Subband Image Coding pp 101-141 | Cite as

# IIR Analysis/Synthesis Systems

Chapter

## Abstract

A subband coding system may be conveniently viewed as having two constituent components: the analysis/synthesis section pair and the coding section pair. The term *analysis* describes the process of splitting the input into critically-sampled frequency related subband signals while the term *synthesis* refers to the dual operation of interpolating and merging the signals to reconstruct the input. The coding section pair, which consists of an encoder and decoder, appears between the analysis and synthesis operations and enables the input to be represented at a reduced bit rate.

## Keywords

Filter Bank Step Response Linear Phase Synthesis Filter Exact Reconstruction
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## Bibliography

- [1]R. Ansari and B. Lui, “A class of low-noise computationally efficient recursive digital filters with applications to sampling rate alterations,”
*IEEE Trans. on Acoustics, Speech, and Signal Process*., vol. ASSP-33, pp. 90–97, 1985.CrossRefGoogle Scholar - [2]T. P. Barnwell III, “Sub-band coder design incorporating recursive quadrature filters and optimum ADPCM coders,”
*IEEE Trans. Acoust., Speech, and Signal Process*., vol. ASSP-30, pp. 751–765, October 1982.CrossRefGoogle Scholar - [3]R. E. Crochiere and L. R. Rabiner,
*Multirate Digital Signal Processing*, Prentice Hall, Englewood Cliffs, NJ, 1983, Ch. 7.7, pp. 376–395.Google Scholar - [4]R. E. Crochiere, S. A. Webber, J. L. Flanagan, “Digital coding of speech in sub-bands,”
*Bell Syst. Tech. J.*, vol 55, pp. 1069–1085, October 1976.Google Scholar - [5]A. Croisier, D. Esteban, C. Galand, “Perfect channel splitting by use of interpolation, decimation and tree decomposition techniques,”
*Proc. of Int. Conf. on InformationSciences/Systems*, Patras, Greece, August 1976, pp. 443–446.Google Scholar - [6]D. Esteban and C. Galand, “Application of quadrature mirror filters to split band voice coding schemes,”
*Proc. Int Conf. on Acoustics, Speech, and Sig. Process*., May 1977, pp. 191–195.Google Scholar - [7]M. J. T. Smith and S. L. Eddins, “Analysis/synthesis techniques for subband image coding”
*IEEE Trans. on Acoustics, Speech, and Signal Process*., August 1990.Google Scholar - [8]H. Gharavi, A. Tabatabai “ Sub-band coding of monochrome and color images,”
*IEEE Trans. Acoust., Speech, Signal Process*., vol. ASSP-35, pp. 207–214, February 1988.Google Scholar - [9]A. V. Oppenheim and R. W. Schafer,
*Digital Signal Processing*, Prentice Hall, Englewood Cliffs, New Jersey, 1975, Ch. 5.5, pp. 239–241.MATHGoogle Scholar - [10]R.M. Gray, “Vector quantization,”
*IEEE, ASSP Magazine*, vol.1, pp. 4–29, April 1984.CrossRefGoogle Scholar - [11]P. Jeanrenaud,
*Subband Coding of Images with Recursive Allpass Filters, using Vector Quantization*, Master’s thesis, Georgia lnstitute of Technology, Atlanta, November 1988Google Scholar - [12]J.D. Johnston, “A filter family designed for use in quadrature mirror filter banks,”
*Proc.Int. Conf. Acoust. Speech and Signal Process*., April 1980, pp. 291–294.Google Scholar - [13]G. Karlsson, and M. Vetterli, “Extension of finite length signals for subband coding,”
*Signal Processing*, no. 17,pp. 161–168, 1989.CrossRefGoogle Scholar - [14]T. Kronander, “A new approach to recursive mirror filters with a special application in subband coding of images,”
*IEEE Trans. on Acoustics, Speech, and Signal Process*., vol. 36, pp. 1496–1500, September 1988.MATHCrossRefGoogle Scholar - [15]V.J. Mathews, R.W. Waite, T.D. Tran, “Image compression using vector quantization of linear (one-step) prediction errors”
*Proc. Int. Conf. Acoust. Speech Signal Process*. Dallas, Texas, April 1987, pp. 733–736.Google Scholar - [16]T.A. Ramstad and O. Foss, “Sub-band coder design using recursive quadrature mirror filters,”
