Conference Paper

Parallel computation of discrete Legendre transforms

Dept. of Electr. Eng., Bucknell Univ., Lewisburg, PA
DOI: 10.1109/ICASSP.1996.550563 Conference: Acoustics, Speech, and Signal Processing, 1996. ICASSP-96. Conference Proceedings., 1996 IEEE International Conference on, Volume: 6
Source: IEEE Xplore

ABSTRACT This paper presents a parallel implementation of the discrete
Legendre transform using SIMD machines, MasPar MP-1 and MP-2. Laguerre,
Hermite, and binomial transforms can be implemented in a similar manner
using some of the computations required to compute the discrete Legendre
transform. The time required to compute the discrete Legendre transform
vs. number of points for an MP-2 machine is included

0 Bookmarks
 · 
44 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: Image coding can be implemented through DPCM, transform, hybrid, or segmentation coding techniques. Some transform coding techniques, such as cosine and Hadamard, have been exhaustively analyzed and evaluated, while others, such as Legendre, have not. This paper introduces the use of Legendre transform in image coding. The transform matrix for different block sizes is calculated, the fast algorithm is derived, and the performance is evaluated through both mean square error and subjective quality. The results obtained have indicated that the system performance is comparable with that of optimum KLT and cosine transforms; moreover, it is simpler in implementation.
    Circuits Systems and Signal Processing 02/1994; 13(1):3-18. · 0.98 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Not Available
    Proceedings of the IEEE 09/1975; 63(8):1264- 1264. · 6.91 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Several texts and monographs are available for the signal processing community that discuss important tools like (orthogonal) transforms for signal coding, subband decomposition of signals and the processing through filter banks and, more recently, wavelet transform techniques. A unified treatment of all those topics is the subject of this book. The general approach is from a practical viewpoint. This can be illustrated by the following examples: The text is not theorem-proof structured, but builds up the theory by gradually generalizing the simpler cases; the different techniques are evaluated by objective criteria, especially compaction performance, not only theoretically, but also on standard test images; the book contains several tables of coefficients for some important filters. It stays on a theoretical level though in the sense that it gives the high level formulas, e.g., on quantization effects, but is not involved in bit manipulations or hardware implementation. First the general principles of filter banks and block transforms are introduced and illustrated by many examples. The optimality of the Karhunen-Loeve transform is derived, but placed against the more practical discrete cosine transform. The lapped orthogonal transforms are introduced as a remedy for the blockiness of the simple block transforms. Their realization as M-band filter banks is started with the development of decimation and interpolation techniques and perfect reconstruction (PR) conditions. The tree structure of the filter banks defines a hierarchy and links this theory to orthogonal wavelet transforms and multiresolution analysis. The previous theory culminates in design and performance analysis of several filter bank families. These involve not only PR properties, but also constraints of linear phase, compaction statistics, cross-correlation of the subbands, etc. Finally, wavelet transforms are introduced as a signal processing tool. This final chapter was carefully prepared by the analysis of the subband tree structure and the emphasis that was put on the PR quadrature mirror filters (QMF). In fact, it is shown that the Daubechies filters are identical with the binomial QMFs that were discussed in a previous chapter. The book may serve as a reference text for practitioners, but also as a didactical text for students. Only a limited knowledge of signal processing and Fourier analysis is needed.
    01/2000;