The linear time frequency analysis toolbox

International Journal of Wavelets, Multiresolution and Information Processing

Volumn 10, Issue 4, 2012, Pages

  SØndergaard, Peter L ^a   TorrÉsani, Bruno ^b   Balazs, Peter ^c  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b AIX MARSEILLE UNIVERSITY   (France)

^c ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

Author keywords

efficient algorithms; Gabor transform; mathematical software; Numerical harmonic analysis; representation of systems; signal processing; time frequency transforms

Indexed keywords

COMPUTATIONAL TOOLS; GABOR TRANSFORM; LINEAR TIME FREQUENCY; MATHEMATICAL SOFTWARE; SIGNAL PROCESSING APPLICATIONS; TIME FREQUENCY ANALYSIS; TIME-FREQUENCY TRANSFORMS;

ALGORITHMS; GABOR FILTERS; HARMONIC ANALYSIS; SIGNAL PROCESSING;

MATHEMATICAL TRANSFORMATIONS;

EID: 84864136055     PISSN: 02196913     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219691312500324     Document Type: Article

References (63)

1. J. Allen, Short term spectral analysis, synthesis, and modification by discrete Fourier transform, IEEE Trans. Acoustics, Speech Signal Process. ASSP-25 (1977) 235-238.
2. F. Auger and P. Flandrin, Improving the readability of time-frequency and time-scale representations by the reassignment method, IEEE Trans. Signal Process. 43 (1995) 1068-1089.
3. P. Balazs, Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl. 325 (2007) 571-585.
4. P. Balazs, Hilbert-Schmidt operators and frames-classification, best approximation by multipliers and algorithms, Int. J. Wavelets, Multiresolut. Inf. Process. 6 (2008) 315-330.
5. P. Balazs, J. Antoine and A. Grybos, Weighted and controlled frames: Mutual relationship and first numerical properties, Int. J. Wavelets, Multiresolut. Inf. Process. 8 (2010) 109.
6. P. Balazs, M. Dörfler, N. Holighaus, F. Jaillet and G. Velasco, Theory, implementation and application of nonstationary Gabor frames, J. Computational Applied Math. 236 (2011) 1481-1496.
7. P. Balazs and N. Engelputzeder, Representation of linear time invariant filters by Gabor multipliers, in preparation (2010).
8. P. Balazs, H. G. Feichtinger, M. Hampejs and G. Kracher, Double preconditioning for Gabor frames, IEEE Trans. Signal Process. 54 (2006) 4597-4610.
9. P. Balazs, B. Laback, G. Eckel and W. A. Deutsch, Time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking, IEEE Trans. Audio, Speech Language Process. 18 (2010) 34-49.
10. H. Bölcskei, Orthogonal frequency division multiplexing based on offset QAM, in Feichtinger and Strohmer, Chap. 12, pp. 321-352.
11. H. Bölcskei, H. G. Feichtinger, K. Gröchenig and F. Hlawatsch, Discrete-time Wilson expansions, in Proc. IEEE-SP 1996 Int. Sympos. Time-Frequency Time-Scale Analysis (1996).
12. H. Bölcskei, F. Hlawatsch and H. G. Feichtinger, Equivalence of DFT filter banks and Gabor expansions, in SPIE 95, Wavelet Appl. Signal Image Process. III, Vol. 2569, Part I (San Diego, July 1995).
13. H. Bölcskei, F. Hlawatsch and H. G. Feichtinger, Frame-theoretic analysis of oversampled filter banks, IEEE Trans. Signal Process. 46 (2002) 3256-3268.
14. R. Carmona, W. Hwang and B. Torŕesani, Practical time-frequency analysis: Continuous wavelet and gabor transforms, with an implementation in S, Wavelet Analysis and Its Applications, Vol. 9 (Academic Press, San Diego, 1998).
