Most existing transceivers are Fourier-centric where complex sinusoids play a central role in the internals of the core building blocks. From the channel perspective, complex sinusoids constitute the fundamental effects in the wireless baseband equivalent channel model; exemplified by the time-invariant and time-varying transfer functions in static and time-varying channel conditions respectively. In addition, complex sinusoids are used as signaling waveforms for data transmission through the channel. The dominant mode of transmission in modern communications is in the form of finite time duration blocks having approximately finite bandwidth. As a result, the time-frequency space becomes projected to a time-frequency subspace having essentially limited support where complex sinusoids suffer from leakage effects due to the finite time extent of a block. In addition, Kronecker delta signals (duals of complex sinusoids) suffer from the same vulnerability due to the finite extent bandwidth. Gabor signaling bases using non-rectangular pulse shapes can attain good confinement in the time-frequency space, however, at the expense of completeness which reduces the utilization efficiency of the time-frequency signaling resources. Over a signaling block period, a doubly dispersive (DD) channel is projected onto an essentially limited time-frequency subspace. In this subspace, the Discrete Prolate Spheroidal (DPS) basis matched to the channel parameters is known to be optimally compact in representing the channel using a basis expansion decomposition. Unlike the Discrete Fourier Transform (DFT) basis which lacks compactness due to the leakage effect. Leakage in the expansion coefficients of a particular channel using the DFT basis has a direct correspondence with the Inter-Symbol Interference (ISI) between the DFT signaling components when transmitted through the same channel. For the DPS basis, however, the correspondence is not as obvious. Nevertheless, DPS when used for signaling results in ISI compactness in the form of an exponential decay of distant ISI components. The efficacy of DPS signaling in DD channels in addition to its efficiency in modeling DD channels motivates the investigation of a new transceiver baseband architecture where DFT is supplanted by DPS. / Ph. D.