the continuous time signal onto the set of basis functions this introduces a trade off between sampling speed reduction and system complexity that is characterized in this disclosure although similar reductions in the speed of the quantizers could be achieved in the time domain by using a time interleaved bank of quantizers synchronization problems the very fine time resolution in high speed applications and the fact that all the adcs see the full bandwidth of the input signal makes it difficult to design the sample hold circuitry and causes the overall design to require significant power in addition the signal expansion approach avoids the sharp rolloff filter bank needed in multi band adc architectures mixing with basis functions followed by integration over a time window required to project the signal generally synthesizes a filter bank with overlapping spectrum and smooth transitions the relaxed implementation requirements are a motivation among others for the ideas discussed herein potential lower bit requirements and or the potential improvement in the distortion of the adc of signal expansions can be achieved by optimally allocating the available number of bits in the quantization of the coefficients obtained through the projection of the continuous time signal over the basis set the possibility of efficiently allocating the available resources in terms of number of bits per sample is a feature that is not available in conventional time domain adc optimal bit allocation is possible in the proposed a d conversion scheme because some signal characteristics that are hidden in the time domain such as power spectral distribution can now be explored by projecting the continuous time signal as a nonlimiting example one can consider a d conversion in the frequency domain in which.