Near-Perfect Reconstruction Oversampled Nonuniform Cosine-Modulated Filter Banks Based on Frequency Warping and Subband Merging
A novel method for designing near-perfect reconstruction oversampled nonuniform cosine-modulated filter banks is proposed, which combines frequency warping and subband merging, and thus offers more flexibility than known techniques. On the one hand, desirable frequency partitionings can be better approximated. On the other hand, at the price of only a small loss in partitioning accuracy, both warping strength and number of channels before merging can be adjusted so as to minimize the computational complexity of a system. In particular, the coefficient of the function behind warping can be constrained to be a negative integer power of two, so that multiplications related to allpass filtering can be replaced with more efficient binary shifts. The main idea is accompanied by some contributions to the theory of warped filter banks. Namely, group delay equalization is thoroughly investigated, and it is shown how to avoid significant aliasing by channel oversampling. Our research revolves around filter banks for perceptual processing of sound, which are required to approximate the psychoacoustic scales well and need not guarantee perfect reconstruction.
Recommendation ITU-R BS.1387-1 — Method for Objective Measurements of Perceived Audio Quality. International Telecommunications Union, 1999, ITU-R.
A. Karmakar, A. Kumar, and R. K. Patney, "Design of optimal wavelet packet trees based on auditory perception criterion," IEEE Signal Process. Lett., vol. 14, no. 4, pp. 240-243, Apr. 2007.
A. Pandharipande and S. Dasgupta, "On biorthogonal nonuniform filter banks and tree structures," IEEE Trans. Circuits Syst. I, vol. 49, no. 10, pp. 1457-1467, Oct. 2002.
W. Zhong, G. Shi, X. Xie, and X. Chen, "Design of linear-phase nonuniform filter banks with partial cosine modulation," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3390-3395, Jun. 2010.
Z. Cvetković and J. D. Johnston, "Nonuniform oversampled filter banks for audio signal processing," IEEE Trans. Speech Audio Process., vol. 11, no. 5, pp. 393-399, Sep. 2003.
E. Galijašević and J. Kliewer, "Design of allpass-based non-uniform oversampled DFT filter banks," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), vol. 2, Orlando, FL, 13-17 May 2002, pp. 1181-1184.
H. W. Löllmann and P. Vary, "Least-squares design of DFT filter-banks based on allpass transformation of higher order," IEEE Trans. Signal Process., vol. 58, no. 4, pp. 2393-2398, Apr. 2010.
X. Xie, S. Chan, and T. Yuk, "Design of linear-phase recombination nonuniform filter banks," IEEE Trans. Signal Process., vol. 54, no. 7, pp. 2809-2814, Jul. 2006.
J. Ogale and S. Ashok, "Cosine modulated non-uniform filter banks," Journal of Signal and Information Processing, vol. 2, pp. 178-183, 2011.
Y. Deng, V. Mathews, and B. Farhang-Boroujeny, "Low-delay nonuniform pseudo-QMF banks with application to speech enhancement," IEEE Trans. Signal Process., vol. 55, no. 5, pp. 2110-2121, May 2007.
J. Li, T. Q. Nguyen, and S. Tantaratana, "A simple design method for near-perfect-reconstruction nonuniform filter banks," IEEE Trans. Signal Process., vol. 45, no. 8, pp. 2105-2109, Aug. 1997.
J. O. Smith III and J. S. Abel, "Bark and ERB bilinear transforms," IEEE Trans. Speech Audio Process., vol. 7, no. 6, pp. 697-708, Nov. 1999.
P. Ghosh and S. Narayanan, "Bark frequency transform using an arbitrary order allpass filter," IEEE Signal Process. Lett., vol. 17, no. 6, pp. 543-546, Jun. 2010.
T. Gülzow, A. Engelsberg, and U. Heute, "Comparison of a discrete wavelet transformation and nonuniform polyphase filterbank applied to spectral-subtraction speech enhancement," Signal Process., vol. 64, no. 1, pp. 5-19, Jan. 1998.
