Software-defined radios have the agility and flexibility to tune performance parameters, allowing them to adapt to environmental changes, adapt to desired modes of operation, and provide varied functionality as needed.  Traditional software-defined radios use a combination of conditional processing and software-tuned hardware to enable these features and will critically sample the spectrum to ensure that only the required bandwidth is digitized.  While flexible, these systems are still constrained to perform only a single function at a time and digitize a single frequency sub-band at time, possibly limiting the radio's effectiveness. Radio systems commonly tune hardware manually or use software controls to digitize sub-bands as needed, critically sampling those sub-bands according to the Nyquist criterion.  Recent technology advancements have enabled efficient and cost-effective over-sampling of the spectrum, allowing all bandwidths of interest to be captured for processing simultaneously, a process known as band-sampling.  Simultaneous access to measurements from all of the frequency sub-bands enables both awareness of the spectrum and seamless operation between radio applications, which is critical to many applications.  Further, more information may be obtained for the spectral content of each sub-band from measurements of other sub-bands that could improve performance in applications such as detecting the presence of interference in weak signal measurements. This thesis presents a new method for confirming the source of detected energy in weak signal measurements by sampling them directly, then estimating their expected effects.  First, we assume that the detected signal is located within the frequency band as measured, and then we assume that the detected signal is, in fact, interference perceived as a result of signal aliasing.  By comparing the expected effects to the entire measurement and assuming the power spectral density of the digitized bandwidth is sparse, we demonstrate the capability to identify the true source of the detected energy.  We also demonstrate the ability of the method to identify interfering signals not by explicitly sampling them, but rather by measuring the signal aliases that they produce.  Finally, we demonstrate that by leveraging techniques developed in the field of Compressed Sensing, the method can recover signal aliases by analyzing less than 25 percent of the total spectrum. / Master of Science