  What is the frequency content of temporal logic formulas? That is, when we
monitor a signal against a formula, which frequency bands of the signal are
relevant to the logic and should be preserved, and which can be safely
discarded? This question is relevant whenever signals are filtered or
compressed before being monitored, which is almost always the case for analog
signals. To answer this question, we focus on monitors that measure the
robustness of a signal relative to a specification in Signal Temporal Logic. We
prove that robustness monitors can be modeled using Volterra series. We then
study the Fourier transforms of these Volterra representations, and provide a
method to derive the Fourier transforms of entire formulas. We also make
explicit the measurement process in temporal logic and re-define it on the
basis of distributions to make it compatible with measurements in signal
processing. Experiments illustrate these results. Beyond compression, this work
enables the integration of temporal logic monitoring into common signal
processing toolchains as just another signal processing operation, and enables
a common formalism to study both logical and non-logical operations in the
frequency domain, which we refer to as Logical Signal Processing.
