spectral - Spectral analysis routines¶
Quaternion PSD¶
- class bispy.spectral.quaternionPSD(N, S0x, Phix, mux, dt=1)[source]¶
Quaternion Power Spectral Density constructor of the form: Gamma_xx(nu) = S_0x(nu)*[1 + Phi_x(nu)*mu_x(nu)]
where S_0x is the PSD of the signal x, Phi_x(nu) is the degree of polarization of the signal and mu_x is the polarization axis.
- Parameters:
- Nint
size of the frequencies array
- S0xarray_type
PSD array of the signal
- Phixarray_type
degree of polarization array
- muxarray_type (quaternion)
polarization axis array
- dtfloat (optional)
time sampling size step
- Attributes:
- S0, S1, S2, S3array_type
Stokes Parameters array
- densityarray_type
quaternion PSD
- farray_type
sampled frequencies array
- Phiarray_type
degree of polarization
- muarray_type
polarization axis
Methods
plot([single_sided])Displays the quaternion PSD
plotStokes([single_sided])Displays Stokes Parameters S0, S1, S2, S3
Periodogram¶
- class bispy.spectral.Periodogram(t, x, computeFlag=True)[source]¶
Compute the periodogram of bivariate signals taken as (1, i)-quaternion valued signals.
- Parameters:
- tarray_type
time samples array
- xarray_type
input signal array (has to be of quaternion dtype)
- computebool, optional
Flag activating computation of the estimate. Default is true. If False one has to run the compute() method manually.
- Attributes:
- tarray_type
time samples array
- signalarray_type
input signal array
- farray_type
sampled frequencies array
- densityarray_type
spectral density quaternion array
- S0, S1, S2, S3array_type
Stokes parameters, non-normalized [w.r.t. S0]
- S1n, S2n, S3narray_type
normalized Stokes parameters [w.r.t. S0] using the tolerance factor tol. They are not computed by default. See normalize.
- Phiarray_type
Degree of polarization. Not computed by default; See normalize.
Methods
compute()Low-level function.
normalize([tol])Normalize Stokes parameters wrt S0.
plot()Generic plot of spectral estimates
- normalize(tol=0.0)[source]¶
Normalize Stokes parameters wrt S0. In addition, compute the degree of polarization Phi.
- Parameters:
- tolfloat, optional
tolerance factor used in Stokes parameters normalization. Default is 0.0
- Returns:
- self.S1n, self.S2n, self.S3narray_type
normalized Stokes parameters
- self.Phiarray_type
degree of polarization
See also
utils.normalizeStokes
Multitaper¶
- class bispy.spectral.Multitaper(t, x, bw=2.5, computeFlag=True)[source]¶
Compute a multitaper spectral estimate of the spectrum of bivariate signals taken as (1, i)-quaternion valued signals. The data tapers are chosen as discrete-prolate spheroidal sequences (dpss or Slepian tapers).
- Parameters:
- tarray_type
time samples array
- xarray_type
input signal array (has to be of quaternion dtype)
- bwfloat, optional
spectral bandwidth. Default is 2.5
- computeFlagbool, optional
Flag activating computation of the estimate. Default is true. If False one has to run the compute() method manually.
- Attributes:
- tarray_type
time samples array
- signalarray_type
input signal array
- farray_type
sampled frequencies array
- densitiesarray_type
spectral density quaternion array for each taper
- densityarray_type
spectral density quaternion array
- dpssarray_type
data tapers used
- S0, S1, S2, S3array_type
Stokes parameters, non-normalized [w.r.t. S0]
- S1n, S2n, S3narray_type
normalized Stokes parameters [w.r.t. S0] using the tolerance factor tol. They are not computed by default. See normalize.
- Phiarray_type
Degree of polarization. Not computed by default; See normalize.
Methods
compute([bw])Low-level method that computes the multitaper estimate
normalize([tol])Normalize Stokes parameters wrt S0.
plot()Generic plot of spectral estimates
- normalize(tol=0.0)[source]¶
Normalize Stokes parameters wrt S0. In addition, compute the degree of polarization Phi.
- Parameters:
- tolfloat, optional
tolerance factor used in Stokes parameters normalization. Default is 0.0
- Returns:
- self.S1n, self.S2n, self.S3narray_type
normalized Stokes parameters
- self.Phiarray_type
degree of polarization
See also
utils.normalizeStokes