The objective of this research is to develop and demonstrate low-complexity, robust, frequency-scalable, wide-band waveform acquisition techniques for testing high speed com- munication systems. High resolution waveform capture is a versatile testing tool that enables flexible test strategies. However, waveform capture at high data rates requires costly hardware because the increased bandwidth of the signal waveform leads to an increase in the sampling rate requirement, cost of front-end components, and sensitivity to phase errors in traditional (source) synchronous Nyquist-rate tester architectures. The hardware cost and complexity of wide-band waveform acquisition systems can, however, be significantly reduced by using (trigger-free) incoherent undersampling to achieve reduced sampling rates and robustness to phase errors in signal paths. Reducing the hardware cost of such a system using incoherent undersampling requires increased signal processing at the back end. This research proposes computationally-efficient, time-domain waveform reconstruction algorithms to improve both performance, and scope of existing incoherent undersampling- based test instrumentation. Supporting hardware architectures are developed to extend the application of incoherent undersampling-based waveform acquisition techniques to linearity testing of high-speed radio-frequency components without any synchronization between the signals involved, and to the acquisition of wide-band signals beyond the track-and-hold bandwidth barrier of the traditional incoherent undersampling architectures, using multi-channel bandwidth interleaving. The bandwidth is extended in a source-incoherent framework by using mixers to down convert high-frequency signal components to base band followed by digitization using undersampling, and back-end signal processing to reconstruct the original wide-band signal from multiple band-pass components.