15. R. Carmona, W. Hwang and B. Torŕesani, Multiridge detection and time-frequency reconstruction, IEEE Trans. Signal Process. 47 (1999) 480-492.
16. O. Christensen, An Introduction to Frames and Riesz Bases (Birkhäuser, 2003).
17. I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Commun. Pure Appl. Math. 57 (2004) 1413-1457.
18. M. Dolson, The phase vocoder: A tutorial, Computer Musical J. 10 (1986) 11-27.
19. D. L. Donoho, De-noising by soft-thresholding, IEEE Trans. Inf. Theory 41 (1995) 613-627.
20. M. Dörfler and B. Torŕesani, Representation of operators in the time-frequency domain and generalized Gabor multipliers, J. Fourier Anal. Appl. 16 (2010) 261-293.
21. H. Feichtinger, M. Hazewinkel, N. Kaiblinger, E. Matusiak and M. Neuhauser, Metaplectic operators on Cn, The Quarterly Journal of Mathematics 59 (2008) 15.
22. H. G. Feichtinger and K. Nowak, A first survey of Gabor multipliers, in Feichtinger and Strohmer, Chap. 5, pp. 99-128.
23. H. G. Feichtinger and T. Strohmer, Gabor Analysis and Algorithms (Birkhäuser, Boston, 1998).
24. H. G. Feichtinger and T. Strohmer, Advances in Gabor Analysis (Birkhäuser, 2003).
25. J. Flanagan, D. Meinhart, R. Golden and M. Sondhi, Phase vocoder, J. Acoust. Soc. America 38 (1965) 939.
26. P. Flandrin, Time-frequency/time-scale analysis, Vol. 10 of Wavelet Analysis Appl. (Academic Press Inc., San Diego, CA, 1999). With a preface by Yves Meyer, Translated from the French by Joachim Stöckler.
27. M. Frigo and S. G. Johnson, The design and implementation of FFTW3. Proc. IEEE 93 (2005) 216-231. Special issue on "Program Generation, Optimization, and Platform Adaptation".
28. D. Griffin and J. Lim, Signal estimation from modified short-time Fourier transform, 32 (1984) 236-243.
29. K. Gröchenig, Foundations of Time-Frequency Analysis (Birkhäuser, 2001).
30. L. Jacques, A. Coron, P. Vandergheynst and A. Rivoldini, The YAWTb toolbox: Yet another wavelet toolbox, 2007. http://rhea.tele.ucl.ac.be/yawtb.
31. F. Jaillet, P. Balazs, M. Dörfler and N. Engelputzeder, Nonstationary Gabor frames, in SAMPTA'09 (Marseille, May 2009), pp. 18-22.
32. A. J. E. M. Janssen and P. L. Soøndergaard. Iterative algorithms to approximate canonical Gabor windows: Computational aspects, J. Fourier Anal. Appl. 13 (2007) 211-241.
33. N. S. Jayant and P. Noll, Digital Coding of Waveforms (Prentice-Hall, 1984).
34. M. Kowalski, Sparse regression using mixed norms, Appl. Comput. Harmonic Anal. 27 (2009) 303-324.
35. M. Kowalski and B. Torŕesani, Sparsity and persistence: Mixed norms provide simple signal models with dependent coefficients, Signal, Image Video Process. 3 (2009) 251-264, doi: 10.1007/s11760-008-0076-1.
36. Y.-P. Lin and P. Vaidyanathan, Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction, IEEE Trans. Signal Process. 43 (1995) 2525-2539.
37. P. Majdak, P. Balazs, W. Kreuzer and M. Dörfler, A time-frequency method for increasing the signal-to-noise ratio in system identification with exponential sweeps, in Proceedings-ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing, 2011.
38. P. Majdak, P. Balazs and B. Laback, Multiple exponential sweep method for fast measurement of head related transfer functions, J. Audio Eng. Soc. 55 (2007) 623-637.
