Analysis of twiddle factor memory complexity of radix-2&lt;sup&gt;i&lt;/sup&gt; pipelined FFTs

Qureshi, Fahad; Gustafsson, Oscar

doi:10.1109/acssc.2009.5470121

Cited by 9 publications

(10 citation statements)

References 12 publications

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“…In order to display results of the best performing implementations in more detail, measurements were sorted by number of cache misses separately for different transform lengths. The five best performing implementations are listed in Fig.9 for five different transform lengths between 2 8 and 2 24 . We notice that implementations relying on additional lookup tables (L) do not appear in any of the truncated lists.…”

Section: Ct Bi Gs Ct Bi S Ct Dr Ct Dr F Ct Dr S Mr Bi Mr Bi F mentioning

confidence: 99%

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A Depth-First Iterative Algorithm for the Conjugate Pair Fast Fourier Transform

Becoulet¹,

Verguet²

2020

Preprint

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The Split-Radix Fast Fourier Transform has the same low arithmetic complexity as the related Conjugate Pair Fast Fourier Transform. Both transforms have an irregular datapath structure which is straightforwardly expressed only in recursive forms. Furthermore, the conjugate pair variant has a complicated input indexing pattern which requires existing iterative implementations to rely on precomputed tables. It however allows optimization of the memory bandwidth as it requires a single twiddle factor load per radix-4 butterfly. In existing algorithms, this comes at the cost of using additional precomputed tables or performing recursive function calls. In this paper we present two novel approaches that handle both the butterfly scheduling and the input index generation of the Conjugate Pair Fast Fourier Transform. The proposed algorithm is cache-friendly because it is depth-first, non-recursive and does not rely on precomputed index tables. In order to achieve this, we relate the butterfly execution pattern of the Split-Radix and Conjugate Pair FFTs to the binary carry sequence. Based on this finding, we describe how common integer arithmetic and bitwise operations can be used to perform input reordering and depth-first traversal of the transform datapath with O(1) space complexity.<br>

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Section: Ct Bi Gs Ct Bi S Ct Dr Ct Dr F Ct Dr S Mr Bi Mr Bi F mentioning

confidence: 99%

“…We can see that when N is large enough, the results do not depend on the transform length. All branch predictor-related results discussed here are related to transforms of length 2 24 . The MR BI S implementation yields a value as low as 0.005 misses per sample.…”

Section: Ct Bi Gs Ct Bi S Ct Dr Ct Dr F Ct Dr S Mr Bi Mr Bi F mentioning

confidence: 99%

A Depth-First Iterative Algorithm for the Conjugate Pair Fast Fourier Transform

Becoulet¹,

Verguet²

2020

Preprint

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“…To exemplify these optimizations, suppose a generator must provide the sine and cosine of nφ in fixed-point notation with 8 fractional bits and no integer bits rounding to the nearest representable value. In this example, φ = 2π/2 11 = π/2 10 , that is, it is trigonometric binary and λ t (φ) = 2 11 is a multiple of 4, and hence, we first apply argument reduction and treat the case n = 2 8 separately as in the example of Section 2. A subgenerator still has to be subsequently implemented with an input space of size 2 8 (w = H t (φ) − 3 = 8).…”

Section: Leading Ones Of the Cosinementioning

confidence: 99%

“…Another example is given by the DFT engines required in applications such as required in Power Line Communications (PLC) [7], Digital Video Broadcasting-Terrestrial 2 (DVB-T2) [8], photon counting [9], and radio astronomy [10]. In those applications, the sequence can be as long as 2 13 , 2 15 , 2 27 , and 2 30 , respectively, and hence the coefficient tables are large in comparison with other elements of the DFT engine [11]. In this paper, we propose an innovative technique to reduce the resources required to implement a sine/cosine generator in application-specific integrated circuit (ASIC) and configurable logic.…”

Section: Introductionmentioning

confidence: 99%

Using the complement of the cosine to compute trigonometric functions

Martos

Calderón

Chico

et al. 2020

EURASIP J. Adv. Signal Process.

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The computation of the sine and cosine functions is required in devices ranging from application-specific signal processors to general purpose floating-point units. Even in the latter case, the required functionality can be reduced to computing the sine and/or cosine of multiples of a constant angle. The latency of a sine/cosine generator can be reduced by using look-up tables. However, a direct implementation with look-up tables may be unfeasible if the input space is huge. In such a case, look-up tables with a number of entries lower than the size of the input space can be used indirectly. In previously published methods, the reduction in the number of table entries is obtained at the expense of increasing the table width and the computational cost. This paper introduces an alternative technique that makes it possible to reduce the size of the look-up tables as well as the required multiplications. The proposed technique can be used to implement sine/cosine generators of huge input space. It has been used to implement several twiddle factor generators in reconfigurable hardware and has enabled the number of look-up tables to be reduced by between 6 and 26% with respect to previous table-based techniques. Also, these implementations are about 50% faster than those based on Volder’s algorithm.

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“…(1) Nilai faktor pemutar yang telah didapatkan menggunakan persamaan (1), kemudian dihitung menggunakan metode kupu-kupu. Hasil dari proses perhitungan dengan metode kupukupu akan membagi data menjadi separuh dari jumlah cuplikan [5]. Apabila jumlah data belum memenuhi N/2 maka akan dihitung kembali dengan metode kupu-kupu.…”

Section: Gambar 2 Diagram Konseptual Rtl-sdr[4]unclassified