

• sigma_w (float) – Width parameter \(\sigma_\omega\) of the complementary Gaussian low-pass.

_abc_impl = <_abc._abc_data object>

_as_expansion() → GaussianTransferExpansion

Convert this transfer into a Gaussian expansion.

Returns:

Expansion of the form

\[H(\omega) = c_0 + c_1 \exp\left[ -\frac{1}{2} \left( \frac{\omega-\omega_0}{\sigma_\omega} \right)^2 \right],\]

with

\[c_0 = 1, \qquad c_1 = -1.\]

Return type:

GaussianTransferExpansion

Notes

This representation allows the transfer to be applied in closed form to Gaussian-closed envelopes.

_is_protocol = False

_signature_tag: ClassVar[str] = 'gauss_highpass'

sigma_w: float

w0: float

_check_gaussian_highpass: TransferFunction