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On the design and realization of a class of uniform single rate FIR DFT filter banks

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Abstract

In this paper we present a computationally efficient realization of single rate uniform FIR filter banks for audio and spectral analysis applications. The channel filters in the analysis bank are represented as modulated versions of a prototype narrowband lowpass FIR filter. Using the IFIR filter design technique [23], [24], this prototype lowpass filter can be designed very efficiently as a cascade of two subfilters. The IFIR filter design is extended for the two-branch realization of uniform filter banks with overlapping channels. A generalized structure is presented which can be used for bothodd andeven stacking arrangements of the channels. The shaping filter structures for the two branches are realized from a single delay line and a single set of filter coefficients, thus conserving the total number of multipliers and delays in the overall realization. The postfilter structure, in conjunction with the Generalized DFT matrices, performs the channel selection. The Generalized DFT matrices are used to provide the necessary modulation for the postfilter coefficients so that the appropriate passbands are selected for each channel of the analysis bank. This leads to a polyphase network realization of the postfilter structure. We derive conditions so that the original input signal can be exactly reconstructed from the channel signals.

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References

  1. R. E. Crochiere and L. R. Rabiner,Multirate Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1983.

    Google Scholar 

  2. K. Swaminathan and P. P. Vaidyanathan, Design of Uniform, DFT, Parallel, FIR Quadrature Mirror Filters,Proc. IEEE Int. Symp. Circuits and Systems, San Jose, pp. 213–216, 1986.

  3. P. P. Vaidyanathan, Theory and Design of M-Channel Maximally-Decimated Quadrature Mirror Filters with ArbitraryM, Having Perfect Reconstruction Property, Technical Report, Department of Electrical Engineering, California Institute of Technology, 1986.

  4. K. Swaminathan and P. P. Vaidyanathan, Theory and Design of Uniform DFT, Parallel, Quadrature Mirror Filter Banks,IEEE Trans. Circuits and Systems, vol. 33, pp. 1170–1191, Dec. 1986.

    Google Scholar 

  5. M. Vetterli, Filter Banks Allowing Perfect Reconstruction,Signal Process., vol. 10, pp. 219–244, Apr. 1986.

    Google Scholar 

  6. H. J. Nussbaumer, Polynomial Transform Implementation of Digital Filter Banks,IEEE Trans. Acoust. Speech Signal Process., vol. 31, pp. 616–622, June 1983.

    Google Scholar 

  7. N. J. Nussbaumer and M. Vetterli, Computationally Efficient QMF Filter Banks,Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, San Diego, pp. 11.3.1–11.3.4, 1984.

  8. C. R. Galand and H. J. Nussbaumer, Quadrature Mirror Filters with Perfect Reconstruction and Reduced Computational Complexity,Proc. IEEE Int. Conf. Acoust., Speech,Signal Processing, Tampa, pp. 525–528, 1985.

  9. H. J. Nussbaumer, Complex Quadrature Mirror Filters,Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Boston, pp. 221–223, 1983.

  10. C. R. Galand and H. J. Nussbaumer, New Quadrature Mirror Filter Structures,IEEE Trans. Acoust. Speech Signal Process., vol. 32, pp. 522–531, June 1984.

    Google Scholar 

  11. V. K. Jain and R. E. Crochiere, A Novel Approach to the Design of Analysis/Synthesis Filter Banks,Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Boston, pp. 228–231, 1983.

  12. M. J. T. Smith and T. P. Barnwell III, A Unifying Framework for Analysis/Synthesis Systems Based on Maximally Decimated Filter Banks,Proc. IEEE Int. Conf. Acoust, Speech, Signal Processing, Tampa, pp. 521–524, 1985.

  13. J. D. Johnston, A Filter Family Designed for Use in Quadrature Mirror Filter Banks,Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Denver, pp. 291–294, 1980.

  14. P. L. Chu, Quadrature Mirror Filter Design for an Arbitrary Number of Equal Bandwidth Channels,IEEE Trans. Acoust. Speech Signal Process., vol. 33, pp. 203–218, Feb. 1985.

