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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,...
An efficient implementation of NCOFDM transceivers for cognitive radios
 in Proc. of 1st Conf. on Cognitive Radio Oriented Wireless Networks and Commun., Mykonos
, 2006
"... In this paper, we present an efficient implementation of a noncontiguous orthogonal frequency division multiplexing (NCOFDM) transceiver for cognitive radio systems. NCOFDM is designed to transmit information in the presence of incumbent users, deactivating subcarriers located in the vicinity of ..."
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Cited by 29 (1 self)
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In this paper, we present an efficient implementation of a noncontiguous orthogonal frequency division multiplexing (NCOFDM) transceiver for cognitive radio systems. NCOFDM is designed to transmit information in the presence of incumbent users, deactivating subcarriers located in the vicinity of these users to avoid interference. Given that the core component of an NCOFDM transceiver is the fast Fourier transform (FFT), and that several of the subcarriers are deactivated, it is possible to reduce the execution time by “pruning ” the FFT. We propose an algorithm that efficiently and quickly prunes the FFT for NCOFDM transceivers. Results show that the proposed algorithm substantially outperforms other FFT pruning algorithms when a medium to large number of subcarriers have been deactivated. 1
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...
Generating highperformance pruned FFT implementations
 in [International Conference on Acoustics, Speech, and Signal Processing (ICASSP
, 2009
"... We derive a recursive generalradix pruned CooleyTukey fast Fourier transform (FFT) algorithm in Kronecker product notation. The algorithm is compatible with vectorization and parallelization required on stateoftheart multicore CPUs. We include the pruned FFT algorithm into the program generatio ..."
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Cited by 4 (1 self)
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We derive a recursive generalradix pruned CooleyTukey fast Fourier transform (FFT) algorithm in Kronecker product notation. The algorithm is compatible with vectorization and parallelization required on stateoftheart multicore CPUs. We include the pruned FFT algorithm into the program generation system Spiral, and automatically generate optimized implementations of the pruned FFT for the Intel Core2Duo multicore processor. Experimental results show that using the pruned FFT can indeed speed up the fastest available FFT implementations by up to 30 % when the problem size and the pattern of unused inputs and outputs are known in advance.
Incremental Refinement Structures for Approximate Signal Processing
, 1997
"... This work investigates approximate signal processing as a design philosophy supporting the realization of efficient, robust, and flexible digital signal processing systems through the use of incremental refinement structures that allow tradeoffs to be easily made between the accuracy or optimality o ..."
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Cited by 4 (1 self)
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This work investigates approximate signal processing as a design philosophy supporting the realization of efficient, robust, and flexible digital signal processing systems through the use of incremental refinement structures that allow tradeoffs to be easily made between the accuracy or optimality of results and the utilization of computing resources such as time, power, and chip area. The value of this approach is demonstrated through the theoretical development of incremental refinement structures for signal detection using the fast Fourier transform (FFT), image decoding using the twodimensional inverse discrete cosine transform (2D IDCT), and spectral analysis using the discrete Fourier transform (DFT). Using both deterministic and probabilistic techniques, the theoretical performance of these structures under various resource constraints is quantified in terms of welldefined measures such as probability of detection, SNR, and frequency resolution. These analyses are verified for...
Highquality twostage resampling for 3D volumes in medical imaging
, 2007
"... This paper introduces a simple method of twostage resampling where Fourierdomain upsampling is followed by traditional resampling. Practical aspects as well as efficient implementation techniques are considered. A new version of pruned FFT algorithms to calculate the upsampling stage is also int ..."
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This paper introduces a simple method of twostage resampling where Fourierdomain upsampling is followed by traditional resampling. Practical aspects as well as efficient implementation techniques are considered. A new version of pruned FFT algorithms to calculate the upsampling stage is also introduced. The suggested twostage resampling method provides very highquality results exceeding those of the previous algorithms. It excels with higher dimensional datasets due to its ability to employ smallsupport kernels. The applied FFT algorithms make the method most efficient with dataset sizes of powers of two. These reasons and the importance of minimal resampling artifacts make the suggested method especially suitable for 3D volumes in medical imaging. Furthermore, for repeated uses, only the second stage is recalculated allowing an increase in performance for motion correction applications in functional magnetic resonance imaging (fMRI), for example. Ó 2007 Elsevier B.V. All rights reserved.
Review Multicarrier Spread Spectrum Modulation Schemes and Efficient FFT Algorithms for Cognitive Radio Systems
, 2014
"... www.mdpi.com/journal/electronics ..."
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DSA Networks
, 2007
"... With the advent of new high data rate wireless applications, as well as growth of existing wireless services, demand for additional bandwidth is rapidly increasing. Existing “commandandcontrol ” spectrum allocations defined by government regulatory agencies, such as federal communications commissi ..."
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With the advent of new high data rate wireless applications, as well as growth of existing wireless services, demand for additional bandwidth is rapidly increasing. Existing “commandandcontrol ” spectrum allocations defined by government regulatory agencies, such as federal communications commission (FCC), prohibit unlicensed access to licensed spectrum, constraining them instead to several heavily populated, interferenceprone frequency bands. However, it has been shown that the spectrum is not utilized efficiently across time and frequency. Therefore, FCC is currently working on the concept of unlicensed users “borrowing ” spectrum from incumbent license holders temporarily to improve the spectrum utilization. This concept is called dynamic spectrum access (DSA). Cognitive radios offer versatile, powerful, and portable wireless transceivers enabling DSA. This dissertation investigates physical layer techniques to enhance a cognitive radio performance. Multicarrier techniques, such as orthogonal frequency division multiplexing (OFDM), support huge data rates that are robust to channel impairments. However, with a growing
1Pruned BitReversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures
"... A mathematical characterization of seriallypruned permutations (SPPs) employed in variablelength permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct ..."
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A mathematical characterization of seriallypruned permutations (SPPs) employed in variablelength permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct to coding for error correction. Typically only a small set of discrete permuter lengths are supported. Serial pruning is a simple technique to alter the length of a permutation to support a wider range of lengths, but results in a serial processing bottleneck. In this paper, parallelizing SPPs is formulated in terms of recursively computing sums involving integer floor and related functions using integer operations, in a fashion analogous to evaluating Dedekind sums. A mathematical treatment for bitreversal permutations (BRPs) is presented, and closedform expressions for BRP statistics including descents/ascents, major index, excedances/descedances, inversions, and serial correlations are derived. It is shown that BRP sequences have weak correlation properties. Moreover, a new statistic called permutation inliers that characterizes the pruning gap of pruned interleavers is proposed. Using this statistic, a recursive algorithm that computes the minimum inliers count of a pruned BR interleaver (PBRI) in logarithmic time complexity is presented. This algorithm enables parallelizing a serial PBRI algorithm by any desired parallelism factor by computing the pruning gap in lookahead rather than a serial fashion, resulting in significant reduction in interleaving latency and memory overhead. Extensions to 2D block and stream interleavers, as well as applications to pruned fast Fourier transforms and LTE turbo interleavers, are also presented. Moreover, hardwareefficient architectures for the proposed algorithms are developed. Simulation results of interleavers employed in modern communication standards demonstrate 3 to 4 orders of magnitude improvement in interleaving time compared to existing approaches.