G. Evangelista and S. Cavaliere, "Discrete frequency warped wavelets: Theory and applications," IEEE Trans. Signal Process., vol. 46, no. 4, pp. 874-885, Apr. 1998.
A. Petrovsky, M. Parfieniuk, and K. Bielawski, "Psychoacoustically motivated nonuniform cosine modulated polyphase filter bank," in Proc. 2nd Int. Workshop on Spectral Methods and Multirate Signal Process. (SMMSP), Toulouse, France, 7-8 Sep. 2002, pp. 95-101.
X. Zhang, L. Huang, and G. Evangelista, "Warped filter banks used in noisy speech recognition," in Proc. 4th Int. Conf. Innovative Computing, Information and Control (ICICIC), 7-9 Dec. 2009.
M. Livshitz, M. Parfieniuk, and A. Petrovsky, "Wideband CELP coder with multiband excitation and multilevel vector quantization based on reconfigurable codebook," Digital Signal Process. (KBWP, Moscow, Russia), no. 2, pp. 20-35, 2005, in Russian.
A. Borowicz, M. Parfieniuk, and A. Petrovsky, "An application of the warped discrete Fourier transform in the perceptual speech enhancement," Speech Comm., vol. 48, pp. 1024-1036, 2006.
H. W. Löllmann and P. Vary, "Uniform and warped low delay filterbanks for speech enhancement," Speech Communication, vol. 49, no. 207, pp. 574-587, 2007.
B. Shankar and A. Makur, "Allpass delay chain-based IIR PR filterbank and its application to multiple description subband coding," IEEE Trans. Signal Process., vol. 50, no. 4, pp. 814-823, Apr. 2002.
S. Caporale, L. De Marchi, and N. Speciale, "Frequency warping biorthogonal frames," IEEE Trans. Signal Process., vol. 59, no. 6, pp. 2575-2584, Jun. 2011.
W. H. Chin and B. Farhang-Boroujeny, "Subband adaptive filtering with real-valued subband signals for acoustic echo cancellation," IEE Proc.- Vis. Image Signal Process., vol. 148, no. 4, pp. 283-288, 2001.
A. Datar, A. Jain, and P. Sharma, "Design of Kaiser window based optimized prototype filter for cosine modulated filter banks," Signal Processing, vol. 90, pp. 1742-1749, 2010.
P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
P. Vary, "Digital filter banks with unequal resolution," in Proc. EUSIPCO Short Communication Digest, Lausanne, Switzerland, Sep. 1980, pp. 41-42.
G. Doblinger, "An efficient algorithm for uniform and nonuniform digital filter banks," in Proc. of Int. Symp. on Circuits and Systems (ISCAS), vol. 1, Singapore, Jun. 1991, pp. 646-649.
A. G. Constantinides, "Spectral transformations for digital filters," IEE Proc., vol. 117, no. 8, pp. 1585-1590, 1970.
M. Kappellan, B. Strauss, and P. Vary, "Flexible nonuniform filterbanks using allpass transformation of multiple order," in Proc. 8th European Signal Process. Conf. (EUSIPCO), vol. 3, Trieste, Italy, 7-13 Sep. 1996, pp. 1745-1748.
T. von Schroeter, "Frequency warping with arbitrary allpass maps," IEEE Signal Process. Lett., vol. 6, no. 5, pp. 116-118, May 1999.
M. Parfieniuk and A. Petrovsky, "Reduced complexity synthesis part of non-uniform near-perfect-reconstruction DFT filter bank based on all-pass transformation," in Proc. 16th European Conf. on Circuits Theory and Design (ECCTD), vol. III, Cracow, Poland, 1-4 Sep. 2003, pp. III-5-III-8.
H. W. Löllmann and P. Vary, "Parametric phase equalizers for warped filter-banks," in Proc. 14th European Signal Processing Conf. (EUSIPCO), Florence, Italy, 4-8 Sep. 2006.
