Spectral Transforms

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Massimo Poncino - One of the best experts on this subject based on the ideXlab platform.

  • stream synthesis for efficient power simulation based on Spectral Transforms
    IEEE Transactions on Very Large Scale Integration Systems, 2001
    Co-Authors: Alberto Macii, Massimo Poncino, Enrico Macii, R Scarsi
    Abstract:

    One way of minimizing the time required to perform simulation-based power estimation is that of reducing the length of the input trace to be fed to the simulator. Obviously, the use of a reduced stream may introduce some errors in the estimation results. The generation (or synthesis) of the short input sequence to be used for power simulation should then be carried out in such a way that the resulting error is minimized. Existing techniques exploit the knowledge of some statistical and correlation characteristics concerning the original input trace to generate a reduced stream that closely matches such characteristics. In this paper, we introduce a new stream synthesis method. Its distinguishing feature is the use of Spectral analysis based on the discrete Fourier transform to determine a reduced sequence of vectors that enables us to shorten the overall power simulation time at a very limited penalty in accuracy. The effectiveness and the robustness, in terms of estimation accuracy, of the proposed synthesis procedure are demonstrated by the experimental results we have obtained on standard combinational benchmarks for a variety of input streams with different statistical and correlation properties. Data for sequential circuits are also reported.

  • stream synthesis for efficient power simulation based on Spectral Transforms
    International Symposium on Low Power Electronics and Design, 1998
    Co-Authors: Alberto Macii, Massimo Poncino, Enrico Macii, R Scarsi
    Abstract:

    In this paper, we present a power estimation technique for control-flow intensive designs that is tailored towards driving iterative high-level synthesis systems, where hundreds of architectural trade-offs are explored and compared. Our method is fast and relatively accurate. The algorithm utilizes the behavioral information to extract branch probabilities, and uses these in conjunction with switching activity and circuit capacitance information, to estimate the power consumption of a given architecture. We test our algorithm using a series of experiments, each geared towards measuring a different indicator. The first set of experiments measures the algorithm's accuracy when compared to the actual circuit power. The second set of experiments measures the average tracking index, and tracking index fidelity for a series of architectures. This index measures how well the algorithm makes decisions when comparing the relative power consumption of two architectures contending as low-power candidates. Results indicate that our algorithm achieved an average estimation error of 11.8% and an average tracking index of 0.95 over all examples.

  • stream synthesis for efficient power simulation based on Spectral Transforms cmos logic
    International Symposium on Low Power Electronics and Design, 1998
    Co-Authors: Alberto Macii, Massimo Poncino, Enrico Macii, R Scarsi
    Abstract:

    One way of minimizing the time required to perform simulation based power estimation is that of reducing the length of the input trace to be fed to the simulator. Obviously, the use of a reduced stream may introduce some errors in the estimation results. The generation (or synthesis) of the short input sequence to be used for power simulation must then be done in such a way that the resulting error is minimized. This paper introduces a new stream synthesis method whose peculiar feature is that of using Spectral analysis techniques based on the discrete Fourier transform to determine a reduced sequence of vectors that enables to shorten the overall power simulation time at a very limited accuracy decrease. The effectiveness of the proposed synthesis procedure is demonstrated by the results we have obtained on the Iscas'85 combinational benchmarks for a variety of input streams characterized by different statistical and correlation properties.

  • using symbolic rademacher walsh Spectral Transforms to evaluate the agreement between boolean functions
    IEE Proceedings - Computers and Digital Techniques, 1996
    Co-Authors: E Macii, Massimo Poncino
    Abstract:

    With the advent of symbolic techniques for Boolean and pseudoBoolean function manipulation, Spectral transformations have become more relevant in the areas of logic synthesis and formal verification. The authors propose a symbolic algorithm based on algebraic decision diagrams, a data structure for the efficient manipulation of matrices and graphs, to compute the agreement between pairs of Boolean functions. Such an algorithm, operating in the transform domain, allows Boolean functions of over 80 input variables to be handled in a very short time.

  • using symbolic rademacher walsh Spectral Transforms to evaluate the correlation between boolean functions
    Great Lakes Symposium on VLSI, 1995
    Co-Authors: E Macci, Massimo Poncino
    Abstract:

    The use of symbolic techniques to store integer-valued functions has been shown to be extremely effective in handling both transform matrices and Spectral representations of large Boolean functions. In this paper we propose a novel application of symbolic Rademacher-Walsh Spectral Transforms to the evaluation of Boolean function correlation. In particular, we present an ADD-based algorithm to compute the agreement between two Boolean functions starting from their Spectral representations. The method, operating in the transform domain, has appeared to be more advantageous than traditional approaches, using operations in the Boolean domain, concerning both memory occupation and execution time on some classes of functions.

