The classical approach to sampling time-invariant spatial fields uses static sensors distributed over space. We study a new approach involving mobile sensors that move through space measuring the field values along their paths. A single moving sensor can take measurements over a wide spatial area thus acting as a substitute for a potentially large number of static sensors. A moving sensor encounters the spatial field in its path in the form of a time-domain signal. Hence a time-domain anti-aliasing filter can be employed at the mobile sensor to limit the amount of out-of-band noise prior to sampling. We analytically quantify the advantage of mobile sensing over static sensing in rejecting out-of-band noise. We also demonstrate via simulations the improvement in reconstruction accuracy that can be obtained using mobile sensors and filtering in a temperature measurement problem.