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In this paper, jitter analysis algorithms for characterizing timing jitter of multi-Gbps pseudo-random bit sequences (PRBSs) are presented. For signal acquisition, incoherent sub-sampling is employed to increase the effective sampling rate of a digitizer and to simplify its signal acquisition architecture by removing the need for timing synchronization circuits. As a substitute for these circuits, algorithms for signal clock recovery (CR) and waveform reconstruction from the acquired data are developed in this research. The algorithms utilize peak identification of the sampled signal spectrum and the sparsity of the reconstructed waveform in the frequency domain as decision making criteria for accurate signal reconstruction. The jitter value of such a reconstructed waveform is quantified with the use of a wavelet based denoising method to generate a self-reference signal against which zero-crossing times are compared to generate jitter statistics. In addition, the data dependent jitter components can be differentiated from the original jitter by analyzing zero-crossing discrepancies of the self-reference signal.