Radomir S. Stankovic - One of the best experts on this subject based on the ideXlab platform.

  • FFT and decision diagram methods for calculation of discrete Spectral Transforms
    Facta universitatis - series: Electronics and Energetics, 2003
    Co-Authors: Radomir S. Stankovic
    Abstract:

    In this paper, we discuss FFT and Decision diagrams (DD) methods for calculation of discrete Spectral Transforms of signals represented by large sequences. It has been pointed out that DD-methods are performing of FFT-like algorithms over decision diagrams instead of vectors. Differences between these methods are discussed and it is explained where from DD-methods take the advantages in processing of large functions.

  • Fibonacci Spectral Transforms: calculation, algorithms and circuit realizations
    Systems Analysis Modelling Simulation, 2003
    Co-Authors: Milena Stankovic, Radomir S. Stankovic, Jaakko Astola, Karen Egiazarian
    Abstract:

    In this article, we define the Fibonacci decision diagrams (FibDDs) permitting representation of functions defined in a number of points different from N = 2n by decision diagrams consisting of nodes with two outgoing edges.We show the relationships between the FibDDs and the contracted Fibonacci codes and propose a procedure for calculation of the generalized Fibonacci Transforms through FibDDs. This procedure permits calculation of the generalized Fibonacci spectra of functions defined in a number of points equal to a large generalized Fibonacci number. We use FibDDs to design architectures for realization of discrete functions and calculation of the generalized Fibonacci p-Transforms. We also consider the circuit realizations of functions represented by FibDDs and the circuit realizations of Fibonacci Spectral Transforms.

  • Spectral Transforms Calculation through Decision Diagrams
    VLSI Design, 2002
    Co-Authors: Radomir S. Stankovic, Bogdan J. Falkowski
    Abstract:

    In this paper, calculation of Spectral Transforms through Decision diagrams (DDs) and relationship of this method with FFT-like algorithms is discussed. It is shown that in DDs methods the basic operations in FFT-like algorithms are performed not on vectors but instead on parts of DDs as a data structure. Such a data structure represents the input signals, the intermediate results obtained during the calculation as well as the final output results. It should be noticed that, unlike FFT-like algorithms, DDs methods permit to take advantages from both, the properties of the transform matrices and the particular properties of the processed signals.

  • ISMVL - Design of Haar wavelet Transforms and Haar Spectral transform decision diagrams for multiple-valued functions
    Proceedings 31st IEEE International Symposium on Multiple-Valued Logic, 1
    Co-Authors: Radomir S. Stankovic, Milena Stankovic, Claudio Moraga
    Abstract:

    In Spectral interpretation, decision diagrams (DDs) are defined in terms of some Spectral Transforms. For a given DD, the related transform is determined by an analysis of expansion rules used in the nodes and the related labels of edges. The converse task, design of a DD in terms of a given Spectral transform often requires decomposition of basic functions in Spectral transform to determine the corresponding expansion rules and labels at the edges. We point out that this problem relates to the assignment of nodes in Pseudo-Kronecker DDs(PKDDs). Due to that, we generalize the definition of Haar Spectral transform DDs (HSTDDs) to multiple-valued (MV) functions. Conversely, from such defined HSTDDs, we derive various Haar Transforms for MV functions.

  • FFT and decision diagrams based methods for calculation of Spectral Transforms
    Proceedings of ICICS 1997 International Conference on Information Communications and Signal Processing. Theme: Trends in Information Systems Engineeri, 1
    Co-Authors: Radomir S. Stankovic, Bogdan J. Falkowski
    Abstract:

    This paper discusses the basic features and points out the relation between FFT and decision diagram based methods for the calculation of Spectral Transforms on finite Abelian groups. The presentation is illustrated on the example of complex Hadamard transform and some experimental results are presented.

Karen Egiazarian - One of the best experts on this subject based on the ideXlab platform.

