On Lossless Causal Compression of Periodic Signals

We present and study a scheme for lossless causal compression of periodic real-valued signals. In particular, our technique compresses a vector-valued signal to a scalar-valued signal by mixing it with another periodic signal. The conditions for being able to reconstruct the original signal then amount to certain non-resonances between the periods of the two signals. The proposed compression scheme turns out to implicitly be inherent to communication networks with round-robin scheduling and digital photography with active pixel sensors.