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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 FFT for OFDM based cognitive radio on a reconfigurable architecture
 in Communications, ICC '07. IEEE International Conference
, 2007
"... Abstract — Cognitive Radio is a promising technology to utilize nonused parts of the spectrum that actually are assigned to licensed services. An adaptive OFDM based Cognitive Radio system has the capacity to nullify individual carriers to avoid interference to the licensed user. Therefore, there c ..."
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Cited by 11 (3 self)
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Abstract — Cognitive Radio is a promising technology to utilize nonused parts of the spectrum that actually are assigned to licensed services. An adaptive OFDM based Cognitive Radio system has the capacity to nullify individual carriers to avoid interference to the licensed user. Therefore, there could be a considerably large number of zerovalued inputs/outputs for the IFFT/FFT in the OFDM transceiver. Due to the wasted operations on zero values, the standard FFT is no longer efficient. Based on this observation, we propose to use a computationally efficient IFFT/FFT as an option for OFDM based Cognitive Radio. Mapping this algorithm onto a reconfigurable architecture is discussed. I.
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...
The Quick Fourier Transform: An FFT Based on Symmetries
, 1996
"... This paper looks at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of the discrete Fourier transform (DFT). We develop an algorithm, called the quick Fourier transform (QFT), that reduces the number of floating point operations necessary to ..."
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Cited by 4 (0 self)
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This paper looks at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of the discrete Fourier transform (DFT). We develop an algorithm, called the quick Fourier transform (QFT), that reduces the number of floating point operations necessary to compute the DFT by a factor of two or four over direct methods or Goertzel's method for prime lengths. Buy further application of the idea to the calculation of a DFT of length2 M , we construct a new O(N log N) algorithm, with computational complexities comparable to the CooleyTukey algorithm. We show the poweroftwo QFT can be implemented in terms of discrete sine and cosine transforms. The algorithm can be easily modified to compute the DFT with only a subset of either input or output points, and reduces by nearly half the number of operations when the data are real. List of Tables 1 Comparison of the number of operations for O(N 2 ) DFT algorithms. . . . . . . . . . . . . . . ...
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...
An Efficient (n, k) Information Dispersal Algorithm based on Fermat Number Transforms
"... Abstract—The (n, k) information dispersal algorithm (IDA) is a coding technique converting a digital source file into n small digital files (shadows), and the receipt of any k out of the n shadows can losslessly reconstruct the source file. This paper presents an encoding and two decoding algorithms ..."
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Abstract—The (n, k) information dispersal algorithm (IDA) is a coding technique converting a digital source file into n small digital files (shadows), and the receipt of any k out of the n shadows can losslessly reconstruct the source file. This paper presents an encoding and two decoding algorithms of (n, k) IDA via the fast Fermat number transform (FNT). The proposed encoding algorithm requires O(n log k) arithmetic operations, and the two decoding algorithms have complexities O(n log k) and O(k log2 k) for a reasonably large file. As compared with existing work, the proposed algorithms generate significant improvement in the throughput in the low code rate k/n ≤ 1/2 settings. Index Terms—Erasure codes, fast Fourier transforms, Galois fields, information dispersal algorithm (IDA), ReedSolomon codes. I.
A LOW DELAY, VARIABLE RESOLUTION, PERFECT RECONSTRUCTION SPECTRAL ANALYSISSYNTHESIS SYSTEM FOR SPEECH ENHANCEMENT
"... The choice of the window function and window length in short time analysissynthesis (AS) systems based on the discrete Fourier transform (DFT) has to balance conflicting requirements: Long windows provide high spectral resolution while short windows allow for high temporal resolution. Furthermore ..."
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The choice of the window function and window length in short time analysissynthesis (AS) systems based on the discrete Fourier transform (DFT) has to balance conflicting requirements: Long windows provide high spectral resolution while short windows allow for high temporal resolution. Furthermore, for many applications a low algorithmic delay is desirable. Therefore, long standard windows such as the Hann or Hamming windows cannot be used. In this contribution we propose a novel AS system which achieves perfect reconstruction (PR) and a low delay by using a variable length analysis window and a relatively short synthesis window. The variable length analysis windows allow a spectral analysis that is adapted to the signals span of stationarity. The AS windows are designed such that they can be switched at any time instant without violating PR. We show that the spectral representation of typical speech data is improved as compared to AS systems with standard windows. 1.