A time domain view of filter banks and wavelets

@article{Nayebi1991ATD,
  title={A time domain view of filter banks and wavelets},
  author={Kambiz Nayebi and Thomas P. Barnwell and Mark J. T. Smith},
  journal={[1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems \& Computers},
  year={1991},
  pages={736-740 vol.2}
}
The authors consider a time domain approach to the reconstruction problem for filter bank and wavelet decompositions. The procedure for the design of general decomposition and reconstruction systems, called generalized lapped transforms (GLTs), is discussed. GLTs include many classical transforms and the discrete-time wavelet transform (DTWT) as special cases. The proposed design procedure is used to design wavelets and DTWT systems. Because of the generality of the framework, regularity and… 
On the design of FIR analysis-synthesis filter banks with high computational efficiency
TLDR
The design procedure is based on a time domain formulation of analysis-synthesis filter banks in which each individual channel filter is constrained to be a cosine modulated versions of a baseband filter.
Analysis-synthesis systems with time-varying filter bank structures
TLDR
The reconstruction problem is studied and it is shown that perfect reconstruction can be achieved and a design approach to solve the problem is presented.
Conjointly well localized modulated lapped orthogonal transforms
  • P. Tay, Yanjun Yan
  • Mathematics, Computer Science
    2015 49th Asilomar Conference on Signals, Systems and Computers
  • 2015
TLDR
The particle swarm optimization method is proposed to determine conjointly time-frequency well localized filters that constitute a multi-channel perfect reconstruction filterbank to determine optimal complex modulated lapped transform filters.
A conjointly well localized quadrature mirror filterbank
  • P. Tay
  • Mathematics, Computer Science
    2015 IEEE International Conference on Image Processing (ICIP)
  • 2015
TLDR
An in depth analysis of parameter selection and novel use of polynomial fitting to ensure perfection reconstruction of the optimal quadrature mirror filterbank are provided.

References

SHOWING 1-10 OF 13 REFERENCES
Wavelets and filter banks: relationships and new results
  • M. Vetterli, Cormac Herley
  • Mathematics, Computer Science
    International Conference on Acoustics, Speech, and Signal Processing
  • 1990
The discrete version of the wavelet transform, which has recently emerged as a powerful tool for nonstationary signal analysis is closely related to filter banks, which have been studied in digital
The design of perfect reconstruction nonuniform band filter banks
The authors describe a general procedure for the design of analysis-synthesis systems based on nonuniform filter banks. The procedure is based on a time-domain analysis which results in a set of
The time domain analysis and design of exactly reconstructing FIR analysis/synthesis filter banks
A time-domain framework is introduced for the analysis and design of general M-band analysis/synthesis filter banks. The derivation results in a set of time-domain conditions for reconstruction which
A general time domain analysis and design framework for exactly reconstructing FIR analysis/synthesis filter banks
A general framework is presented for analyzing and designing exactly reconstructing FIR (finite-impulse response) filter banks. This framework is based completely on the time-domain analysis of the
Time-frequency representation of digital signals and systems based on short-time Fourier analysis
This paper develops a representation for discrete-time signals and systems based on short-time Fourier analysis. The short-time Fourier transform and the time-varying frequency response are reviewed
Time-domain filter bank analysis: a new design theory
TLDR
A set of time-domain conditions for reconstruction which can be used directly in a filter bank design procedure is derived, which allows for the design of many useful banks.
Perfect reconstruction FIR filter banks: lapped transforms, pseudo QMFs and paraunitary matrices
Perfect-reconstruction FIR (finite-impulse-response) filter banks are analyzed in both the z-transform and time domains. A condition for equal-length analysis and synthesis filters is given in terms
Analysis/Synthesis filter bank design based on time domain aliasing cancellation
TLDR
A single-sideband analysis/synthesis system is proposed which provides perfect reconstruction of a signal from a set of critically sampled analysis signals and allows overlap between adjacent time windows, implying that time domain aliasing is introduced in the analysis; however, thisAliasing is cancelled in the synthesis process, and the system can provide perfect reconstruction.
Exact reconstruction techniques for tree-structured subband coders
TLDR
It is shown that it is possible to design tree-structured analysis/reconstruction systems which meet the sampling rate condition and which result in exact reconstruction of the input signal.
Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property
  • P. Vaidyanathan
  • Mathematics, Computer Science
    IEEE Trans. Acoust. Speech Signal Process.
  • 1987
TLDR
A general class of maximally decimated M-channel quadrature mirror filter banks that lead to perfect reconstruction is derived, and it is shown that such a property can be satisfied if the alias component matrix is unitary on the unit circle of the z plane.
...
1
2
...