A conventional wisdom is that a bandlimited signal can be sampled at twice its maximum frequency to prevent any loss of information. For signals having high frequency components, sampling them requires fast analog-to-digital converters (ADC) that are difficult to design without increasing their cost and noise. In this paper, we show that high-resolution samples of any signal, bandlimited or unbandlimited, can be accurately approximated using multiple sequences of low-resolution samples taken from the same analog signal, probably with fractional delays, using slow ADCs. The approximation is enabled by designing a set of synthesis filters, without any knowledge of the signals to be sampled, to minimize an induced error system in the minimax sense. The approximation performance is guaranteed to be robust even when using estimates of the system parameters (such as antialiasing filters and fractional delays). We present experiments to confirm the potential of our approach.