current ADC's model signals using the basis function of a step function,  and in the process introduce the artifacts.

use the progression of anti-aliasing starting with area sampling.

The question then becomes, what are other basis functions we might use to model an incoming analogy signal and what are the pro's and con's?

Sines and Cosines

Lines

Quadratics

Polynomials

Splines

Fuzzies

Piecewise Sines and Cosines.

concurrent with the modeling that we do (by choice of basis function) is the problem of whether we uniformly sample in time and in intensity.

Non-uniform sampling in time and intensity has enormous advantages, but creates some problems of its own.

FPGA or DSP or Graphics Card... that is the question... using the graphics card might be smart because much of the aliasing and filtering issues have already been worked out in a similar context, albeit low frequency and two dimensionally. If one could trade the large number of pixels in an image for the large number of samples in an RF signal, one might be able to leap frog and exploit graphics card technology for 1 dimensional RF signal processing...