Oversampled filter banks as error correcting codes: theory and impulse noise correction

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/sup -3/.

I. Introduction

Multirate systems based on filter banks [1] often use maximally decimated filter banks. In this paper, we investigate oversampled filter banks (OFBs), i.e., banks composed of different filters, but where each filter output is subsampled by a factor . Advances in their theory [2], [3] have been motivated by new applications requiring their specific properties. For instance, subband adaptive filtering is an area in which oversampled filter banks can be used [4]–[6], due to their higher attenuation in the stop-band [7], leading to lower levels of aliasing. Related areas of application are echo cancellation in subbands [8] or blind source separation in subbands. In all those cases, the main goal is to reduce the aliasing distortion thanks to oversampling, while still exploiting the computationally attractive subband setting.