The theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite-precision amplitude values. This thesis explores signal representation and recovery based on uniform amplitude sampling with either assuming infinite-precision timing information or time restricted to a uniform grid. If time is allowed to lie on the continuum, the approach is based on a structure that is equivalent to reversibly transforming the input signal into a monotonic function which is then uniformly sampled in amplitude. In effect, the source signal is then implicitly represented by the times at which the monotonic function crosses a predefined set of amplitude values. We refer to this technique as amplitude sampling. This approach can be viewed alternatively as nonuniform time sampling of the original source signal whereas the resulting monotonic signal produces an associated amplitude-time function which is uniformly sampled in amplitude. The duality and frequency-domain properties for the functions involved in the transformation are derived. Reconstruction from amplitude samples is shown to be possible through iterative algorithms. If both time and amplitude are restricted to equally-spaced values, then the sampling strategy, referred to as lattice sampling, simultaneously uses both uniform amplitude and uniform time sampling. A class of bandlimited signals is characterized that can be sampled and reconstructed in this manner in order to derive spectral characteristics of quantized discrete-time signals.