Lower bounds on the L2-norms of digital resampling filters with zero-valued input samples

This paper derives lower bounds on the L2-norms of digital resampling filters with zero-valued input samples. This emanates from uniform-grid sampling but where some of the samples are missing. One application is found in timeinterleaved analog-to-digital converters with missing samples due to calibration at certain time instances. The square of the L2-norms correspond to scaling of the round-off noise that in practice is always present at the input of the resampling filter. As will be shown through the derived bounds, the L2-norm of the corresponding filter that recovers the missing samples is generally much larger than unity. Consequently, the noise variance is generally much larger for the recovered samples than for the other samples obtained in the sampling process. Based on this observation, the paper also proposes an alternative resampling scheme for which the maximum of all L2-norms in the resampling is reduced.