Influence of weight function nonorthogonality on performance of sampling and reconstruction with internal filtering

Novel sampling and reconstruction techniques with internal filtering have been proposed and described in earlier papers by the authors. Properties of these techniques are determined by their weight functions. Practical requirements for these functions and mathematical restrictions imposed on them are discussed in this paper. The attention is focused on the weight functions used for sampling because they should satisfy more challenging requirements. Qualitative and quantitative analysis has shown that, on the one hand, adequately selected weight functions allow radical improvement of dynamic range and other parameters of the equipment where sampling with internal antialiasing filtering is used; on the other hand, it is very difficult to satisfy practical requirements for the weight functions due to their complexity and contradictoriness. Therefore, multiple tradeoffs are necessary for the weight function implementation. At the same time, mathematical restrictions imposed on these functions are so loose that virtually any physically realizable weight function satisfies these restrictions. In particular, it is shown that the weight functions should not necessarily be orthogonal or even meet less restraining Riesz conditions. The looseness of the mathematical restrictions is caused by the fact that, in practice, sampling frequency is always higher than the Nyquist rate. As a result, many imperfections of antialiasing filtering within the passband can be compensated after analog-to-digital conversion