Velocity Aliasing
Aliasing of data
occurs when the sampling rate of an observed phenomenon is
too low to adequately resolve variations in the phenomenon.
Example:
Suppose the true variation of a high frequency physical
phenomenon is described by the blue curve in the figure
below. And suppose we sample that phenomenon (i.e. make
measurements of it) at a lower frequency indicated by the
orange boxes. This frequency of sampling is not enough
to resolve the true variations in the blue curve.

If we fit a new curve to our measurements we may think we
are seeing variation at the frequency shown by the pink
curve. This is an artifact our inadequate sampling
rate.

Another classic aliasing example can be seen in the
so-called wagon
wheel effect making car wheels appear to spin
backwards at times, or my personal favorite, western movies
where the stage coach wheels appear to be rotating
backwards (at roughly 30 and 53 seconds into this Youtube
clip). This is because the sampling rate, i.e.,
the number of picture frames per second is not enough to
resolve the forward movement of the spokes--they look like
they're turning backwards.
A somewhat different variation of aliasing can be seen
here.
Here is a link to a film of helicopter blades that appear to
accelerate, then turn
backwards due to aliasing. The apparent
backwards turning is due to the camera frames per second not
being adequate to resolve the true motion of the blades.
The sampling rate for a
NEXRAD is the pulse repetition frequency (PRF) (see Doppler
formulas ). When the sampling rate is not great
enough to resolve a certain frequency shift, this limits the
velocities that can be resolved. This limit is called
the maximum unambiguous
velocity. Velocities that are greater than
the maximum unambiguous velocity are said to be aliased (also see velocity
aliasing), because they cannot be distinguished from
lower velocities of opposite sign.
By convention, incoming motions are
defined negative, and outgoing motions are positive.
The doppler radar measures the shift in frequency due to
incoming or outgoing radial motion of a target.
This frequency shift can be translated into a phase shift, that is, a
shift in position of a reference point on a wave with
respect to an arbitrary location on the graph, such as the
zero point.
The phase is the relative position of the wave form with
respect to some starting point. Waves that are in
phase have the same y-value at the x=0 point and other
points along the wave.
The following example depicts how phase shifts
occur. For example, a phase shift of 30 degrees and
-30 degrees yields the following curves:

At phase shifts of + or - 170 degrees we see that the
phase-shifted curves are near each other:

At + or - 180 degrees the two curves are on top of each
other:
Velocity aliasing occurs when the phase
shift is 180 degrees or more, which occurs at or above the maximum unambiguous velocity.
At these velocities, the phase shift is
such that the radar cannot distinguish between the velocity
above maximum unambiguous velocity that has a phase shift of
above 180 degrees, and that of a lower phase shift of
opposite sign. For example, an aliased velocity with a
phase shift of 210 degrees (180 + 30 degrees) is not
distinguishable from an unaliased velocity with a
phase shift of -150 degrees (-180 + 30 degrees):
