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This paper presents a high-speed periodic signal acquisition technique using incoherent sub-sampling and back-end signal reconstruction algorithms. The signal reconstruction algorithms employ a frequency domain analysis for frequency estimation, and suppression of jitter-induced sampling noise. By switching the sampling rate of a digitizer, the analog frequency value of the sampled signal can be recovered. The proposed signal reconstruction uses incoherent sub-sampling to reduce hardware complexity. The results of simulation and hardware experiments indicate that the proposed signal reconstruction algorithms are able to reconstruct multi-tone high-speed periodic signals in the discrete time domain. The new signal acquisition technique simplifies signal acquisition hardware for testing and characterization of high-speed analog and digital signals.