  • Fibonacci Spectral Transforms: calculation, algorithms and circuit realizations
    Systems Analysis Modelling Simulation, 2003
    Co-Authors: Milena Stankovic, Radomir S. Stankovic, Jaakko Astola, Karen Egiazarian
    Abstract:

    In this article, we define the Fibonacci decision diagrams (FibDDs) permitting representation of functions defined in a number of points different from N = 2n by decision diagrams consisting of nodes with two outgoing edges.We show the relationships between the FibDDs and the contracted Fibonacci codes and propose a procedure for calculation of the generalized Fibonacci Transforms through FibDDs. This procedure permits calculation of the generalized Fibonacci spectra of functions defined in a number of points equal to a large generalized Fibonacci number. We use FibDDs to design architectures for realization of discrete functions and calculation of the generalized Fibonacci p-Transforms. We also consider the circuit realizations of functions represented by FibDDs and the circuit realizations of Fibonacci Spectral Transforms.

  • circuit realization of Spectral Transforms in fibonacci interconnection topologies
    International Symposium on Circuits and Systems, 2001
    Co-Authors: Milena Stankovic, Ratko Stankovic, Jaakko Astola, Karen Egiazarian
    Abstract:

    We present a method for design of networks for realization of functions represented by Fibonacci decision diagrams (FibDDs) and for calculation of the generalized Fibonacci Spectral Transforms. For a given function f, the structure of the network which realizes f is derived from the FibDD for f. We extend this method to design circuits for calculation of the generalized Fibonacci spectra from FibDDs.

  • ISCAS (4) - Circuit realization of Spectral Transforms in Fibonacci interconnection topologies
    ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 1
    Co-Authors: Milena Stankovic, Radomir S. Stankovic, Jaakko Astola, Karen Egiazarian
    Abstract:

    We present a method for design of networks for realization of functions represented by Fibonacci decision diagrams (FibDDs) and for calculation of the generalized Fibonacci Spectral Transforms. For a given function f, the structure of the network which realizes f is derived from the FibDD for f. We extend this method to design circuits for calculation of the generalized Fibonacci spectra from FibDDs.

Milena Stankovic - One of the best experts on this subject based on the ideXlab platform.

  • Fibonacci Spectral Transforms: calculation, algorithms and circuit realizations
    Systems Analysis Modelling Simulation, 2003
    Co-Authors: Milena Stankovic, Radomir S. Stankovic, Jaakko Astola, Karen Egiazarian
    Abstract:

    In this article, we define the Fibonacci decision diagrams (FibDDs) permitting representation of functions defined in a number of points different from N = 2n by decision diagrams consisting of nodes with two outgoing edges.We show the relationships between the FibDDs and the contracted Fibonacci codes and propose a procedure for calculation of the generalized Fibonacci Transforms through FibDDs. This procedure permits calculation of the generalized Fibonacci spectra of functions defined in a number of points equal to a large generalized Fibonacci number. We use FibDDs to design architectures for realization of discrete functions and calculation of the generalized Fibonacci p-Transforms. We also consider the circuit realizations of functions represented by FibDDs and the circuit realizations of Fibonacci Spectral Transforms.

  • design of haar wavelet Transforms and haar Spectral transform decision diagrams for multiple valued functions
    International Symposium on Multiple-Valued Logic, 2001
    Co-Authors: Ratko Stankovic, Milena Stankovic, Claudio Moraga
    Abstract:

    In Spectral interpretation, decision diagrams (DDs) are defined in terms of some Spectral Transforms. For a given DD, the related transform is determined by an analysis of expansion rules used in the nodes and the related labels of edges. The converse task, design of a DD in terms of a given Spectral transform often requires decomposition of basic functions in Spectral transform to determine the corresponding expansion rules and labels at the edges. We point out that this problem relates to the assignment of nodes in Pseudo-Kronecker DDs(PKDDs). Due to that, we generalize the definition of Haar Spectral transform DDs (HSTDDs) to multiple-valued (MV) functions. Conversely, from such defined HSTDDs, we derive various Haar Transforms for MV functions.

  • circuit realization of Spectral Transforms in fibonacci interconnection topologies
    International Symposium on Circuits and Systems, 2001
    Co-Authors: Milena Stankovic, Ratko Stankovic, Jaakko Astola, Karen Egiazarian
    Abstract:

    We present a method for design of networks for realization of functions represented by Fibonacci decision diagrams (FibDDs) and for calculation of the generalized Fibonacci Spectral Transforms. For a given function f, the structure of the network which realizes f is derived from the FibDD for f. We extend this method to design circuits for calculation of the generalized Fibonacci spectra from FibDDs.

