Logical Signal Processing: a Fourier Analysis of Temporal Logic

@article{Basnet2020LogicalSP,
  title={Logical Signal Processing: a Fourier Analysis of Temporal Logic},
  author={Niraj Basnet and Houssam Abbas},
  journal={ArXiv},
  year={2020},
  volume={abs/2009.08090}
}
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… 
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