Abstract
In this paper, we propose a novel method to test if a non-uniform filter bank can achieve perfect reconstruction via a tree structure. The set of decimators is first sorted in an ascending order. A non-uniform filter bank can achieve perfect reconstruction via a tree structure if and only if some or all of the channels corresponding to the maximum decimation ratio can be grouped into one channel, and the procedure can be repeated until all the channels are grouped together.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Vaidyanathan P. P.: Lossless Systems in Wavelet Transforms. IEEE International Symposium on Circuits and Systems, ISCAS, Vol. 1. (1991) 116–119.
Soman A. K. and Vaidyanathan P. P.: Paraunitary Filter Banks and Wavelet Packets. IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP, Vol. 4. (1992) 397–400.
Bamberger R. H., Eddins S. L. and Nuri V.: Generalizing Symmetric Extension: Multiple Nonuniform Channels and Multidimensional Nonseparable IIR Filter Banks. IEEE International Symposium on Circuits and Systems, ISCAS, Vol. 2. (1992) 991–994.
Sodagar I., Nayebi K. and Barnwell T. P.: A Class of Time-Varying Wavelet Transforms. IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP, Vol. 3. (1993) 201–204.
Soman A. K. and Vaidyanathan P. P.: On Orthonormal Wavelets and Paraunitary Filter Banks. IEEE Transactions on Signal Processing, Vol. 41, No. 3. (1993) 1170–1183.
Vaidyanathan P. P.: Orthonormal and Biorthonormal Filter Banks as Convolvers, and Convolutional Coding Gain. IEEE Transactions on Signal Processing, Vol. 41, No. 6. (1993) 2110–2130.
Soman A. K. and Vaidyanathan P. P.: Coding Gain in Paraunitary Analysis/Synthesis Systems. IEEE Transactions on Signal Processing, Vol. 41, No. 5. (1993) 1824–1835.
Kovaèeviæ J. and Vetterli M.: Perfect Reconstruction Filter Banks with Rational Sampling Factors. IEEE Transactions on Signal Processing, Vol. 41, No. 6. (1993) 2047–2066.
Bamberger R. H., Eddins S. L. and Nuri V.: Generalized Symmetric Extension for Size-Limited Multirate Filter Banks. IEEE Transactions on Image Processing, Vol. 3, No. 1. (1994) 82–87.
Makur A.: BOT’ s Based on Nonuniform Filter Banks. IEEE Transactions on Signal Processing, Vol. 44, No. 8. (1996) 1971–1981.
Li J., Nguyen T. Q. and Tantaratana S.: A Simple Design Method for Near-Perfect-Reconstruction Nonuniform Filter Banks. IEEE Transactions on Signal Processing, Vol. 45, No. 8. (1997) 2105–2109.
Akkarakaran S. and Vaidyanathan P. P.: New Results and Open Problems on Nonuniform Filter-Banks. IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP, Vol. 3,. (1999) 1501–1504.
Omiya N., Nagai T., Ikehara M. and Takahashi S. I.: Organization of Optimal Nonuniform Lapped Biorthogonal Transforms Based on Coding Efficiency. IEEE International Conference on Image Processing, ICIP, Vol. 1. (1999) 624–627.
Vaidyanathan P. P.: Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice Hall, 1993.
Hoang P. Q. and Vaidyanathan P. P.: Non-Uniform Multirate Filter Banks: Theory and Design. IEEE International Symposium on Circuits and Systems, ISCAS, Vol. 1. (1989) 371–374.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ling, Wk., Tam, P.KS. (2001). Set of Perfect Reconstruction Non-uniform Filter Banks via a Tree Structure. In: Tang, Y.Y., Yuen, P.C., Li, Ch., Wickerhauser, V. (eds) Wavelet Analysis and Its Applications. WAA 2001. Lecture Notes in Computer Science, vol 2251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45333-4_43
Download citation
DOI: https://doi.org/10.1007/3-540-45333-4_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43034-6
Online ISBN: 978-3-540-45333-8
eBook Packages: Springer Book Archive