In reality, this function corresponds to a two-dimensional convolution between the scattering function
and the joint probability distribution of synchronization errors in time and frequency.
In the WSSUS case it can be shown that the scattering function
of the channel is proportional to the joint delay Doppler pdf .
the measured scattering law [S.sub.R](Q, [omega]) reduces to a time average of the intermediate scattering function
Rigid bodies are characterized by a time-invariant scattering function
h(r), while the distance R to a reference point is allowed to vary with time according to target motion.
Isotope incoherence implies scattering that is both Q-independent (so the [lambda]-dependence of the scattering function
can be ignored).
The scattered intensity as a function of scattering angle and time-of-flight, I (2[theta], t), is converted to a weighted scattering function
, S([[vector].Q], [omega]), or to a related quantity such as the generalized density of states.
For an assembly of monodisperse spheres of radius and volume [V.sub.s], the scattering function
is given by (28)
Because the instruments had different bandwidths, the measured irradiances were convolved to common bandwidths by using both triangular and Gaussian slit scattering functions
and the filter transmittances of the filter-based instruments.
In this representation, M(s,t) can be interpreted as the filtered projection of the Wigner function, with the scattering operator exp(isr) as the filter, modified by the scattering functions
He discusses the theory of uniform waveguides, the theory of transmission lines, wave variables and the scattering matrix, signal analysis of multiport networks, mode wave variables and mixed mode scattering matrix of differential networks, noise wave variables and the scattering matrix, analyzing the noise of multiport networks, and scattering functions
in the non-linear modeling of microwave devices.
Chapter 5 explains the "scattering functions
" black-box frequency domain behavioral modeling technique.
Volume scattering functions
for selected ocean waters.