zbMATH — the first resource for mathematics

The discrete W transform. (English) Zbl 0567.65096
Four different versions of the discrete W-transform (DWT) are introduced. The DWT procedure is useful for analyzing integer and fractional harmonics. The version of the DWT is chosen depending on the symmetry of the data sequence in the spatial domain and in the frequency domain. The DWT is decomposed into the discrete cosine transform (DCT) and the discrete sine transform (DST). Eight versions of both DCT and DST are associated with the four versions of the DWT. The relation among different versions of the DWT and that between them and discrete Fourier transform are discussed. Periodic and non-periodic convolutions and cross correlations are given.
Reviewer: Y.Kobayashi

65T40 Numerical methods for trigonometric approximation and interpolation
65R10 Numerical methods for integral transforms
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
PDF BibTeX Cite
Full Text: DOI
[1] Wang, Z., Harmonic analysis with a real frequency function. I. aperiodic case, Appl. math. comput., 9, 53-73, (1981) · Zbl 0483.42008
[2] Wang, Z., Harmonic analysis with a real frequency function. II. periodic and bounded cases, Appl. math. comput., 9, 153-163, (1981) · Zbl 0536.42004
[3] Wang, Z., Harmonic analysis with a real frequency function. III. data sequence, Appl. math. comput., 9, 245-255, (1981) · Zbl 0536.42004
[4] Andrews, H.C.; Pratt, W.K., Fourier transform coding of image, Hawaii international conference on system science, 677-679, (Jan. 1968)
[5] Andrews, H.C.; Pratt, W.K., Television bandwidth reduction by encoding spatial frequencies, Soc. motion picture and television engrs., 77, 1279-1281, (1968)
[6] Andrews, H.C.; Pratt, W.K., Transform image coding, (), 63-84
[7] Pratt, W.K.; Kane, J.; Andrews, H.C., Hadamard transform image coding, Proc. IEEE, 57, 58-68, (1969)
[8] Jain, A.K., A fast Karhunen-loeve transform for a class of stochastic processes, IEEE trans. comm., COM-24, 1023-1029, (1976) · Zbl 0357.62081
[9] Ahmed, H.; Natarajan, T.; Rao, K.R., Discrete cosine transform, IEEE trans. comput., C-23, 90-93, (1974) · Zbl 0273.65097
[10] Kekre, H.B.; Solanki, J.K., Comparative performance of various trigonometric unitary transforms for transform image coding, Internat. J. electron., 44, 305-315, (1978)
[11] Pratt, W.K., Digital image processing, (1978), Wiley New York, Chapters 10, 23
[12] Jain, A.K., A sinusoidal family of unitary transform, IEEE trans., PAMI-1, 356-365, (1979) · Zbl 0437.65110
[13] Z. Wang and B.R. Hunt, The discrete cosine transform—a new version, in Proceedings of 1983 International Conference on Acoustics, Speech, and Signal Processing.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.