*Signal Processing: Theories and Applications*, 1980, pp. 747–752.Google Scholar - [17]T.A. Ramstad, “IIR filterbank for subband coding of images,”
*Proc. of Int. Symposium on Cir. and Systems*, June, 1988, Espoo, Finland, pp. 827–834.Google Scholar - [18]M.R. Schroeder and B.S. Atal, “Code-excited linear prediction (CELP): High quality speech at very low bit rates”
*Proc. Int. Conf. Acoust. Speech Signal Process*., Tampa, Florida, March 1985, pp. 937–940.Google Scholar - [19]C. R. Galand and H. J. Nussbaumer, “Quadrature mirror filters with perfect reconstruction and reduced computational complexity,”
*Proc. Int. Conf. Acoust. Speech Signal Process*., April 1985, pp. 525–528.Google Scholar - [20]M.J.T. Smith, T.P. Barnwell III, “Exact reconstruction techniques for tree structured subband coders,”
*IEEE Trans. Acoust., Speech, and Signal Process*., vol. ASSP-34, pp. 434–441, June 1986.CrossRefGoogle Scholar - [21]M.J.T. Smith, S.L. Eddins, “Sub-band coding of images with octave band tree structures,”
*Proc. Int. Conf. Acousi. Speech and Signal Process*. Dallas, Texas, April 6–9, pp. 1382–1385.Google Scholar - [22]M.J.T. Smith, R.M. Mersereau, and T. P. Barnwell “Exact reconstruction recursive filter banks for sub-band image coding,”
*Proc. of IEEE Miami Technicon 87*, Miami, Florida, October 1987, pp. 121–124.Google Scholar - [23]P.P. Vaidyanathan, “Quadrature mirror filter banks, M-band extensions and perfect reconstruction techniques,”
*ASSP Magazine*, vol.4, pp. 4–20, July 1987.CrossRefGoogle Scholar - [24]M. Smith and T. Barnwell, “A new filter bank theory for time-frequency representation,”
*IEEE Trans. on Acoustics, Speech, and Signal Process*., vol. 35, pp. 314–327, March 1987.CrossRefGoogle Scholar - [25]P.P. Vaidyanathan, S. K. Mitra, and Y. Neuvo, “A new approach to the realization of low-sensitivity IIR digital filters,”
*IEEE Trans. on Acoustics, Speech, and Signal Process*., vol. ASSP-34, pp. 350–361, April 1986.CrossRefGoogle Scholar - [26]M. Vetterli, “Multidimensional sub-band coding: some theory and algorithms,”
*Signal Processing*, vol. 6, pp. 97–112, April 1984.MathSciNetCrossRefGoogle Scholar - [27]P. H. Westerink, J. Biemond, and D. Boeckee, “An optimal bit allocation algorithm for sub-band coding”
*Proc. Int. Conf. Acoust. Speech Signal Process*., New York, April 1988, pp. 757–760.Google Scholar - [28]J.W. Woods and S.D. O’Neill, “Sub-band coding of images,”
*IEEE Trans. Acoust., Speech, and Signal Process*., vol. ASSP-34, pp.1278–1288, October 1986.CrossRefGoogle Scholar - [29]J. H. Husoy, T. A. Ramstad, “Application of an efficient parallel IIR filterbank to image subband coding,” submitted to
*Signal Processing*. Google Scholar - [30]A. Fettweis, J. A. Nossek, and K. Meerkotter, “Reconstruction of signals after filtering and sampling-rate reduction,”
*Proc. Int. Conf. Acoustics, Speech, and Signal Process*., San Diego, CA, March 1984, pp. 11.7.1–11.7.4.Google Scholar - [31]A. Constantinides and R. Valenzuela, “An efficient and modular transmultiplexer design,”
*IEEE Trans. on Communications*, vol. COM-30, pp. 1629–1641, July 1982.CrossRefGoogle Scholar - [32]R. Ansari and S. H. Lee, “Two-dimensional multirate processing on non-rectangular grids: Theory and filtering procedures,” to appear
*in IEEE Trans. on Circuits and Systems*, 1989.Google Scholar - [33]M. Vetterli, “A theory of multirate filter banks,”
*IEEE Trans. on Acoustics, Speech, and Signal Process*., vol. ASSP-35, pp. 356–372, March 1987.CrossRefGoogle Scholar - [34]J. H. Rothweiler, “Polyphase quadrature filters, a new sub-band coding technique,”
*Proc. Int. Conf on Acoust., Speech, and Signal Process*., Boston MA, April 1983.Google Scholar - [35]P. L. Chu, “Quadrature mirror filter design for an arbitrary number of equal bandwidth channels,”
*IEEE Trans. on Acoust. Speech, and Sig. Process*., vol. 33, pp. 203–328, February, 1985.CrossRefGoogle Scholar - [36]K. Swaminathan and P.P. Vaidyanathan, “Theory and design of uniform DFT, parallel, quadrature mirror filter banks,”
