Linear Periodic Systems and Multirate Filter Design

IEEE Transactions on Signal Processing

Volumn 42, Issue 9, 1994, Pages 2242-2256

  Shenoy, Ram G ^a   Burnside, Daniel ^b   Parks, Thomas W ^b  

^a SCHLUMBERGER DOLL RESEARCH   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIGITAL FILTERS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC NETWORK SYNTHESIS; ERRORS; FOURIER TRANSFORMS; INVARIANCE; LINEAR CONTROL SYSTEMS; LINEAR PROGRAMMING; NUMERICAL ANALYSIS; TIME VARYING SYSTEMS;

ERROR CRITERIA; LINEAR PERIODIC SYSTEMS; MULTIRATE FILTERS;

SIGNAL FILTERING AND PREDICTION;

EID: 0028499486     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.317847     Document Type: Article

References (51)

1. P. P. Vaidyanathan, “Multirate digital filters, filter banks polyphase networks, and applications: A tutorial,” Proc. IEEE, vol. 78, pp. 56–93, Jan. 1990.
2. M. Vetterli, “A theory of multirate filter banks,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-35, pp. 356–372, Mar. 1987.
3. R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1983.
4. R. G. Pridham and R. A. Mucci, “Digital interpolation beamforming for low-pass and bandpass signals,” Proc. IEEE, vol. 67, pp. 904–919, June 1979.
5. D. J. Scheibner and T. W. Parks, “Slowness aliasing in the discrete Radon transform: A multirate system approach to beamforming,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-32, pp. 1160–1165, Dec. 1984.
6. W. H. Mayne, “Common reflection point horizontal data stacking techniques,” Geophys., vol. 27, pp. 927–938, Dec. 1962.
7. G. Cortelazzo, “On the role of input signals in deterministic linear filtering,” IEEE Trans. Acoust. Speech Signal Process., vol. ASSP-34, pp. 203–205, Feb. 1986.
8. B. A. Weisbum, T. W. Parks, and R. G. Shenoy, “Error criteria for filter design,” in Proc. ICASSP '94, pp. 565–568, vol. 3.
9. R. G. Shenoy and T. W. Parks, “An optimal recovery approach to interpolation,” IEEE Trans. Signal Processing, vol. 40, pp, 1987–1996, Aug. 1992.
10. M. J. T. Smith and T. P. Barnwell, “A new filter bans theory for time-frequency representation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 314–327, Mar. 1987.
11. T. Ramstad, “Analysis/synthesis filterbanks with critical simpling,” in Proc. IEEE Conf. DSP, Nov. 1984.
12. P. P. Vaidyanathan, Multirate Systems and Filterbanks. Englewood Cliffs, NJ: Prentice Hall, 1993.
13. F. Mintzer and B. Liu, “Aliasing error in the design of mull irate filters,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-26, pp. 76–88, Feb. 1978.
14. C. M. Loeffler and C. S. Burrus, “Optimal design of periodically time-varying and multirate digital filters,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 991–997, Oct. 1984.
15. L. Zadeh, “Time-varying networks - 1,” in Proc. IRE, 1961, pp. 1488–1503.
16. L. Zadeh. “Frequency analysis of variable networks,” in Proc. IRE, 1950, pp. 291–299, vol. 38.
17. J. W. Adams, “FIR digital filters with least-squares stopbands subject to peak-gain constraints,” IEEE Trans. Circuits Syst., vol. 39, pp. 376–388, Apr. 1991.
18. M. G. Bellanger, G. Bonnerot, and M. Coudreuse, “Digital filtering by polyphase network: Application to sampling rate alteration and filter banks,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-24, pp. 109–114, Apr. 1976.
19. G. Oetken and H. W. Schüβler, “On the design of digital filters for interpolation,” A.E.V., vol. 27, no. 1, pp. 471–476, 1973.
20. G. Oetken, T. W. Parks, and H. W. SchiiBler, “New results in the design of digital interpolators,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-23, pp. 301–309, June 1975.
21. G. Oetken, “A new approach for the design of digital interpolating filters,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, pp. 637–643, Dec. 1979.
22. P. P. Vaidyanathan, “Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect reconstruction property,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 476–492, Apr. 1987.
