Design of simultaneous sampling systems based on fractional delay Lagrange filters

Digital filtering is a common approach to achieve simultaneous sampling of several input signals acquired with a multiplexing delay. In this work, an error bound is obtained for Lagrange interpolation filters as a function of the oversampling ratio of the input signals, the fractional delay, and the filter's order. This bound can be used to ensure that the error is small enough to maintain a desired resolution (number of significant bits), thus leading to design equations for simultaneous sampling systems. For example, using these equations, we are able to find that an oversampling ratio of 71 is necessary to maintain a resolution of 12 bits with a first order Lagrange's filter, while a sixth-order filter is required when the oversampling ratio is only five. The theoretical results are validated through simulation, and the computational cost of the Lagrange's interpolator is compared with a polyphase filter.