A unified approach to fast computation of discrete sinusoidal transforms I: DCT and DST transforms

Computers and Artificial Intelligence

Volumn 17, Issue 6, 1998, Pages 583-607

  Britaňák, Vladimír ^a  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Discrete Cosine Transform; Discrete Sine Transform; Discrete Sinusoidal Transforms; Discrete Trigonometric Transforms; Orthogonal Transforms

Indexed keywords

EID: 33748891622     PISSN: 02320274     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (55)

1. JAIN, A. K.: A Sinusoidal Family of Unitary Transforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-1, 1979, No. 4, pp. 356-365.
2. WANG, Z.: Fast Algorithms for the Discrete W Transform and for the Discrete Fourier Transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-32, 1984, No. 4, pp. 803-816.
3. FARRELLE, P. M. - SRINIVASAN, S. - JAIN, A. K.: A Unified Transform Architecture. In: Proc. IEEE of International Conference on Acoustics, Speech and Signal Processing, Tokyo, Japan, April 7-11, 1986, pp. 293-296.
4. ERSOY, O. - HU, N. C.: A Unified Approach to the Fast Computation of all Discrete Trigonometric Transforms. In: Proc. IEEE of International Conference on Acoustics, Speech and Signal Processing, Dallas, TX, April 6-9, 1987, pp. 1843-1846.
5. YIP, P. - RAO, K. R.: Fast Decimation-in-Time Algorithms for a Family of Discrete Sine and Cosine Transforms. Circuits, Systems and Signal Processing, Vol. 3, 1984, pp. 387-408.
6. YIP, P. - RAO, K. R.: The Decimation-in-Frequency Algorithms for a Family of Discrete Sine and Cosine Transforms. Circuits, Systems and Signal Processing, Vol. 7, 1988, No. 1, pp. 3-19.
7. VENKATARAMAN, S. - KANGHAN, V. R. - RAO, K. R. - MOHANTY, M.: Discrete Transforms via the Walsh-Hadamard Transform. Signal Processing, Vol. 14, 1988, No. 4, pp. 371-382.
8. CHAN, S. C. - HO, K. L.: Direct Methods for Computing Discrete Sinusoidal Transforms. IEE Proceedings-F: Radar and Signal Processing, Vol. 137, 1990, pp. 433-442.
9. WANG, Z.: Fast Discrete Sine Transform Algorithms, Signal Processing, Vol. 19, 1990, No. 2, pp. 91-102.
10. ELLIOT, D. F. - RAO, K. R.: Fast Transforms: Algorithms, Analyses, Applications. Academic Press, New York, 1982.
11. STOER, J. - BULIRSCH, R.: Introduction to Numerical Analysis. Springer Verlag, New York 1980, Chapter 2, Section 2.3 Trigonometric Interpolation, pp. 72-93.
12. AHMED, N. - RAO, K. R.: Orthogonal Transforms for Digital Signal Processing. Springer Verlag, Berlin, 1975.
13. RAO, K. R. - YIP, P.: Discrete Cosine Transform: Algorithms, Advantages and Applications. Academic Press, Boston, 1990.
14. CLARKE, R. J.: Transform Coding of Images. Academic Press, London, 1990.
15. PRATT, W. K.: Digital Image Processing. Wiley-Interscience, 2nd Edition, New York, 1991.
16. ROSENFELD, A. - KAK, A. C.: Digital Picture Processing. 2nd Edition, Vol. 1, Academic Press, San Diego, 1982.
17. JAIN, A. K.: Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
18. GONZALEZ, R. C. - WOODS, R. E.: Digital Image Processing. Addison-Wesley, Reading, Massachusetts, 1992.
19. PITAS, I.: Digital Image Processing Algorithms. Prentice-Hall, New York 1993.
20. PRATT, W. K.: Image Transmission Techniques. Academic Press, New York 1979.
21. RABBANI, M. - JONES, P. W.: Digital Image Compression Techniques. SPIE Optical Engineering Press, Tutorial text in optical engineering, Vol. TT 7, Washington 1991.
22. JAIN, A. K.: A Fast Karhunen-Loève Transform for a Class of Random Processes. IEEE Transactions on Communications, Vol. COM-24, 1976, pp. 1023-1029.
23. KEKRE, H. B. - SOLANKI, J. K.: Comparative Performance of Various Trigonometric Unitary Transforms for Transform Image Coding, International Journal of Electronics. Vol. 44, 1978, No. 3, pp. 305-315.
24. AHMED, N. - NATARAJAN, T. - RAO, K. R.: Discrete Cosine Transform. IEEE Transactions on Computers, Vol. C-23, 1974, No. 1, pp. 88-93.
25. LEE, B. G.: A New Algorithm to Compute the Discrete Cosine Transform. IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-32, 1984, No. 6, pp. 1243-1245.
26. HOU, H. S.: A Fast Recursive Algorithm for Computing the Discrete Cosine Transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-35, 1987, No. 10, pp. 1455-1461.
27. VETTERLI, M. - NUSSBAUMER, H. J.: Simple FFT and DCT Algorithms with Reduced Number of Operations, Signal Processing, Vol. 6, 1984, pp. 267-278.
