Design of Two-Channel Quadrature Mirror Filter Banks Using Digital All-Pass Filters

Authors: Ju-Hong Lee, Yi-Lin Shieh

Abstract:

The paper deals with the minimax design of two-channel linear-phase (LP) quadrature mirror filter (QMF) banks using infinite impulse response (IIR) digital all-pass filters (DAFs). Based on the theory of two-channel QMF banks using two IIR DAFs, the design problem is appropriately formulated to result in an appropriate Chebyshev approximation for the desired group delay responses of the IIR DAFs and the magnitude response of the low-pass analysis filter. Through a frequency sampling and iterative approximation method, the design problem can be solved by utilizing a weighted least squares approach. The resulting two-channel QMF banks can possess approximately LP response without magnitude distortion. Simulation results are presented for illustration and comparison.

Keywords: Chebyshev approximation, Digital All-Pass Filter, Quadrature Mirror Filter, Weighted Least Squares.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088298

References:

[1] R. E. Crochiere, “Digital signal processor: sub-band coding,” Bell Syst. Tech. J., vol. 60, pp. 1633-1653, 1981.
[2] M. G. Bellanger and J. L. Daguet, “TDM-FDM transmultiplexer: digital polyphase and FFT,” IEEE Trans. Commun., vol. 22, pp. 1199-1205, Sept. 1974.
[3] P. Vary and U. Heute, “A short-time spectrum analyzer with polyphase network and DFT,” Signal Processing, vol. 2, pp. 55-65, Jan. 1980.
[4] J. W. Woods and S. D. O’Neil, “Subband coding of images,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 34, pp. 1278-1288, Oct. 1986.
[5] S. Basu, C. Chiang, and H. Choi, “Wavelets and perfect reconstruction coding with causal stable IIR filters,” IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol. 42, pp. 24-38, Jan. 1995.
[6] M. M. Ekanayake and K. Premaratne, “Two-channel IIR QMF banks with approximately linear-phase analysis and synthesis filters,” IEEE Trans. Signal Processing, vol. 43, pp. 2313-2322, Oct. 1995.
[7] C. D. Creusere and S. K. Mitra, “Image coding using wavelets based on perfect reconstruction IIR filter banks,” IEEE Trans. Circuits and Systems for Video Technology, vol. 6, pp. 447-458, Oct. 1996,
[8] S. Summerfield and C.-K. Lu, “Design and VLSI implementation of multirate filter banks based on approximately linear phase allpass sections,” Proc. of Int’l Symposium on Circuits and Systems, Monterey, CA, pp. 413-416, June 1998.
[9] S. S. Lawson and A. Klouche-Djedid, “Technique for design of two-channel approximately linear phase QMF bank and its application to image compression,” IEE Proc. – Vision, Image and Signal Processing, vol. 148, no. 2, pp. 85-92, Apr. 2001.
[10] J.-H. Lee and I.-C. Niu, “Minimax design of two-channel IIR QMF banks with arbitrary group delay,” IEE Proc. – Vision, Image and Signal Processing, vol. 148, no. 6, pp. 384-390, Dec. 2001.
[11] J.-H. Lee and Y.-H. Yang, “Design of two-channel linear phase QMF banks based on real IIR all-pass filters,” IEE Proc.-Vision, Image and Signal Processing, vol. 150, no. 5, pp.331-338, Oct. 2003.
[12] Y.-C. Lim, J.-H. Lee, C.-K. Chen, and R.H. Yang, “A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design,” IEEE Trans. on Signal Processing, vol.40, pp.551-558, Mar. 1992.
[13] P. P. Vaidyanathan, Multirate Systems and Filter Banks, Englewood Cliffs, New Jersey: Prentice-Hall, 1992.
[14] Cheney, E. W., Introduction to Approximation Theory, New York: McGraw-Hill, 1966.
[15] Nelder, J. A. and Meade, R., “A simplex method for function minimization,” Comput. J., vol. 7, pp. 308-313, 1965.