Abstract
The design of general nonuniform filter banks is studied. Contrary to uniform filter banks, in nonuniform filter banks, it may not be possible to achieve perfect reconstruction, but in some cases by using optimization techniques, we can design acceptable filter banks. Here, the initial finite impulse response (FIR) analysis filters are designed according to the characteristics of the input. By the design procedure, the FIR synthesis filters are found so that theH-norm of an error system is minimized over all synthesis filters that have a prespecified order. Then, the synthesis filters obtained in the previous step are fixed, and the analysis filters are found similarly. By iteration, theH-norm of the error system decreases until it converges to its final value. At each iteration, the coefficients of the analysis or synthesis filters are obtained by finding the least squares solution of a system of linear equations. If necessary, the frequency characteristics of the filters can be altered by adding penalty terms to the objective function.
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References
T. Chen, Nonuniform multirate filter banks: Analysis and design with anH ∞ performance measure,IEEE Trans. Signal Process., 35, pp. 572–582, 1997.
T. Chen and B. A. Francis, Design of multirate filter banks byH ∞ optimization,IEEE Trans. Signal Process., 43, pp. 2822–2830, 1995.
T. Chen and L. Qiu, Linear periodically time-varying discrete-time systems: Aliasing and LTI approximations,Systems and Control Lett., vol. 30, pp. 225–235, 1997.
T. Chen, L. Qiu, and E. Bai, General multirate building structures with application to nonuniform filter banks, Special Issue on Multirate Systems, Filter Banks, Wavelets, and Applications,IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, 45, pp. 948–958, 1998.
R.E. Crochiere and L.R. Rabiner,Multirate Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1983.
P.-Q. Hoang and P.P. Vaidyanathan, Non-uniform multirate filter banks: Theory and design,Proc. IEEE Int. Symp. Circuits and Systems, Portland, OR, 1989, pp. 371–374.
M. R. K. Khansari and A. Leon-Garcia, Subband decomposition of signals with generalized sampling,IEEE Trans. Signal Process., 41, pp. 3365–3376, 1993.
J. Kovačević and M. Vetterli, Perfect reconstruction filter banks with rational sampling factors,IEEE Trans. Signal Process., 41, pp. 2047–2064, 1993.
T. Miyawaki and C.W. Barnes, Multirate recursive digital filters—A general approach and block structures,IEEE Trans. Acoust. Speech Signal Process., 31, pp. 1148–1154, Oct. 1983.
K. Nayebi, T.P. Barnwell, III, and M.J.T. Smith, Nonuniform filter banks: A reconstruction and design theory,IEEE Trans. Acoust. Speech Signal Process., 41, pp. 1114–1127, 1993.
P.P. Vaidyanathan,Multirate Systems and Filter Banks, Prentice-Hall, Englewood Cliffs, NJ, 1993.
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This research was supported by the Natural Sciences and Engineering Research Council of Canada.
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Mehr, A.S., Chen, T. Optimal design of nonuniform multirate filter banks. Circuits Systems and Signal Process 18, 505–521 (1999). https://doi.org/10.1007/BF01387469
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DOI: https://doi.org/10.1007/BF01387469