A novel and low-complexity approach for reconstructing periodic erasure bursts in data sampled at greater than the Nyquist rate, using cosine modulated filterbanks, is described. In the case of interpolation of erasure singlets or doublets periodically repeated over 2M samples, the cosine modulated filterbank approach is shown to have a lower complexity (for a given restoration error) than a standard FIR interpolator. In the case of erasure triplets or quadruplets, periodically repeated over 2M samples, the restoration error is primarily related to whether theM-channel filterbank’s stopband suppression is better than the condition number of a 2 × 2 matrix, whereM is determined by the oversampling factor of the data. While the method used for erasure triplets and quadruplets extends to arbitrary erasure bursts, the condition numbers of the associated (larger dimension) matrices deteriorate rapidly with the increase in erasure length, posing practical problems such as the design of very high-attenuation filterbanks and large required implementation wordlengths.