Linda Bai(University of Washington), “Compressive Detection and Estimation with Applications to Cognitive Radio and Radar”, Advisor: Sumit Roy (2013) According to Nyquist Sampling theorem, a band-limited signal can be reconstructed accurately if the sampling rate exceeds twice the maximum frequency of the signal. In many scenarios, this Nyquist sampling rate cannot be achieved due to hardware limitations. Compressive sensing (CS) is a technique to reconstruct a signal from sub-Nyquist samples, given that the signal is sparse in a known domain. The CS technique has been applied to different areas in the field of communications and networking. Of fundamental importance to current research is the need to adapt CS according to different requirements and constraints in each area. This thesis discussed the following issues. In Chapter 2, for detection of one idle channel, the author proposed a multi-resolution spectrum sensing scheme based on the principle of under-sampling (bandpass sampling). In Chapter 3, the author proposed a new compressive spectrum sensing architecture based on bandpass sampling to detect all the idle channels in the given spectrum. In Chapter 4, the application of compressive sensing to clutter subspace estimation in cognitive radar was discussed. For details, please contact the author or visit the thesis page.