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High speed signal acquisition and characterization contributes a significant amount to the total test cost of the finished product in modern high speed systems. Incoherent under-sampling allows robust and low cost signal acquisition without requiring a prior accurate knowledge of signal period. In this paper we propose a frequency estimation and signal reconstruction technique for incoherently sub-sampled periodic waveforms that is based on a time domain cost function. The method reduces the per iteration cost by a factor of log N compared to frequency domain cost functions. The proposed method estimates the period of a test signal with much fewer samples without degradation of accuracy.