טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGedalyahu Kfir
SubjectSampling Signals from a Parameterized Union of Subspaces
DepartmentDepartment of Electrical Engineering
Supervisor Professor Yonina Eldar
Full Thesis textFull thesis text - English Version


Abstract

Digital signal processing relies on sampling of a continuous-time signal in order to obtain a discrete-time representation of it. One of the traditional assumptions in sampling theory suggests that in order to perfectly reconstruct an analog signal from its samples, it must be sampled at the Nyquist rate, i.e, twice its highest frequency. This assumption is required when the only prior on the signal is that it is bandlimited. Other priors on the signal's structure can lead to more efficient sampling schemes. The goal of this work is to develop low-rate sampling strategies for signals which are comprised of short pulses, as well as for broader classes of structured analog signals. We start by presenting a new framework, which we refer to as a parameterized union of subspaces. This framework includes analog signals in various applications, including communication and radar. Describing such signals using the proposed model can lead to efficient sampling and reconstruction schemes.

We next address two related time delay estimation problems which can be formalized using our framework. In the first problem, the signal is comprised of a stream of delayed and weighted pulses, and there is no assumption on the pulse time support. The signal is divided into periods, where it is assumed that the delays in each period are constant. The second problem addresses a similar parametric model, however without constraining the delays to be constant in each period, and with the additional requirement that the pulses have finite time support. For both settings sampling at the Nyquist rate is highly inefficient, since the bandwidth of the pulses can be very large. By addressing these models as signals in a parameterized union of subspaces, we derive sub-Nyquist sampling architectures, allowing the recovery of the pulses delays and amplitudes, from samples taken at the minimal theoretical rate.