    Google Scholar 

  15. R. V. Cox, Quadrature Mirror Filters for Speech and Audio Processing,Proc. IEEE Int. Symp. Circuits and Systems, San Jose, pp. 285–288, 1986.

  16. R. V. Cox, The Design of Uniformly and Nonuniformly Spaced Pseudoquadrature Mirror Filters,IEEE Trans. Acoust. Speech Signal Process., vol. 34, pp. 1090–1096, Oct. 1986.

    Google Scholar 

  17. M. J. Narasimha, Design of FIR Filter Banks for a 24-Channel Transmultiplexer,IEEE Trans. Comm., vol. 30, pp. 1506–1510, July 1982.

    Google Scholar 

  18. J. P. Princen and A. B. Bradley, Analysis/Synthesis Filter Bank Design Based on Time Domain Cancellation,IEEE Trans. Acoust. Speech Signal Process., vol. 34, pp. 1153–1162, Oct. 1986.

    Google Scholar 

  19. Y. C. Lim, A Digital Filter Bank for Digital Audio Systems,IEEE Trans. Circuits and Systems, vol. 33, pp. 848–849, Aug. 1986.

    Google Scholar 

  20. M. G. Bellanger, G. Bonnerot, and M. Coudreuse, Digital Filtering by Polyphase Network: Application to Sample-Rate Alteration and Filter Banks,IEEE Trans. Acoust. Speech Signal Process., vol. 24, pp. 109–114, April 1976.

    Google Scholar 

  21. P. Vary and U. Heute, A Short-Time Spectrum Analyzer with Polyphase-Network and DFT,Signal Process., vol. 2, pp. 55–65, Jan. 1980.

    Google Scholar 

  22. U. Heute and P. Vary, A Digital Filter Bank with Polyphase Network and FFT Hardware: Measurements and Applications,Signal Process., vol. 3, pp. 307–319, Oct. 1981.

    Google Scholar 

  23. Y. Neuvo, C. Y. Dong, and S. K. Mitra, Interpolated Finite Impulse Filters,IEEE Trans. Acoust. Speech Signal Process., vol. 32, pp. 563–570, June 1984.

    Google Scholar 

  24. T. Saramäki, Y. Neuvo, and S. K. Mitra, Design of Computationally Efficient Interpolated FIR Filters,IEEE Trans. Circuits and Systems, vol. 35, pp. 70–88, Jan. 1988.

    Google Scholar 

  25. F. Mintzer, On Half-Band, Third-Band andNth-Band FIR Filters and Their Design,IEEE Trans. Acoust. Speech Signal Process., vol. 30, pp. 734–738, Oct. 1982.

    Google Scholar 

  26. J. K. Liang, R. J. P. DeFigueiredo, and F. C. Lu, Design of Optimal Nyquist, Partial Response,Nth Band and Nonuniform Tap Spacing FIR Digital Filters Using Linear Programming Techniques,IEEE Trans. Circuits and Systems, vol. 32, pp. 386–392, Apr. 1985.

    Google Scholar 

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Authors and Affiliations

  1. Tektronix, Inc., P.O. Box 500, 97077, Beaverton, Oregon, USA

    G. Rajan

  2. Signal Processing Laboratory, Department of Electrical Engineering, University of California, 93106, Santa Barbara, California, USA

    S. K. Mitra

  3. Department of Electrical Engineering, California Institute of Technology, 91125, Pasadena, California, USA

    P. P. Vaidyanathan

  4. Department of Electrical Engineering, Tampere University of Technology, SF-33101, Tampere, Finland

    Y. Neuvo

Authors
  1. G. Rajan
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  2. S. K. Mitra
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  3. P. P. Vaidyanathan
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  4. Y. Neuvo
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Additional information

This work was supported in part by the National Science Foundation under Grant MIP 85-08017 and in part by a University of California MICRO Grant with matching support from the Rockwell Corporation and the Intel Corporation.

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Rajan, G., Mitra, S.K., Vaidyanathan, P.P. et al. On the design and realization of a class of uniform single rate FIR DFT filter banks. Circuits Systems and Signal Process 9, 99–121 (1990). https://doi.org/10.1007/BF01187723

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  • DOI: https://doi.org/10.1007/BF01187723

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