39. H. S. Malvar, Signal Processing with Lapped Transforms (Artech House Publishers, 1992).
40. G. Matz and F. Hlawatsch, Linear time-frequency filters: On-line algorithms and applications, in Application in Time-Frequency Signal Processing, Chap. 6, eds. A. Papandreou-Suppappola, Boca Raton (FL) (CRC Press, 2002), pp. 205-271.
41. D. Mugler, S. Clary and Y. Wu, Discrete Hermite expansion of digital signals: Applications to ECG signals, Digital Signal Processing Workshop, 2002 and the 2nd Signal Processing Education Workshop. Proceedings of 2002 IEEE 10th (2002), pp. 262-267.
42. S. Nadarajah, GG DCT coefficient models, Int. J. Wavelets, Multiresolut. Inf. Process. 8 (2010) 793-812.
43. A. V. Oppenheim and R. W. Schafer, Discrete-time Signal Processing (Prentice Hall, Englewood Cliffs, NJ, 1989).
44. H. M. Ozaktas, Z. Zalevsky and M. A. Kutay, The Fractional Fourier Transform (John Wiley and Sons, 2001).
45. J. P. Princen and A. B. Bradley, Analysis/synthesis filter bank design based on time domain aliasing cancellation, IEEE Trans. Acoustics, Speech, Signal Process. ASSP-34 (1986) 1153-1161.
46. J. P. Princen, A. W. Johnson and A. B. Bradley, Subband/transform coding using filter bank designs based on time domain aliasing cancellation, Proceedings-ICASSP, IEEE Int. Conference Acoustics, Speech Signal Process. (1987), pp. 2161-2164.
47. P. Prinz, Calculating the dual Gabor window for general sampling sets, IEEE Trans. Signal Process. 44 (1996) 2078-2082.
48. K. Rao and P. Yip, Discrete Cosine Transform, Algorithms, Advantages, Applications (Academic Press, 1990).
49. P. L. Soøndergaard, Finite Discrete Gabor Analysis, Ph.D. thesis, 2007.
50. P. L. Soøndergaard, Symmetric, discrete fractional splines and Gabor systems, preprint, 2008.
51. P. L. Soøndergaard, Efficient algorithms for the discrete Gabor transform with a long FIR window, J. Fourier Anal. Appl. 18 (2011) 456-470. DOI 10.1007/500041-011-9210-5.
52. J. Strawn, Digital Audio Signal Processing-An Anthology (William Kaufmann, Inc., 1985).
53. T. Strohmer, Numerical algorithms for discrete Gabor expansions, in Feichtinger and Strohmer, Chap. 8, pp. 267-294.
54. T. Strohmer, Approximation of dual Gabor frames, window decay, and wireless communications, Appl. Comput. Harmon. Anal. 11 (2001) 243-262.
55. P. Tseng, Dual coordinate ascent methods for non-stricly convex minimization, Math. Programming 59 (1993) 231-247.
56. M. Vetterli and J. Kovacevíc, Wavelets and Subband Coding, Signal Processing Series (Prentice Hall, Englewood Cliffs, NJ, 1995).
57. E. Wesfreid and M. Wickerhauser, Adapted local trigonometric transforms and speech processing, IEEE Trans. Signal Process. 41 (1993) 3596-3600.
58. M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software (Wellesley-Cambridge Press, Wellesley, MA, 1994).
59. B.Widrow and S. D. Stearns, Adaptive Signal Process. (Prentice-Hall, Inc., Englewood Cliffs, NJ, 1985).
60. Wikipedia, List of audio codecs, 2007
61. Wikipedia, Noise reduction, 2010.
62. P. Wojdllo, Wilson system for triple redundancy, Int. J. Wavelets, Multiresolut. Inf. Process. 9 (2011) 151-167.
63. O. Yilmaz and S. Rickard, Blind separation of speech mixtures via time-frequency masking, IEEE Trans. Signal Process. 52 (2004) 1830-1847.