28. n DCT Algorithms Suitable for VLSI Implementation. IEEE Proceedings of International Conference on Acoustics, Speech, and Signal Processing, Dallas, TX, April 6-9, 1987, pp. 1805-1808.
29. VETTERLI, M. - DUHAMEL, P. - GUILLEMOT, CH.: Trade-off's of Mono- and Multi-Dimensional DCT's. IEEE Proceedings of International Conference on Acoustics, Speech, and Signal Processing, Glasgow, Scotland, May 23-26, 1989, pp. 999-1002.
30. ARGUELLO, F. - ZAPATA, E. L.: Fast Cosine Transform based on the Successive Doubling Method, Electronics Letters, Vol. 26, 1990, No. 19, pp. 1616-1618.
31. WANG, Z.: Pruning the Fast Discrete Cosine Transform. IEEE Transactions on Communications, Vol. 39, 1991, No. 5, pp. 640-643.
32. SKODRAS, A. N.: Fast Discrete Cosine Transform Pruning. IEEE Transactions on Signal Processing, Vol. 42, 1994, No. 7, pp. 1833-1837.
33. WANG, Z.: A Fast Algorithm for the Discrete Sine Transform Implemented by the Fast Cosine Transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-30, 1982, No. 5, pp. 814-815.
34. WANG, Z. - HUNT, B. R.: Comparative Performance of Two Different Versions of the Discrete Cosine Transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-32, 1984, No. 2, pp. 450-453.
35. WANG, Z.: On Computing the Discrete Fourier and Cosine Transforms. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-33, 1985, No. 4, pp. 1341-1344.
36. SUEHIRO, N. - HATORI, M.: Fast Algorithms for the DFT and Other Sinusoidal Transforms. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-34, 1986, No. 3, pp. 642-644.
37. HEIN, D. - AHMED, N.: On a Real-Time Walsh-Hadamard/Cosine Transform Image Processor. IEEE Transactions on Electromagnetic Compatibility, Vol. EMC-20, 1978, No. 3, pp. 453-457.
38. KITAJIMA, H.: A Symmetric Cosine Transform. IEEE Transactions on Computers, Vol. C-29, 1980, No. 4, pp. 317-323.
39. YIP, P. - RAO, K. R.: On the Computation, the Effectiveness of Discrete Sine Transform. Computers, Electrical Engineering, Vol. 7, 1980, No. 1, pp. 45-55.
40. YIP, P. - RAO, K. R.: A Fast Computational Algorithm for the Discrete Sine Transform. IEEE Transactions on Communications, Vol. COM-28, 1980, No. 2, pp. 304-307.
41. WANG, Z.: Comments on a Fast Computational Algorithm for the Discrete Sine Transform. IEEE Transactions on Communications, Vol. COM-34, 1986, No. 2, pp. 204-205.
42. SUN, C. W. - YIP, P.: Split-Radix Algorithms for DCT and DST, Asilomar Conference on Signals. Systems and Computers, Pacific Grove, CA, November 1989, pp. 508-512.
43. YAO, J. C. - HSU, C. Y.: New Approach for Fast Sine Transform. Electronics Letters, Vol. 28, 1992, No. 15, pp. 1398-1399.
44. YAO, J. C. - HSU, C. Y.: Further Results on New Recursive Algorithms for the Discrete Cosine and Sine Transforms. IEEE Transactions on Signal Processing, Vol. 42, 1994, No. 11, pp. 3254-3255.
45. LEE, P. Z. - HUANG, F. Y.: Restructured Recursive DCT and DST Algorithms. IEEE Transactions on Signal Processing, Vol. 42, 1994, No. 7, pp. 1600-1609.
46. BISHERURWA, E. J. K. - COAKLEY, F. P.: New Fast Discrete Sine Transform with offset. Electronics Letters, Vol. 17, 1981, No. 21, pp. 803-805.
47. GUPTA, A. - RAO, K. R.: A Fast Recursive Algorithm for the Discrete Sine Transform. IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-38, 1990, No. 3, pp. 553-557.
48. CVETKOVIC, Z. - POPOVIC, M. V.: New Fast Algorithms for the Computation Discrete Cosine and Sine Transforms. IEEE Transactions on Signal Processing, Vol. 40, 1992, No. 8, pp. 2083-2086.
49. YIP, P. - RAO, K. R.: On the Shift Property of DCT's and DST's. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-35, 1987, No. 3, pp. 404-406.
50. BRITANAK, V.: On the Discrete Cosine Transform Computation. Signal Processing, Vol. 40, 1994, No. 2-3, pp. 183-194.
51. BRITANAK, V.: A Unified Discrete Cosine and Discrete Sine Transform Computation. Signal Processing, Vol. 43, 1995, No. 3, pp.333-339.
52. WANG, F. - YIP, P.: Cepstrum Analysis Using Discrete Trigonometric Transforms. IEEE Transactions on Signal Processing, Vol. 39, 1991, No. 2, pp. 538-541.
53. WANG, Z. - WANG, L.: Interpolation Using the Fast Discrete Sine Transform. Signal Processing, Vol. 26, 1992, No. 1, pp. 131-137.
54. MARTUCCI, S. A.: Symmetric Convolution and the Discrete Sine and Cosine Transforms. IEEE Transactions on Signal Processing, Vol. 42, 1994, No. 5, pp. 1038-1051.
55. WANG, Z. - HUNT, B. R.: The Discrete W Transform, Applied Mathematics and Computation, Vol. 16, 1985, pp. 19-48.