Abstract
This chapter provides a detailed implementation of speech enhancement algorithm using fractional Fourier transform technique. Dual channel adaptive noise cancellation setup has been considered for the present study. Two adaptive algorithms, viz. LMS and NLMS algorithms, are implemented in FrFT domain. FrFT-based adaptive filters overcome the difficulties of adaptation in time-varying signal environment by transforming the signals into fractional Fourier domain, where signals vary slowly. The advantage of using the fractional Fourier domain is that the non-bandlimited signal in Fourier domain may be bandlimited in the fractional Fourier domain for a certain value of angle. In this chapter, special attention has been given to the concepts of continuous fractional Fourier transform (CFrFT) technique and its digital implementation. As preliminaries, the basics of ANC and adaptive filters are described in Sect. 3.1. Adaptive filters are described in Sect. 3.2. Adaptive filters in FrFT domain and the application of FrFT-based adaptive filters to speech enhancement are discussed in Sect. 3.3. The mathematical formulae and the background concepts of objective measures used for the evaluation of algorithms have also been presented. Results, analysis, and the conclusions of this chapter are given in Sects. 3.4 and 3.5, respectively.
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References
Almeida, L. B. (1994). The fractional Fourier transform and time-frequency representations. IEEE Transactions on Signal Processing, 42(11), 3084–3091.
ANSI. (1997). Methods for calculation of the speech intelligibility index. Technical report S3.5-1997. New York: American National Standards Institute.
Douglas, S. C. (1994). A family of normalized LMS algorithms. IEEE Signal Processing Letters, 1(3), 49.
Hayes, M. H. (2000). Statistical digital signal processing and modeling. New York: Wiley. ISBN: 0-471-59431-8.
Haykin, S. (2001). Adaptive filter theory (4th ed.). Upper Saddle River: Prentice Hall.
Haykin, S. S., & Widrow, B. (Eds.). (2003). Least-mean-square adaptive filters. Hoboken: Wiley.
Kutay, M. A., Ozaktas, H. M., Onural, L., & Arıkan, O. (1995). Optimal filtering in fractional Fourier domains. In Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing (pp. 937–940).
Lohmann, A. W. (1993). Image rotation, Wigner rotation and the fractional Fourier transform. Journal of the Optical Society of America A, 10, 2181–2186.
Ma, J., Loizou, P. C., & Loss, S. N. R. (2011). A new objective measure for predicting speech intelligibility of noise-suppressed speech. Speech Communication, 53(3), 340–354.
McBride, A. C., & Kerr, F. H. (1987). On namias’ fractional Fourier transforms. IMA Journal of Applied Mathematics, 39, 159–175.
Mendlovic, D., & Ozaktas, H. M. (1993). Fractional Fourier transformations and their optical implementation: Part I. Journal of the Optical Society of America A, 10, 1875–1881.
Mendlovic, D., Ozaktas, H. M., & Lohmann, A. W. (1993). Fourier transforms of fractional order and their optical interpretation. In Proceedings of the Topical Meeting on Optical Computing, OSA Technical Digest Series, Washington, DC (pp. 127–130).
Namias, V. (1980). The fractional order Fourier transform and its application to quantum mechanics. IMA Journal of Applied Mathematics, 25, 241–265.
Ozaktas, H. M., & Mendlovic, D. (1993a). Fourier transforms of fractional order and their optical interpretation. Optics Communication, 101, 163–169.
Ozaktas, H. M., & Mendlovic, D. (1993b). Fractional Fourier transformations and their optical implementation: Part II. Journal of the Optical Society of America A, 10, 2522–2531.
Ozaktas, H. M., & Mendlovic, D. (1995). Fractional Fourier optics. Journal of the Optical Society of America A, 12, 743–751.
Ozaktas, H. M., Zalevsky, Z., & Kutay, M. A. (2001). The fractional Fourier transform. Chichester: Wiley.
Pei, S. C., & Ding, J. J. (2003). Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms. Journal of the Optical Society of America A, 20(3), 522–532.
Pei, S. C., & Ding, J. J. (2007a). Relations between Gabor transforms and fractional Fourier transforms and their applications for signal processing. IEEE Transactions on Signal Processing, 55(10), 4839–4850.
Pei, S. C., & Ding, J. J. (2007b). Eigen functions of Fourier and fractional Fourier transforms with complex offsets and parameters. IEEE Transactions on Signal Processing, 54(7), 1599–1611.
Pei, S. C., Hsue, W. L., & Ding, J. J. (2006). Discrete fractional Fourier transform based on new nearly tridiagonal commuting matrices. IEEE Transactions on Signal Processing, 54(10), 3815–3828.
Pei, S. C., & Yeh, M. H. (1997). Improved discrete fractional Fourier transform. Optics Letters, 22, 1047–1049.
Santhanam, B., & McClellan, J. H. (1995). The DRFT—A rotation in time frequency space. In Proceedings of the ICASSP (pp. 921–924).
Treichler, J. R., Johnson, C. R., & Larimore, M. G. (1987). Theory and design of adaptive filters. New York: Wiley.
Widrow, B., & Stearns, S. (1985). Adaptive signal processing. Englewood Cliffs, NJ: Prentice Hall.
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Kunche, P., Manikanthababu, N. (2020). Dual Channel Speech Enhancement Based on Fractional Fourier Transform. In: Fractional Fourier Transform Techniques for Speech Enhancement. SpringerBriefs in Speech Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-42746-7_3
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