Economical Sampling of Parametric Signals

This thesis proposes architectures and algorithms for digital acquisition of parametric sig-nals. It furthermore provides bounds for the performance of these systems in the presence of noise. Our simple acquisition circuitry and low sampling rate enable accurate parameter estimation to be achieved economically. In present practice, sampling and estimation are not integrated: the sampling device does not take advantage of the parametric model, and the estimation assumes that noise in the data is signal-independent additive white Gaussian noise. We focus on estimating the timing information in signals that are linear combinations of scales and shifts of a known pulse. This signal model is well-known in a variety of disciplines such as ultra-wideband signaling, neurobiology, etc. The signal is completely determined by the amplitudes and shifts of the summands. The delays determine a subspace that contains the signals, so estimating the shifts is equivalent to subspace estimation. By contrast, conventional sampling theory yields a least-squares approximation to a signal from a fixe