| Nonuniform sampling occurs in many applications due to imperfect sensors, mismatched clocks or event-triggered phenomena. Indeed, natural images, biomedical responses and sensor network transmission have bursty structure so in order to obtain samples that correspond to the information content of the signal, one needs to collect more samples when the signal changes fast and fewer samples otherwise which creates nonuniformly distributed samples. On the other hand, with the advancements in the integrated circuit technology, small scale and ultra low-power devices are available for several applications ranging from invasive biomedical implants to environmental monitoring. However the advancements in the device technologies also require data acquisition methods to be changed from the uniform (clock based, synchronous) to nonuniform (clockless, asynchronous) processing. An important advancement is in the data reconstruction theorems from sub-Nyquist rate samples which was recently introduced as compressive sensing and that redefines the uncertainty principle. In this dissertation, we considered the problem of signal reconstruction from nonuniform samples. Our method is based on the Prolate Spheroidal Wave Functions (PSWF) which can be used in the reconstruction of time-limited and essentially band-limited signals from missing samples, in event-driven sampling and in the case of asynchronous sigma delta modulation.;We provide an implementable, general reconstruction framework for the issues related to reduction in the number of samples and estimation of nonuniform sample times. We also provide a reconstruction method for level crossing sampling with regularization. Another way is to use projection onto convex sets (POCS) method. In this method we combine a time-frequency approach with the POCS iterative method and use PSWF for the reconstruction when there are missing samples. Additionally, we realize time decoding modulation for an asynchronous sigma delta modulator which has potential applications in low-power biomedical implants. |