J. M. de Haan, I. Claesson, and H. Gustafsson, "Least squares design of nonuniform filter banks with evaluation in speech enhancement," in Proc. Int. Conf. Acoustics, Speech, Signal Process. (ICASSP), vol. VI, Hong Kong, China, Apr. 2003, pp. 109-112.
B. Vo and S. Nordholm, "Non-uniform DFT filter bank design with semi-definite programming," in Proc. Int. Symp. Signal Process. Information Technology (ISSPIT), Darmstadt, Germany, 2003, pp. 42-45.
G. Kumar, P. Reddy, and B. Charles, "Design of non-uniform filter banks: Quadratic optimization with linear constraints," ARPN J. Engineering Applied Sciences, vol. 2, no. 3, pp. 24-27, Jun. 2007.
M. Parfieniuk and A. Petrovsky, "Simple rule of selection of subsampling ratios for warped filter banks," in Proc. VIII Int. Conf. "Modern Communication Systems", Naroch, Belarus, 29 Sep.-3 Oct. 2003, pp. 130-134, haapec. Issue of Trans. Belarus. Eng. Acad., No. 1(15)/3.
E. Galijašević and J. Kliewer, "Non-uniform near-perfect-reconstruction oversampled DFT filter banks based on allpass transforms," in Proc. 9th IEEE DSP Workshop (DSP 2000), Hunt, TX, 15-18 Oct. 2000.
A. Piotrowski and M. Parfieniuk, Digital Filter Banks: Analysis, Synthesis, and Implementation for Multimedia Systems. Bialystok, Poland: Wydawnictwo Politechniki Bialostockiej, 2006, in Polish.
H. W. Löllmann and P. Vary, "Improved design of oversampled allpass transformed DFT filter-banks with near-perfect reconstruction," in Proc. 15th European Signal Process. Conf. (EUSIPCO), Poznan, Poland, 3-7 Sep. 2007, pp. 50-54.
S. K. Mitra and K. Hirano, "Digital all-pass networks," IEEE Trans. Circuits Syst. I, vol. 21, no. 5, pp. 688-700, Sep. 1974.
B. Scharf, "Critical bands," in Foundations of Modern Auditory Theory, J. Tobias, Ed. New York, NY: Academic Press, 1970, pp. 159-202.
C. D. Creusere and S. K. Mitra, "Efficient audio coding using perfect reconstruction noncausal IIR filter banks," IEEE Trans. Speech Audio Process., vol. 4, no. 2, pp. 115-123, Mar. 1996.
G. Evangelista and S. Cavaliere, "Time-varying frequency warping: Results and experiments," in Proc. 2nd COST G-6 Workshop on Digital Audio Effects (DAFx), Trondheim, Norway, 9-11 Dec. 1999, pp. 13-16.
M. Quélhas and A. Petraglia, "Optimum design of group delay equalizers," Digital Signal Processing, vol. 21, pp. 1-12, 2011.
C. Feldbauer and G. Kubin, "Critically sampled frequency-warped perfect reconstruction filter bank," in Proc. European Conf. on Circuit Theory and Design (ECCTD), vol. III, Cracow, Poland, 1-4 Sep. 2003, pp. III-109-III-112.
R. G. Vaughan, N. L. Scott, and D. R. White, "The theory of bandpass sampling," IEEE Trans. Signal Process., vol. 39, no. 9, pp. 1973-1984, Sep. 1991.
P. Q. Hoang and P. P. Vaidyanathan, "Non-uniform multirate filter banks: Theory and design," in Proc. IEEE Int. Symp. Circuits Systems (ISCAS), Portland, OR, 8-11 May 1989, pp. 371-374.
J. D. Griesbach, M. R. Lightner, and D. M. Etter, "Subband adaptive filtering decimation constraints for oversampled nonuniform filterbanks," IEEE Trans. Circuits Syst. II, vol. 49, no. 10, pp. 677-681, Oct. 2002.