  The time-frequency integrals and the two-dimensional stationary phase method
are applied to study the electromagnetic waves radiated by moving modulated
sources in dispersive media. We show that such unified approach leads to
explicit expressions for the field amplitudes and simple relations for the
field eigenfrequencies and the retardation time that become the coupled
variables. The main features of the technique are illustrated by examples of
the moving source fields in the plasma and the Cherenkov radiation. It is
emphasized that the deeper insight to the wave effects in dispersive case
already requires the explicit formulation of the dispersive material model. As
the advanced application we have considered the Doppler frequency shift in a
complex single-resonant dispersive metamaterial (Lorenz) model where in some
frequency ranges the negativity of the real part of the refraction index can be
reached. We have demonstrated that in dispersive case the Doppler frequency
shift acquires a nonlinear dependence on the modulating frequency of the
radiated particle. The detailed frequency dependence of such a shift and
spectral behavior of phase and group velocities (that have the opposite
directions) are studied numerically.
