Simple FFT and DCT algorithms with reduced number of operations

Vetterli, Martin; Eurasip, Member; Nussbaumer, Henri J.

doi:10.1016/0165-1684(84)90059-8

Cited by 299 publications

(100 citation statements)

References 13 publications

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“…In 1984, four papers appeared or were submitted almost simultaneously [27, 40,46,51] and presented so-called 'split-radix' algorithms. The basic idea is simply to use a different radix for the even part of the transform (radix-2) and for the odd part (radix-4).…”

Section: Signal Processing Tutorial On Fast Fourier Transformsmentioning

confidence: 99%

“…Note, however, that these algorithms generally have a more involved structure than their complex counterparts (especially in the PFA and WFTA case). Some algorithms have been developed which are inherently 'real', like the real factor FFTs [44,22] or the FFCT algorithm [51], and do not require substantial changes for real input.…”

Section: Dft Algorithms For Real Datamentioning

confidence: 99%

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Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

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Rrsum4. La publication de l'algorithme de Cooley-Tukey pour la transformation de Fourier rapide a ouvert une nouvelle ~re dans le traitement num6rique des signaux, en r4duisant l'ordre de complexit6 de probl~mes cruciaux, comme la transformation de Fourier ou la convolution, de N 2 ~ N log2 N (oh N est la taille du probl~me). Le drvelopment des algorithmes principaux (Cooley-Tukey, split-radix FFT, algorithmes des facteurs premiers, et transform6e rapide de Winograd) est drcrit. Ensuite, l'&at de l'art est donn4, et on parle des probl~mes ouverts et des implantations.

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Section: Signal Processing Tutorial On Fast Fourier Transformsmentioning

confidence: 99%

Section: Dft Algorithms For Real Datamentioning

confidence: 99%

Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

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“…This algorithm, however, exhibits an irregular data flow and corresponding architectures cannot easily be parametrized to support different problem sizes. Another direct approach is the recursive method proposed in [38], which is more efficient than [37] (in terms of operation count and memory), but still lacks a regular data flow. Another line of fast DCT algorithms relies on the well-established fast Fourier transform (FFT).…”

Section: ) Algorithm Evaluationmentioning

confidence: 99%

“…The corresponding algorithm and the resulting VLSI architec- [37] −− − ++ Recursive method [38] − ++ ++ Via 2M -point FFT [39] + − − Via M -point FFT [40] + + + Via M/2-point FFT [40] + ++ ++ ture are detailed in Section IV-C. The additions required to implement the identity basis are carried out in the R-CALC unit.…”

Section: B Amp-t: Transformation-based Amp Architecturementioning

confidence: 99%

VLSI Design of Approximate Message Passing for Signal Restoration and Compressive Sensing

Maechler

Studer

Bellasi

et al. 2012

IEEE J. Emerg. Sel. Topics Circuits Syst.

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Abstract-Sparse signal recovery finds use in a variety of practical applications, such as signal and image restoration and the recovery of signals acquired by compressive sensing. In this paper, we present two generic VLSI architectures that implement the approximate message passing (AMP) algorithm for sparse signal recovery. The first architecture, referred to as AMP-M, employs parallel multiply-accumulate units and is suitable for recovery problems based on unstructured (e.g., random) matrices. The second architecture, referred to as AMP-T, takes advantage of fast linear transforms, which arise in many real-world applications. To demonstrate the effectiveness of both architectures, we present corresponding VLSI and FPGA implementation results for an audio restoration application. We show that AMP-T is superior to AMP-M with respect to silicon area, throughput, and power consumption, whereas AMP-M offers more flexibility.Index Terms-Approximate message passing (AMP), compressive sensing, fast discrete cosine transform, field-programmable gate array (FPGA), 1-norm minimization, signal restoration, sparse signal recovery, very-large scale integration (VLSI).

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“…Research in this domain can be classified into three parts. The first part is the earliest and concerns the reduction of the number of arithmetic operators required for DCT computation [7][8][9][10][11][12][13]. The second research thematic relates to the computation of DCT using multiple constant multiplication schemes [14][15][16][17][18][19][20][21][22][23][24][25] for hardware implementation.…”

Section: Introductionmentioning

confidence: 99%

Optimized Architecture Using a Novel Subexpression Elimination on Loeffler Algorithm for DCT‐Based Image Compression

2012

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The canonical signed digit (CSD) representation of constant coefficients is a unique signed data representation containing the fewest number of nonzero bits. Consequently, for constant multipliers, the number of additions and subtractions is minimized by CSD representation of constant coefficients. This technique is mainly used for finite impulse response (FIR) filter by reducing the number of partial products. In this paper, we use CSD with a novel common subexpression elimination (CSE) scheme on the optimal Loeffler algorithm for the computation of discrete cosine transform (DCT). To meet the challenges of low-power and high-speed processing, we present an optimized image compression scheme based on two-dimensional DCT. Finally, a novel and a simple reconfigurable quantization method combined with DCT computation is presented to effectively save the computational complexity. We present here a new DCT architecture based on the proposed technique. From the experimental results obtained from the FPGA prototype we find that the proposed design has several advantages in terms of power reduction, speed performance, and saving of silicon area along with PSNR improvement over the existing designs as well as the Xilinx core.

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Simple FFT and DCT algorithms with reduced number of operations

Cited by 299 publications

References 13 publications

Fast fourier transforms: A tutorial review and a state of the art

Fast fourier transforms: A tutorial review and a state of the art

VLSI Design of Approximate Message Passing for Signal Restoration and Compressive Sensing

Optimized Architecture Using a Novel Subexpression Elimination on Loeffler Algorithm for DCT‐Based Image Compression

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