On perfect reconstruction with lost channel data in lapped pseudo-orthogonal transform

We address a problem to reconstruct the original signal with lost data by using FIR synthesis filters in a class of linear-phase perfect reconstruction (PR) oversampled filter banks (FB) called lapped pseudo-orthogonal transform (LPOT), which belongs to a class of overcomplete linear-phase paraunitary FB's, in which the synthesis filters are given as the paraconjugate of the analysis filters. When some subband coefficients are lost, the use of the Moore-Penrose pseudo-inverse of the analysis FB can achieve PR, but the corresponding synthesis filters can have IIR. We firstly discuss the possibility of PR with FIR filters of the same length as the analysis filters, and show the synthesis filters which can optimally suppress additive noise in some sense. We then show an example of the resulting synthesis filters. Finally, we suggest some open problems.