Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application

Nonuniform sampling occurs in many applications due to imperfect sensors, mismatchedclocks or event-triggered phenomena. Indeed, natural images, biomedical responses andsensor network transmission have bursty structure so in order to obtain samples that correspondto the information content of the signal, one needs to collect more samples when thesignal changes fast and fewer samples otherwise which creates nonuniformly distibuted samples.On the other hand, with the advancements in the integrated circuit technology, smallscale and ultra low-power devices are available for several applications ranging from invasivebiomedical implants to environmental monitoring. However the advancements in the devicetechnologies also require data acquisition methods to be changed from the uniform (clockbased, synchronous) to nonuniform (clockless, asynchronous) processing. An important advancementis in the data reconstruction theorems from sub-Nyquist rate samples which wasrecently introduced as compressive sensing and that redenes the uncertainty principle. Inthis dissertation, we considered the problem of signal reconstruction from nonuniform samples.Our method is based on the Prolate Spheroidal Wave Functions (PSWF) which can beused in the reconstruction of time-limited and essentially band-limited signals from missingsamples, in event-driven sampling and in the case of asynchronous sigma delta modulation.We provide an implementable, general reconstruction framework for the issues relatedto reduction in the number of samples and estimation of nonuniform sample times. We alsoprovide a reconstruction method for level crossing sampling with regularization. Another way is to use projection onto convex sets (POCS) method. In this method we combinea time-frequency approach with the POCS iterative method and use PSWF for the reconstructionwhen there are missing samples. Additionally, we realize time decoding modulationfor an asynchronous sigma delta modulator which has potential applications in low-powerbiomedical implants

Robust vibration suppression control profile generation

Scope and Method of Study:The control of flexible structures has been extensively studied in recent years. Flexible structures such as high-speed disk drive actuators require extremely precise positioning under very tight time constraints. Whenever a fast motion is commanded, residual vibration in the flexible structure is induced, which increases the settling time. One solution is to design a closed-loop control to damp out vibrations caused by the command inputs and disturbances to the plant. However, the resulting closed-loop response may still be too slow to provide an acceptable settling time. Also, the closed-loop control is not able to compensate for high frequency residual vibration which occurs beyond the closed-loop bandwidth. An alternative approach is to develop an appropriate reference trajectory that is able to minimize the excitation energy imparted to the system at its natural frequencies.Findings and Conclusions:A robust vibration suppression control profile is generated which suppresses all the high frequency vibrations in a flexible dynamic system. This robust control profile is the shifted time-limited version of the functions that optimally achieve the energy concentration property. The robust control profile is designed by considering the first resonance frequency. In practical system, a lower resonance frequency mode may exist which is located far from the high frequency resonance modes. In this case, a robust control profile is generated which suppresses one specific resonant mode in a flexible dynamic system. This robust control profile is a smooth function which can be used as a robust velocity profile, or as a robust shape filter to an arbitrary control command. The robustness can be arbitrarily improved, which brings about a smoother profile. Combination of high frequency vibration suppression control profile and low frequency vibration suppression control profile generates a robust vibration suppression control profile that is able to suppress all the resonant dynamics in a flexible dynamic system. The technique can be applied to both open-loop and closed-loop systems

A non-controllability result for the half-heat equation on the whole line based on the prolate spheroidal wave functions and its application to the Grushin equation

In this article, we revisit a result by A. Koenig concerning the non-controllability of the half-heat equation posed on R, with a control domain that is an open set whose exterior contains an interval. The main novelty of the present article is to disprove the corresponding observability inequality by using as an initial condition a family of prolate spheroidal wave function (PSWF) translated in the Fourier space, associated to a parameter c that goes to ∞. The proof is essentially based on the dual nature of the PSWF together with direct computations, showing that the solution "does not spread out" too much during time. As a consequence, we obtain a new non-controllability result on the Grushin equation posed on R × R

Ultra-wideband systems exploiting orthonormal waveforms

textElectrical and Computer Engineerin

Applications of Continuous Spatial Models in Multiple Antenna Signal Processing

This thesis covers the investigation and application of continuous spatial models for multiple antenna signal processing. The use of antenna arrays for advanced sensing and communications systems has been facilitated by the rapid increase in the capabilities of digital signal processing systems. The wireless communications channel will vary across space as different signal paths from the same source combine and interfere. This creates a level of spatial diversity that can be exploited to improve the robustness and overall capacity of the wireless channel. Conventional approaches to using spatial diversity have centered on smart, adaptive antennas and spatial beam forming. Recently, the more general theory of multiple input, multiple output (MIMO) systems has been developed to utilise the independent spatial communication modes offered in a scattering environment. ¶ ..