Reducing power consumption of radio receivers is becoming more critical with the advancement of biomedical portable and implantable devices due to the stringent power requirements in such applications. Compressive sensing promises to tremendously reduce the power of radio receivers by allowing the reconstruction of sparse signals from measurements acquired at a sub-Nyquist rate. A key component in compressive sensing systems is the random signal which is used to acquire the measurements. Most e orts have been devoted to the design of signals with high randomness but little have been devoted to manipulating the random signal to suite a speci fic application, meet certain specifi cations, or enhance the performance of the system. This thesis tackles compressive sensing systems from this angle. We first propose an architecture that alleviates a critical requirement in compressive sensing: that the random signal should run at the Nyquist rate, which becomes prohibitive as the signal bandwidth increases. We provide theoretical and experimental results that demonstrate the e ectiveness of the proposed architecture. Secondly, we propose a framework for manipulating the random signal in the frequency domain as suitable for speci c applications. We use the framework to develop an architecture for recon gurable ultra wide-band radios.