filters - LTI filters for bivariate signals

Unitary Filter

class bispy.filters.UnitaryFilter(N, mu, alpha, phi, dt=1.0)[source]

Unitary filter for bivariate signals. The Unitary filtering relation reads in the QFT spectral domain:

Y(nu) = exp(mu(nu)*alpha(nu) / 2)*X(nu)exp(1j*phi(nu))

where phi is phase delay of the filter, mu its axis and alpha is the birefringence angle.

Parameters:
Nint

length of the filter

muarray_type (quaternion)

birefringence axis quaternion array (should be of size N and of dtype quaternion).

alphaarray_type

birefringence angle array (should be of size N). If alpha is a float, then alpha is assumed constant throughout frequencies.

phiarray_type or float

phase delay array (should be of size N). If phi is a float, then a constant phase delay is assumed throughout frequencies.

dtfloat (optional)

time sampling step (default 1)

Attributes:
Nint

length of the filter

farray_type

sampled frequencies

dtfloat

time sampling step (default 1)

mu, alpha, phiarray_types

filter parameters

Methods

output(x)

returns the output of the filter given an input signal x

output(x)[source]

returns the output of the filter given an input signal x

HermitianFilter

class bispy.filters.HermitianFilter(N, K, eta, mu, dt=1.0)[source]

Hermitian filter for bivariate signals. The Hermitian filtering relations reads in the QFT spectral domain:

Y(nu) = K(nu)*[X(nu) - eta(nu)*mu(nu)*X(nu)*qj]

where K is the homogeneous gain of the filter, eta is the polarizing power and mu the axis of the filter.

Parameters:
Nint

length of the filter

Karray_type or float

homogeneous gain array (should be of size N). If K is a float, then a constant gain is assumed throughout frequencies.

etaarray_type or float

polarizing power array (should be of size N). If eta is a float, then a constant polarizing is assumed throughout frequencies.

muarray_type (quaternion) or quaternion

diattenuation axis quaternion array (should be of size N and of dtype quaternion).

dtfloat (optional)

time sampling step (default 1)

Attributes:
Nint

length of the filter

farray_type

sampled frequencies

dtfloat

time sampling step (default 1)

K, eta, muarray_types

filter parameters

Methods

output(x)

returns the output of the filter given an input signal x

output(x)[source]

returns the output of the filter given an input signal x