*IEEE Trans. on Circuits and Systems*, vol. CAS-33, pp. 1170–1191, December 1986.CrossRefGoogle Scholar - [37]P.P. Vaidyanathan and P. Q. Hoang, “Lattice structures for optimal design and robust implementation of two-channel prefect-reconstruction QMF banks,”
*IEEE Trans. on Acoustics, Speech, and Sig. Process*., vol. ASSP-36, pp. 81–94, January 1988.CrossRefGoogle Scholar - [38]F. Mintzer, “Filters for distortion free two-band multirate filter banks,”
*IEEE Trans. on Acoustics, Speech and Sig. Process*., vol. ASSP-33, pp. 626–630, June 1985.CrossRefGoogle Scholar - [39]C. Galand and H. Nussbaumer, “New quadrature mirror filter design in the time domain,”
*IEEE Trans. on Acoustics, Speech and Sig. Process*., Vol. ASSP-32, pp. 522–531, June 1984.CrossRefGoogle Scholar - [40]H. Göckler, “Design of recursive polyphase networks with optimum magnitude and minimum phase,”
*Signal Processing 3*, 1981, pp. 365–376, North-Holland Publishing Company.CrossRefGoogle Scholar - [41]H. Martinez and T. Parks, “Design of recursive digital filters with optimum magnitude and attenuation poles on the unit circle,”
*IEEE Trans. on Acoustics, Speech and Signal Process*., vol. ASSP-36, April 1978.Google Scholar - [42]M. Smith and T. Barnwell, “A unifying framework for maximally decimated analysis/synthesis systems,”
*Proc. Int. Conf. on Acoustics, Speech, and Signal Process*., March 1985, pp. 521–524.Google Scholar - [43]M. Smith and K. Tracy, “Multi-dimensional frequency domain coding” ,
*Proceedings of IEEE Miami Technicon*, October 1987, pp. 70–73.Google Scholar - [44]P. Jeanrenaud and M. Smith, “Recursive subband image coding using adaptive prediction and finite state vector quantization,”
*Signal Processing*, May 1990.Google Scholar - [45]M. Smith and T. Barnwell, “A procedure for designing exact reconstruction filter banks for tree-structured subband coders,”
*Proc. Int. Conf. on Acoustics, Speech, and Signal Process*., March 1984, pp. 27.1.1–27.1.4.Google Scholar - [46]T. Nguyen and P.P. Vaidyanathan, “Manual: PRQMFs Two Channel PR FIR QMF Bank Design Package,” Dept. of Electrical Engineering, California Institute of Technology, Pasadena, CA 1952.Google Scholar
- [47]D. Le Gall and A. Tabatabai, “Subband coding of digital images using symmetric short kernel filters and arithmetic coding techniques”,
*Proc. Int. Conf. on Acoustics, Speech, and Signal Process*., April 1988, New York, pp. 761–764.Google Scholar - [48]M. Bellanger, G. Bonnerot and M. Coudreuse, “Digital filtering by polyphase network: Application to sample rate alteration and filter banks,”
*IEEE Trans. on Acoust. Speech and Signal Process*., vol. 24, pp. 109–114, April 1976.CrossRefGoogle Scholar - [49]T. Nguyen and P.P. Vaidyanathan, “Two-channel perfect reconstruction FIR QMF structures which yield linear phase FIR analysis and synthesis filters,”
*IEEE Trans. on Acoustics, Speech and Signal Process*., vol. ASSP-37, pp. 676–690, May 1989.CrossRefGoogle Scholar - [50]P. P. Vaidyanathan, “Perfect reconstruction QMF banks for two dimensional applications”,
*IEEE Trans. on Circuits and Systems*, vol. 34, pp. 976–978, August 1987CrossRefGoogle Scholar - [51]P. P. Vaidyanathan, “Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect reconstruction property,”
*IEEE Trans. on Acoustics, Speech and Signal Process*., vol. ASSP-35, pp. 476–492, April 1987.MATHCrossRefGoogle Scholar - [52]R. H. Bamberger and M. Smith, “ Filter banks for the directional decomposition of images: Theory and design,” submitted to
*IEEE Trans. on Acoustics, Speech, and Signal Process*., December, 1989.Google Scholar - [53]P. P. Vaidyanathan, “Multirate digital filters, filter banks, polyphase networks, and applications: A tutorial,”
*Proc. of the IEEE*, December 1989.Google Scholar

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© Springer Science+Business Media Dordrecht 1991