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Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate objective of developing, within the context of signal processing design and implementation,...
Video filtering with Fermat number theoretic transforms using residue number system,” Circuits and Systems for Video Technology
 IEEE Transactions on
, 2006
"... Abstract—We investigate image and video convolutions based on Fermat number transform (FNT) modulo = 2 + 1 where is an integer power of two. These transforms are found to be ideal for image convolutions, except that the choices for the word length, restricted by the transform modulus, are rather lim ..."
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Cited by 6 (0 self)
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Abstract—We investigate image and video convolutions based on Fermat number transform (FNT) modulo = 2 + 1 where is an integer power of two. These transforms are found to be ideal for image convolutions, except that the choices for the word length, restricted by the transform modulus, are rather limited. We discuss two methods to overcome this limitation. First, we allow to be an arbitrary integer. This gives much wider variety in possible moduli, at the cost of decreased transform length of 16 or 32 points for 32. Nevertheless, the transform length appears still to be useful especially with blockbased image and video filtering applications. We call these transforms the generalized FNT (GFNT). The second solution is to use a residue number system (RNS) to enlarge the effective modulus, while performing actual number theoretic transforms with smaller moduli. This approach appears to be particularly useful with moduli
Probabilistic Complexity Analysis for a Class of Approximate DFT Algorithms
, 1996
"... We present a probabilistic complexity analysis of a class of multistage algorithms which incrementally refine DFT approximations. Each stage of any algorithm in this class improves the results of the previous stage by a fixed increment in one of three dimensions: SNR, frequency resolution, or frequ ..."
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Cited by 4 (3 self)
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We present a probabilistic complexity analysis of a class of multistage algorithms which incrementally refine DFT approximations. Each stage of any algorithm in this class improves the results of the previous stage by a fixed increment in one of three dimensions: SNR, frequency resolution, or frequency coverage. However, the complexity of each stage is probabilistically dependent upon certain characteristics of the input signal. Assuming that an algorithm has to be terminated before its arithmetic cost exceeds a given limit, we have formulated a method for predicting the probability of completion of each of the algorithm's stages. This analysis is useful for lowpower and realtime applications where FFT algorithms cannot meet the specified limits on arithmetic cost. I. Introduction While the palette of transforms available to the DSP system designer continues to broaden, the utility of the DFT across a broad range of applications remains unparalleled. This fact can be attributed in p...