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Systematic approaches to parallel architectures for DSP algorithms
SIGNAL
PROCESSING ELSEVIER
Signal Processing
62 (1997) 367-368
Thesis alert David Akopian* Signal Processing Laoratoty, Tampere Unicersi&
ofTechnology, Hermiankatu 12C. P.O. Bm 553, FIN-33101 Tatnpere, Finland
Systematic approaches to parallel architectures for DSP algorithms’ &words: Discrete trigonometric transforms, nonlinear filters, faster regular algorithms, parallel architectures Use of dedicated hardware designed for parallel computations is a necessity for many real-time applications of Digital Signal Processing (DSP). Naturally, it is desired to have a minimal complexity of realization for the given throughput requirements. Parametrized families of architectures for DSP algorithms are somewhat application independent solutions, providing the possibility to find a tradeoff between the complexity and the speed in a concrete situation. Such families can only be designed for algorithms with enough regularity to allow efficient mappings to structures with different degrees of parallelism. In general, these are joint structure-algorithm solutions. In this thesis, systematic architecture design methods are considered for such DSP operations as Discrete Trigonometric Transforms (DTT) and a class of nonlinear filters, namely, stack, generalized stack and threshold Boolean filters (TBF). *Advisor: Professor Jaakko Astola. ‘Acta Polytechnica Scandinavica, Electrical Engineering Technology, ISBN 952-5148-29-7. ISSN 0001-6845.
Elsevier Science B.V
A DTT can be computed using direct or fast algorithms. It is shown that in the direct case existing standard methods of parallelizing can be applied. In this work, regular algorithms with structure similar to that of the Cooley-Turkey fast Fourier transform (FFT) algorithm are derived for DTT. The computational complexities of the proposed algorithms are the same as those of best order recursive algorithms. For FFT systematic methods of mapping to structures with different levels of parallelism are well known, and so these methods can be applied also to other DTT using the presented algorithms. Next, parametrized parallel algorithms and appropriate architectures are proposed for a class of nonlinear filters. In the case of stack filters, these are digit-serial structures realizing fast search procedures to obtain the output. It is shown that lexicographic igned-digit representations can also be used for this kind of parallel design of stack filters. By choosing the parameters one can pick up structures with a suitable tradeoff between the complexity and the speed. An analogous technique is
Series No. 89, Espoo
1997, 149 pp. Published
by the Finnish
Academy
of
368
Thesis alert / Signal Processing 62 (1997) 367-368
developed for generalized stack filters although the resulting structures are not digit-serial. In recent years many algorithms utilizing the possible data serial nature of inputs have been suggested for order
statistic and stack filters. This kind of solution is suggested here for the implementation of Threshold Boolean Filters. The proposed solutions are suitable for architecture libraries in automated design tools.
PROCESSING ELSEVIER
Signal Processing
62 (1997) 367-368
Thesis alert David Akopian* Signal Processing Laoratoty, Tampere Unicersi&
ofTechnology, Hermiankatu 12C. P.O. Bm 553, FIN-33101 Tatnpere, Finland
Systematic approaches to parallel architectures for DSP algorithms’ &words: Discrete trigonometric transforms, nonlinear filters, faster regular algorithms, parallel architectures Use of dedicated hardware designed for parallel computations is a necessity for many real-time applications of Digital Signal Processing (DSP). Naturally, it is desired to have a minimal complexity of realization for the given throughput requirements. Parametrized families of architectures for DSP algorithms are somewhat application independent solutions, providing the possibility to find a tradeoff between the complexity and the speed in a concrete situation. Such families can only be designed for algorithms with enough regularity to allow efficient mappings to structures with different degrees of parallelism. In general, these are joint structure-algorithm solutions. In this thesis, systematic architecture design methods are considered for such DSP operations as Discrete Trigonometric Transforms (DTT) and a class of nonlinear filters, namely, stack, generalized stack and threshold Boolean filters (TBF). *Advisor: Professor Jaakko Astola. ‘Acta Polytechnica Scandinavica, Electrical Engineering Technology, ISBN 952-5148-29-7. ISSN 0001-6845.
Elsevier Science B.V
A DTT can be computed using direct or fast algorithms. It is shown that in the direct case existing standard methods of parallelizing can be applied. In this work, regular algorithms with structure similar to that of the Cooley-Turkey fast Fourier transform (FFT) algorithm are derived for DTT. The computational complexities of the proposed algorithms are the same as those of best order recursive algorithms. For FFT systematic methods of mapping to structures with different levels of parallelism are well known, and so these methods can be applied also to other DTT using the presented algorithms. Next, parametrized parallel algorithms and appropriate architectures are proposed for a class of nonlinear filters. In the case of stack filters, these are digit-serial structures realizing fast search procedures to obtain the output. It is shown that lexicographic igned-digit representations can also be used for this kind of parallel design of stack filters. By choosing the parameters one can pick up structures with a suitable tradeoff between the complexity and the speed. An analogous technique is
Series No. 89, Espoo
1997, 149 pp. Published
by the Finnish
Academy
of
368
Thesis alert / Signal Processing 62 (1997) 367-368
developed for generalized stack filters although the resulting structures are not digit-serial. In recent years many algorithms utilizing the possible data serial nature of inputs have been suggested for order
statistic and stack filters. This kind of solution is suggested here for the implementation of Threshold Boolean Filters. The proposed solutions are suitable for architecture libraries in automated design tools.