Abstract
In addition to the DFT, (WHT) w , (WHT) h , and MWHT, there are several other discrete orthogonal transforms. Of these, we will study the following in this chapter: (1) Generalized transform, (2) Haar transform, (3) slant transform, and (4) the discrete cosine transform.
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References
Ohnsorg, F. R.: Application of Walsh Functions to Complex Signals. Proc. 1970 Symp. Applications of Walsh Functions, 123-127.
Ohnsorg, F. R.: Properties of Complex Walsh Functions. Proc. IEEE Fall Electronics Conf., Chicago, Oct. 18-20, 1971, 383-385.
Rao, K. R., and Ahmed, N.: Complex BIFORE Transform. Int. J. Systems Sci. 2 (1971) 149–162.
Ahmed, N., and Rao, K. R.: Generalized Transform. Proc. 1971 Symp. Applications of Walsh Functions, 60-67.
Ahmed, N., and Rao, K. R.: A Generalized Discrete Transform. Proc. IEEE 59 (1971) 1360–1362.
Rao, K. R., Ahmed, N., and Schultz, R. B.: A Class of Discrete Orthogonal Transforms. Intl. Symp. Circuit Theory, April 9–11, 1973, Toronto, Canada. Published in the Symp. Digest, 189–192.
Rao, K. R., Mrig, L. C., and Ahmed, N.: A Modified Generalized Discrete Transform. Proc. IEEE 61 (1973) 668–669.
Ahmed, N., Natarajan, T., and Rao, K. R.: Some Considerations of the Modified Walsh-Hadamard and Haar Transforms. Proc. 1973 Symp. Applications of Walsh Functions, 91-95.
Andrews, H. C., and Caspari, K. L.: A Generalized Technique for Spectral Analysis. IEEE Trans. Computers C-19 (1970) 16–25.
Cooley, J. W., and Tukey, J. W.: An Algorithm for the Machine Calculation of Complex Fourier Series. Math. Computation 19 (1965) 297–301.
Enomoto, H., and Shibata, K.: Orthogonal Transform Coding System for Television Signals. Proc. 1971 Symp. Applications of Walsh Functions, 11-17.
Pratt, W. K., Welch, L. R., and Chen, W. H.: Slant Transforms for Image Coding. Proc. 1972 Symp. Applications of Walsh Functions, 229-234.
Chen, W. H., and Pratt, W. K.: Color Image Coding with the Slant Transform. Proc. 1973 Symp. Applications of Walsh Functions, 155-161.
Shibata, K.: Waveform Analysis of Image Signals by Orthogonal Transformation. Proc. 1972 Symp. Applications of Walsh Functions, 210-215.
Shibata, K.: Block Waveform Coding of Image Signals by Orthogonal Transformation. Proc. 1973 Symp. Applications of Walsh Functions, 137-143.
Ahmed, N., Natarajan, T., and Rao, K. R.: Discrete Cosine Transform. IEEE Trans. Computers C-23 (1974) 90–93.
Fike, C. T.: Computer Evaluation of Mathematical Functions. Englewood Cliffs, N. J.: Prentice Hall, 1968.
Bellman, R.: Introduction to Matrix Analysis. New York: McGraw-Hill, 1960.
Grenander, V., and Szego, G.: Toeplitz Forms and Their Applications. Berkeley and Los Angeles: University of California Press, 1958.
Andrews, H. C., and Kane, J.: Kronecker Matrices, Computer Implementation, and Generalized Spectra. J. Assoc. Comput. Mach. 17 (1970) 260–268.
Whelchel, J. E., and Guinn, D. F.: The Fast Fourier-Hadamard Transform and Its Use in Signal Representation and Classification. EASCON ’68 Record, 1968, 561-573.
Brigham, E. O., and Morrow, R. E.: The Fast Fourier Transform. IEEE Spectrum 4, Dec. 1967, 63–70.
Glassman, J. A.: A Generalization of the Fast Fourier Transform. IEEE Trans. Computers C-19 (1970) 105–116.
Theilheimer, F.: A Matrix Version of the Fast Fourier Transform. IEEE Trans. Audio and Electroacoustics AU-17 (1969) 158–161.
Gentleman, W. M.: Matrix Multiplication and the Fast Fourier Transform. Bell System Tech. J. 47 (1968) 1099–1103.
Rao, K. R., and Ahmed, N.: Modified Complex BIFORE Transform. Proc. IEEE 60 (1972) 1010–1012.
Rao, K. R., Mrig, L. C., and Ahmed, N.: A Modified Generalized Discrete Transform. Proc. Sixth Asilomar Conf. on Circuits and Systems, 1972, 189-195.
Fino, B. J.: Relations Between Haar and Walsh-Hadamard Transforms. Proc. IEEE 60 (1972) 647–648.
Gibbs, J. E.: Discrete Complex Walsh Functions. Proc. 1970 Symp. Applications of Walsh Functions, 106-122.
Elliott, D. F.: A Class of Generalized Continuous Orthogonal Transforms. IEEE Trans. Acoustics, Speech and Signal Processing ASSP-23 (1974) 245–254.
Ahmed, N., Natarajan, T., and Rao, K. R.: Cooley-Tukey type Algorithm for the Haar Transform. Electronics Letters 9 (1973) 276–278.
Revuluri, K., et al.: Complex Haar Transform. Proc. Seventh Asilomar Conference on Circuits, Systems, and Computers. Pacific Grove, California, Nov. 27-29, 1973, 729-733.
Elliott, D. F.: A Transform Class Governed by Signed-Bit Dyadic Time Shift. 1974 International Symposium on Circuits and Systems, San Francisco, Calif. April 22-24, 1974.
Pratt, W. K., et al.: Slant Transform Image Coding. IEEE Trans. Communications COM-22 (1974) 1075–1093.
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Ahmed, N., Rao, K.R. (1975). Miscellaneous Orthogonal Transforms. In: Orthogonal Transforms for Digital Signal Processing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45450-9_7
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DOI: https://doi.org/10.1007/978-3-642-45450-9_7
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