23. M. Vetterli, “Filter banks allowing perfect reconstruction,” Signal Processing, vol. 10, pp. 219–244, July 1986.
24. P. P. Vaidyanathan, “Quadrature mirror filter banks, M-band extensions and perfect reconstruction techniques,” IEEE ASSP Mag., vol. 4, pp. 4–20, July 1987.
25. M. J. T. Smith and T. P. Barnwell, “A unifying framework for analysis/synthesis systems based upon maximally decimated ftlter banks,” in Proc. IEEE ICASSP 85, Mar. 1985, pp. 521–524.
26. M. J. T. Smith and T. P. Barnwell, “A procedure for designing exact reconstruction filter banks for tree structured sub-band coders,” in Proc. IEEE ICASSP 84 Mar. 1984.
27. M. J. T. Smith and T. P. Barnwell, “Exact reconstruction for tree-structured subband coders,” IEEE Trans. Acoust., Speech, Signal Procesing., vol. 34, pp. 43–441, June 1986.
28. R. A. Meyer and C. S. Burrus, “A unified analysis of multirate and periodically time-varying digital filters,” IEEE Trans. Circuits Syst., vol. CAS-22, pp. 162–168, Mar. 1975.
29. F. S. Cater, Lectures On Real and Complex Vector Spaces Philadelphia: W. B. Saunders, 1966.
30. J. Weidmann, Linear Operators in Hilbert Space. New York: Springer Verlag, 1980.
31. P. R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity. New York: Chelsea, 1957.
32. W. Rudin, Real and Complex Analysis. New York: McGraw-Hill, 1987.
33. W. Rudin, Functional Analysis. New York: McGraw-Hill, 1973.
34. L. B. Jackson, “On the interaction of roundoff noise and dynamic range in digital filters,” Bell Sys. Tech. J., vol. 49, pp. 159–184, Feb. 1970.
35. T. W. Parks and J. H. McClellan, “Chebyshev approximation for nonrecursive digital filters with linear phase,” IEEE Trans. Circuit Theory, vol. CT-19, pp. 189–194, Mar. 1972.
36. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore: Johns Hopkins Univ. Press, 1989.
37. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operatots. New York: American Math. Soc., 1969.
38. R. G. Douglas, Banach Algebra Techniques in Operator Theory. New York: Academic, 1972.
39. R. L. Reng and H. W. Schüβler, “Measurement of aliasing distortions and quantization noise in multirate systems,” in Proc. IEEE ISCAS 1992, 1992, pp. 2328–2331.
40. R. Shenoy, “Mathematics of linear periodic systems.” In preparation.
41. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1975.
42. M. Vetterli, “Invertibility of linear periodically time-varying filters,” IEEE Trans. Circuits Syst., vol. 36, pp. 148–150, Jan. 1989.
43. R. A. Gopinath, W. M. Lawton, and C. S. Burrus, “Wavelet-Galerkin approximation of linear translation invariant operators,” in Proc. IEEE ICASSP 91, May 1991, pp. 2021–2023.
44. T. Miyawaki and C. W. Barnes, “Multirate recursive digital filters—A general approach and block structures,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 1148–1154, Oct. 1983.
45. X. Chen and T. W. Parks, “Design of FIR filters in the complex domain,” IEEE Trans. Acoust., Speech Signal Processing, vol. ASSP-35, pp. 144–153, Feb. 1987.
46. R. L. Streit, “Solution of systems of complex linear equations in the l∞ norm with constraints on the unknowns,” SIAM J. Sci. Stat. Comput., vol. 7, pp. 132–149, Jan 1986.
47. P. T. P. Tang, “A fast algorithm for linear complex Chebyshev approximations,” Math. Comput., vol. 51, no. 3, pp. 721–739, 1988.
48. D. Burnside and T. W. Parks, “Accelerated design of FIR filters in the complex domain,” in Proc. ICASSP 93, Apr. 1993, pp. 81–84, vol. 3.
49. R. L. Streit and A. H. Nutall, “A general Chebyshev complex function approximation procedure and an application to beamforming,” J. Acoust. Soc. Amer., vol. 72, no. 1, pp. 181–190, 1982.
50. L. Veidinger, “On the numerical determination of the best approximations in the Chebyshev sense,” Numerische Mathematik, no. 2, pp. 99–105, 1960.
51. E. J. Anderson and P. Nash, “Linear programming in infinite-dimensional space,” in Discrete Mathematics and Optimization. New York: Wiley, 1987, pp. 35–90.