  • ISMVL - Design of Haar wavelet Transforms and Haar Spectral transform decision diagrams for multiple-valued functions
    Proceedings 31st IEEE International Symposium on Multiple-Valued Logic, 1
    Co-Authors: Radomir S. Stankovic, Milena Stankovic, Claudio Moraga
    Abstract:

    In Spectral interpretation, decision diagrams (DDs) are defined in terms of some Spectral Transforms. For a given DD, the related transform is determined by an analysis of expansion rules used in the nodes and the related labels of edges. The converse task, design of a DD in terms of a given Spectral transform often requires decomposition of basic functions in Spectral transform to determine the corresponding expansion rules and labels at the edges. We point out that this problem relates to the assignment of nodes in Pseudo-Kronecker DDs(PKDDs). Due to that, we generalize the definition of Haar Spectral transform DDs (HSTDDs) to multiple-valued (MV) functions. Conversely, from such defined HSTDDs, we derive various Haar Transforms for MV functions.

  • ISCAS (4) - Circuit realization of Spectral Transforms in Fibonacci interconnection topologies
    ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 1
    Co-Authors: Milena Stankovic, Radomir S. Stankovic, Jaakko Astola, Karen Egiazarian
    Abstract:

    We present a method for design of networks for realization of functions represented by Fibonacci decision diagrams (FibDDs) and for calculation of the generalized Fibonacci Spectral Transforms. For a given function f, the structure of the network which realizes f is derived from the FibDD for f. We extend this method to design circuits for calculation of the generalized Fibonacci spectra from FibDDs.

R Scarsi - One of the best experts on this subject based on the ideXlab platform.

  • stream synthesis for efficient power simulation based on Spectral Transforms
    IEEE Transactions on Very Large Scale Integration Systems, 2001
    Co-Authors: Alberto Macii, Massimo Poncino, Enrico Macii, R Scarsi
    Abstract:

    One way of minimizing the time required to perform simulation-based power estimation is that of reducing the length of the input trace to be fed to the simulator. Obviously, the use of a reduced stream may introduce some errors in the estimation results. The generation (or synthesis) of the short input sequence to be used for power simulation should then be carried out in such a way that the resulting error is minimized. Existing techniques exploit the knowledge of some statistical and correlation characteristics concerning the original input trace to generate a reduced stream that closely matches such characteristics. In this paper, we introduce a new stream synthesis method. Its distinguishing feature is the use of Spectral analysis based on the discrete Fourier transform to determine a reduced sequence of vectors that enables us to shorten the overall power simulation time at a very limited penalty in accuracy. The effectiveness and the robustness, in terms of estimation accuracy, of the proposed synthesis procedure are demonstrated by the experimental results we have obtained on standard combinational benchmarks for a variety of input streams with different statistical and correlation properties. Data for sequential circuits are also reported.

  • stream synthesis for efficient power simulation based on Spectral Transforms
    International Symposium on Low Power Electronics and Design, 1998
    Co-Authors: Alberto Macii, Massimo Poncino, Enrico Macii, R Scarsi
    Abstract:

    In this paper, we present a power estimation technique for control-flow intensive designs that is tailored towards driving iterative high-level synthesis systems, where hundreds of architectural trade-offs are explored and compared. Our method is fast and relatively accurate. The algorithm utilizes the behavioral information to extract branch probabilities, and uses these in conjunction with switching activity and circuit capacitance information, to estimate the power consumption of a given architecture. We test our algorithm using a series of experiments, each geared towards measuring a different indicator. The first set of experiments measures the algorithm's accuracy when compared to the actual circuit power. The second set of experiments measures the average tracking index, and tracking index fidelity for a series of architectures. This index measures how well the algorithm makes decisions when comparing the relative power consumption of two architectures contending as low-power candidates. Results indicate that our algorithm achieved an average estimation error of 11.8% and an average tracking index of 0.95 over all examples.

  • stream synthesis for efficient power simulation based on Spectral Transforms cmos logic
    International Symposium on Low Power Electronics and Design, 1998
    Co-Authors: Alberto Macii, Massimo Poncino, Enrico Macii, R Scarsi
    Abstract:

    One way of minimizing the time required to perform simulation based power estimation is that of reducing the length of the input trace to be fed to the simulator. Obviously, the use of a reduced stream may introduce some errors in the estimation results. The generation (or synthesis) of the short input sequence to be used for power simulation must then be done in such a way that the resulting error is minimized. This paper introduces a new stream synthesis method whose peculiar feature is that of using Spectral analysis techniques based on the discrete Fourier transform to determine a reduced sequence of vectors that enables to shorten the overall power simulation time at a very limited accuracy decrease. The effectiveness of the proposed synthesis procedure is demonstrated by the results we have obtained on the Iscas'85 combinational benchmarks for a variety of input streams characterized by different statistical and correlation properties.