Border recovery for subband processing of finite-length signals. Application to time-varying filter banks

In the context of subband processing of finite-length signals using FIR filter banks, a new technique is derived for achieving exact reconstruction when subband signals are truncated to the same number of samples as the original signal. Using a delayed truncation method in the subbands, it is shown that the missing samples can be recovered exactly by inverting small linear systems. Our approach also applies to time-varying filter banks or wavelet transforms where filters are switched between consecutive input blocks