  We explore the effect of sampling rates when measuring data given by $Mf$ for
special operators $M$ arising in Thermoacoustic Tomography. We start with
sampling requirements on $Mf$ given $f$ satisfying certain conditions. After
this we discuss the resolution limit on $f$ posed by the sampling rate of $Mf$
without assuming any conditions on these sampling rates. Next we discuss
aliasing artifacts when $Mf$ is known to be under sampled in one or more of its
variables. Finally, we discuss averaging of measurement data and resulting
aliasing and artifacts, along with a scheme for anti-aliasing.
