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We consider analog to digital (A/D) conversion, based on the quantization of coefficients obtained via the projection of a continuous time signal over a set of basis functions. The framework presented here for A/D conversion is motivated by the sampling of an input signal in domains which may lead to significantly less demanding A/D conversion characteristics, i.e., lower sampling rates and lower bit resolution requirements. We show that the proposed system efficiently parallelizes the analog to digital converter (ADC), which lowers the sampling rate requirements by increasing the number of basis functions on which the continuous time signal is projected, leading to a tradeoff between sampling rate reduction and system complexity. Additionally, the A/D conversion resolution requirements can be reduced by optimally assigning the available number of bits according to the variance distribution of the coefficients obtained from the signal projection over the new A/D conversion domain. In particular, we study A/D conversion in the frequency domain, where samples of the continuous signal spectrum are taken such that no time aliasing occurs in the discrete time version of the signal. We show that the frequency domain ADC overcomes some of the difficulties encountered in conventional time-domain methods for A/D conversion of signals with very large bandwidths, such as ultra-wideband (UWB) signals. The proposed A/D conversion method is compared with conventional ADCs based on pulse code modulation (PCM). Fundamental figures of merit in A/D conversion and system tradeoffs are discussed for the proposed ADC. The signal-to-noise and distortion ratios of the frequency domain ADC are presented, which quantify the impact of the most critical impairments of the proposed ADC technique. We also consider application to communications receivers, and provide a design example of a multi-carrier UWB receiver.