| In this dissertation we investigate the problem of asynchronous representation and processing of analog sparse signals using a time-scale framework. Recently, in the design of signal representations the focus has been on the use of application-driven constraints for optimality purposes. Appearing in many fields such as neuroscience, implantable biomedical diagnostic devices, and sensor network applications, sparse or burst--like signals are of great interest.;A common challenge in the representation of such signals is that they exhibit non-- stationary behavior with frequency--varying spectra. By ignoring that the maximum frequency of their spectra is changing with time, uniformly sampling sparse signals collects samples in quiescent segments and results in high power dissipation. Also, continuous monitoring of signals challenges data acquisition, storage, and processing; especially if remote monitoring is desired, as this would require that a large number of samples be generated, stored and transmitted. Power consumption and the type of processing imposed by the size of the devices in the aforementioned applications has motivated the use of asynchronous approaches in our research. First, we work on establishing a new paradigm for the representation of analog sparse signals using a time-frequency representation. Second, we develop a scale-based signal decomposition framework which uses filter-bank structures for the representation-analysis-compression scheme of the sparse information. Using an asynchronous signal decomposition scheme leads to reduced computational requirements and lower power consumption; thus it is promising for hardware implementation. In addition, the proposed algorithm does not require prior knowledge of the bandwidth of the signal and the effect of noise can still be alleviated. Finally, we consider the synthesis step, where the target signal is reconstructed from compressed data. We implement a perfect reconstruction filter bank based on Slepian wavelets to use in the reconstruction of sparse signals from non--uniform samples.;In this work, experiments on primary biomedical signal applications, such as electrocardiogram (EEG), swallowing signals and heart sound recordings have achieved significant improvements over traditional methods in the sensing and processing of sparse data. The results are also promising in applications including compression and denoising. |
