Paraunitary oversampled filter bank design for channel coding
EURASIP Journal on Applied Signal Processing
Foundations and Trends in Signal Processing
Wavelet codes: detection and correction using Kalman estimation
IEEE Transactions on Signal Processing
Optimization of synthesis oversampled complex filter banks
IEEE Transactions on Signal Processing
Optimal noise reduction in oversampled PR filter banks
IEEE Transactions on Signal Processing
An iterative Bayesian algorithm for sparse component analysis in presence of noise
IEEE Transactions on Signal Processing
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Oversampled filter banks (OFBs) provide an overcomplete representation of their input signal. This paper describes how OFBs can be considered as error-correcting codes acting on real or complex sequences, very much like classical binary convolutional codes act on binary sequences. The structured redundancy introduced by OFBs in subband signals can be used to increase robustness to noise. In this paper, we define the notions of code subspace, syndrome, and parity-check polynomial matrix for OFBs. Furthermore, we derive generic expressions for projection-based decoding, suitable for the case when a simple second-order model completely characterizes the noise incurred by subband signals. We also develop a nonlinear hypotheses-test based decoding algorithm for the case when the noise in subbands is constituted by a Gaussian background noise and impulsive errors (a model that adequately describes the action of both quantization noise and transmission errors). Simulation results show that the algorithm effectively removes the effect of impulsive errors occurring with a probability of 10-3.