A two-channel perfect reconstruction filter bank associated with the linear canonical transform

International Journal of Electronics

Volumn 2, Issue 2, 2014, Pages 72-82

  Fan, Shuai Shuai ^a   Li, Bing Zhao ^a   Xu, Tian Zhou ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Linear canonical transform (LCT); Perfect reconstruction (PR); Sampling rate conversion; Scaling operation; Two channel filer bank

Indexed keywords

BANDPASS FILTERS; FILTER BANKS; IMPORTANCE SAMPLING; SIGNAL PROCESSING;

LINEAR CANONICAL TRANSFORM; PERFECT RECONSTRUCTION; SAMPLING RATE CONVERSION; SCALING OPERATION; TWO CHANNEL;

MATHEMATICAL TRANSFORMATIONS;

EID: 84996490274     PISSN: 00207217     EISSN: 13623060     Source Type: Journal    
DOI: 10.1080/00207217.2014.880954     Document Type: Article

References (34)

1. Bai, R.-F., Li, B.-Z., & Cheng, Q.-Y. (2012). Wigner-Ville distribution associated with the linear canonical transform. Journal of Applied Mathematics, 2012, 1-11.
2. Barshan, B., Kutay, M. A., & Ozaktas, H. M. (1997). Optimal filters with linear canonical transformations. Optical Communications, 135, 32-36.
3. Deng, B., Tao, R., & Wang, Y. (2006). Convolution theorems for the linear canonical transform and their applications. Science in China Series F: Information Sciences, 49, 592-603
4. Ding, J.-J., & Pei, S.-C. (2013). Heisenberg’s uncertainty principles for the 2-D nonseparable linear canonical transforms. Signal Processing, 93, 1027-1043.
5. Fliege, N. J. (2000). Multirate digital signal processing: Multirate systems-filter banks-wavelets. New York: Wiley.
6. Healy, J. J., & Sheridan, J. T. (2009). Sampling and discretization of the linear canonical transform. Signal Processing, 89, 641-648.
7. Koc, A., Ozaktas, H. M., Candan, C., & Kutay, M. A. (2008). Digital computation of linear canonical transforms. IEEE Transactions on Signal Processing, 56, 2383-2394
8. Kou, K., Morais, J., & Zhang, Y. (2013). Generalized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis. Mathematical Methods in the Applied Science, 36, 1028-1041.
9. Lee, S., Zhao, W., Narasimha, R., & Rao, R.-M. (2003). Discrete-time models for statistically self-similar signals. IEEE Transactions on Signal Processing, 51, 1221-1230
10. Li, B.-Z., Tao, R., & Wang, Y. (2007). New sampling formulate related to linear canonical trans-form. Signal Processing, 87, 983-990.
11. Li, B.-Z., & Xu, T.-Z. (2012). Sampling in the linear canonical transform domain. Mathematical Problems in Engineering, 2012, 1-14.
12. Li, B.-Z., & Xu, T.-Z. (2012). Spectral analysis of sampled signals in the linear canonical transform domain. Mathematical Problems in Engineering, 2012, 1-19.
13. Li, C.-P., Li, B.-Z., & Xu, T.-Z. (2012). Approximating bandlimited signals associated with the LCT domain from nonuniform samples at unknown locations. Signal Processing, 92, 1658-1664
14. Meng, X.-Y., Tao, R., & Wang, Y. (2007). The fractional Fourier domain analysis of decimation and interpolation. Science in China Series F: Information Sciences, 50, 521-538.
15. Oktem, F. S., & Ozaktas, H. M. (2009). Exact relation between continuous and discrete linear canonical transforms. IEEE Transactions on Signal Processing, 57, 727-730
16. Ozaktas, H. M., Kutay, M. A., & Zalevsky, Z. (2000). The fractional fourier transform with applications in optics and signal processing. New York: Wiley.
17. Pei, S.-C., & Ding, J.-J. (2002). Eigenfunctions of linear canonical transform. IEEE Transactions on Signal Processing, 50, 11-26.
18. Pei, S.-C., & Kao, M.-P. (2005). A two-channel nonuniform perfect reconstruction filter bank with irrational down-sampling factors. IEEE Signal Processing Letters, 12, 116-119
19. Qiu, W., Li, B.-Z., & Li, X.-W. (2013). Speech recovery based on the linear canonical transform. Speech Communication, 55, 40-50.
20. Ramstad, T. A. (1984). Digital methods for conversion between arbitrary sampling frequencies. IEEE Transactions on Acoustic, Speech, Signal Processing, 30-32, 577-591
21. Sharma, K. K., & Joshi, S. D. (2006). Signal separation using linear canonical and fractional Fourier transforms. Optical Communications, 265, 454-460.
22. Tao, R., Deng, B., & Wang, Y. (2009). Theory and applications of the fractional fourier transform. Beijing: Tsinghua University Press.
23. Tao, R., Li, B.-Z., & Wang, Y. (2008). On sampling of bandlimited signals associated with the linear canonical transform. IEEE Transactions on Signal Processing, 56, 5454-5464
24. Vaidyanathan, P. P. (1992). Multirate systems and filter banks. Upper Saddle River, NJ: Prentice Hall
25. We, D., Ran, Q., & Li, Y. (2012). A convolution and correlation theorem for the cinear canonical transform and its application. Circuits, Systems, and Signal Processing, 31, 301-312
26. We, D., Ran, Q., & Li, Y. (2013). Sampling of bandlimited signals in the linear canonical transform domain. Signal Image and Video Processing, 7, 553-558.
27. Wei, D., Ran, Q., & Li, Y. (2011). Reconstruction of band-limited signals from multichannel and periodic nonuniform samples in the linear canonical transform domain. Optics Communications, 284, 4307-4315.
28. Wei, D., Ran, Q., Li, Y., & Ma, J. (2009). A convolution and product theorem for the linear canonical transform. IEEE Signal Processing Letters, 16, 853-856.
29. Wolf, K. B. (1979). Integral transform in science and engineering. New York: Plenum Press.
30. Xiao, L., & Sun, W. (2013). Sampling theorems for signals periodic in the linear canonical transform domain. Optical Communications, 290, 14-18.
31. Xu, T.-Z., & Li, B.-Z. (2013). Linear canonical transform and its applications. Beijing: Science Press.
32. Yan, J.-P., Li, B.-Z., Chen, Y.-H., & Cheng, Q.-Y. (2013). Wigner distribution moments associated with the linear canonical transform. International Journal of Electronics, 100, 473-481
33. Zhao, J., Tao, R., Li, Y.-L., & Wang, Y. (2009). Uncertainty principles for linear canonical trans-form. IEEE Transactions on Signal Processing, 57, 2856-2858.
34. Zhao, J., Tao, R., & Wang, Y. (2008). Sampling rate conversion for linear canonical transform. Signal Processing, 88, 2825-2832.