Analog to digital conversion of ultra-wideband signals in orthogonal spaces

This paper introduces novel techniques to perform analog to digital (AJD) conversion, based on the quantization of the coefficients obtained by the projection of a continuous-time signal over an orthogonal space. The new A/D techniques proposed here are motivated by the sampling of the input signal in domains which may lead to lower levels of signal distortion and significantly less demanding A/D conversion characteristics. As a particular case, we study A/D conversion in the frequency domain where samples of the signal spectrum are taken such that no time-aliasing occurs in the discrete-time version of the signal. We show that the frequency domain analog to digital converter (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 discrete frequency samples are then passed through a vector quantizer with relaxed characteristics, operating over DC levels that change with a speed that is much lower than that required for time-domain A/D conversion. Fundamental figures of merit in A/D conversion and important system trade-offs are discussed for the proposed frequency domain ADC. As an example of this approach, we consider a multi-carrier UWB communications scheme.