257 research outputs found
Filter Bank Fusion Frames
In this paper we characterize and construct novel oversampled filter banks
implementing fusion frames. A fusion frame is a sequence of orthogonal
projection operators whose sum can be inverted in a numerically stable way.
When properly designed, fusion frames can provide redundant encodings of
signals which are optimally robust against certain types of noise and erasures.
However, up to this point, few implementable constructions of such frames were
known; we show how to construct them using oversampled filter banks. In this
work, we first provide polyphase domain characterizations of filter bank fusion
frames. We then use these characterizations to construct filter bank fusion
frame versions of discrete wavelet and Gabor transforms, emphasizing those
specific finite impulse response filters whose frequency responses are
well-behaved.Comment: keywords: filter banks, frames, tight, fusion, erasures, polyphas
Computation of the para-pseudoinverse for oversampled filter banks: Forward and backward Greville formulas
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience. In frame expansions, the least square signal reconstruction operator is called the dual frame, which can be obtained by choosing the synthesis filter bank as the para-pseudoinverse of the analysis bank. In this paper, we study the computation of the dual frame by exploiting the Greville formula, which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended. Here, we first develop the backward Greville formula to handle the case of row deletion. Based on the forward Greville formula, we then study the computation of para-pseudoinverse for extended filter banks and Laplacian pyramids. Through the backward Greville formula, we investigate the frame-based error resilient transmission over erasure channels. The necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived. A postfiltering structure is also presented to implement the para-pseudoinverse when the transform coefficients in one subband are completely lost
Frame expansions with erasures: an approach through the non-commutative operator theory
In modern communication systems such as the Internet, random losses of
information can be mitigated by oversampling the source. This is equivalent to
expanding the source using overcomplete systems of vectors (frames), as opposed
to the traditional basis expansions. Dependencies among the coefficients in
frame expansions often allow for better performance comparing to bases under
random losses of coefficients. We show that for any n-dimensional frame, any
source can be linearly reconstructed from only (n log n) randomly chosen frame
coefficients, with a small error and with high probability. Thus every frame
expansion withstands random losses better (for worst case sources) than the
orthogonal basis expansion, for which the (n log n) bound is attained. The
proof reduces to M.Rudelson's selection theorem on random vectors in the
isotropic position, which is based on the non-commutative Khinchine's
inequality.Comment: 12 page
Parity-check matrix calculation for paraunitary oversampled DFT filter banks
International audienceOversampled filter banks, interpreted as error correction codes, were recently introduced in the literature. We here present an efficient calculation and implementation of the parity-check polynomial matrices for oversampled DFT filter banks. If desired, the calculation of the partity-check polynomials can be performed as part of the prototype filter design procedure. We compare our method to those previously presented in the literature
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