Design of high order FIR Unimodular Filter Banks and its application in combatting instantaneous erasures

FIR Unimodular Filter Banks (UFBs) offer the minimum possible delay among all the filter banks with the same downsampling rate. Although Order-one UFBs can be factorized into degree-one unimodular matrices, this factorization is not possible for higher order UFBs. This is unfavorable because in most applications, banks with longer length filters result in better performance. In this paper, we investigate the design of high order FIR UFBs using a time domain approach. We show that due to the flexibility of this method, long filters with decent frequency responses are achievable. We also propose a special factorization for high order UFBs which reduces the large number of free parameters of time domain approach. Although this factorization is not complete, we show that it can give reasonably good filters. Finally we use the designed filters in the application of reconstructing the output of an Oversampled FB in the case of instantaneous erasure in sub-band domain. Instantaneous erasure accounts for a situation where the sub-band samples are erased based on different patterns in each time instance and the minimum delay of the OFB is crucial for reconstructing the output.