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A Theoretical Analysis of the Projection Error onto Discrete Wavelet Subspaces

Michaël Unser, Thierry Blu

A filterbank decomposition can be seen as a series of projections onto several discrete wavelet subspaces. In this presentation, we analyze the projection onto one of them—the low-pass one, since many signals tend to be low-pass. We prove a general but sim ...

SPIE1999

Oversampled Filter Banks

Martin Vetterli

Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in t(2)(Z), These frames are the subject of this paper. First, necessary and sufficient conditions on a filter bank for implementing a frame or a tight frame exp ...

1998

Investigation of a possible process identity between DRM and Linear Filtering

Sacha Krstulovic

The classical analogy between linear filtering and acoustical filtering by tubes is applied in the non-classical case where the tubes are made of unequal-length sections (such as the DRM case). It is shown that the filtering process identity is substantial ...

IDIAP1997

FCO sampling of digital video using perfect reconstruction filter banks

Martin Vetterli

Three-dimensional nonseparable perfect reconstruction filter banks using three-dimensional nonseparable sampling by two, FCO, are proposed. Filter structures are derived and applied to digital video. Separation into two bands is obtained, and it is shown t ...

1993

A high-performance cost-effective pole-zero MMSE-DFE

Ali H. Sayed

In this paper we derive a computationally efficient algorithm for accurately approximatinga long FIR filter by a reduced-parameter pole-zero filter. Our derivation successfully extends the "embedding" approach of [1,2] to the case of an unequal number of p ...

1993

Wavelets and recursive filter banks

Martin Vetterli

It is shown that infinite impulse response (IIR) filters lead to more general wavelets of infinite support than finite impulse response (FIR) filters. A complete constructive method that yields all orthogonal two channel filter banks, where the filters hav ...

1993