Periodic Signal Compressors

We propose and study a compression scheme for lossless causal compression of periodic signals. Our compressors produce scalar-valued signals from periodic vector-valued input signals by taking the inner product with another periodic signal. In the simplest case, this amounts to switching through the different components of the input signal with a periodic switch. We refer to such compressors as periodic compressors. In both continuous and discrete time, we investigate conditions under which the original signal can be reconstructed from the compressed signal, i.e., we characterize lossless periodic compressors. Our conditions amount to certain non-resonances between the periods of our two signals. Finally, we insert our periodic compressor into a feedback loop and investigate how this affects the stability properties of a control system.