H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. Acoust., Speech, Signal Proc., 31(2):378--387, April 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....over split trees with no leaves of , the total number of trees that need to be timed can be greatly reduced, but still becomes intractable at larger sizes. A common approach for searching the very large space of possible implementations of signal transforms has been to use dynamic programming [Johnson and Burrus, 1983; Frigo and Johnson, 1998; Haentjens, 2000; Sepiashvili, 2000] This approach maintains a list of the fastest formulas it has found for each transform and size. When trying to find the fastest formula for a particular transform and size, it considers all possible splits of the root node. For each ....

H. Johnson and C. Burrus. The design of optimal DFT algorithms using dynamic programming. In IEEE Transactions on Acoustics, Speech, and Signal Processing, volume 31, 1983.

....space of formulas. We have implemented the following search methods. Exhaustive Search: Determines the fastest formula, but becomes infeasible even at modest transform sizes since there is a large number of formulas. Dynamic Programming: A common approach has been to use dynamic programming (DP) [15]. DP maintains a list of the fastest formulas it has found for each transform and size. For a particular transform and its applicable rules, DP considers all possible sets of children. For each child, DP substitutes the best ruletree found for that transform. DP makes the assumption that the ....

H. W. Johnson and C. S. Burrus, "The design of optimal DFT algorithms using dynamic programming," [EEE Trans, on Acoustics, Speech, and Signal Processing, vol. ASSP-31, pp. 378 387, 1983.

....number of trees that need to be timed can be greatly reduced (for example, from 51,819 to 101 trees for size 2) but still becomes intractable at larger sizes. A common approach for searching the very large space of possible implementations of signal transforms has been to use dynamic programming [19], 10] 20] 21] This approach maintains a list of the fastest formulas it has found for each transform and size. When trying to find the fastest formula for a particular transform and size, it considers all possible splits of the root node. For each child of the root node, dynamic programming ....

Howard W. Johnson and C. Sidney Burrus, "The design of optimal DFT algorithms using dynamic programming," in IEEE Transactions on Acoustics, Speech, and Signal Processing, April 1983, vol. 31, pp. 378 387.

....numbers without the exponent delimiter E , and this makes them illegal in FORTRAN statements. 152 FFT algorithm. This program is limited to complex transforms of size n,wheren must be factorable into mutually prime factors in the set #; #; #; #; #; #; ###. Johnson and Burrus [86] applied dynamic programming to the automatic design of DFT modules. Selesnick and Burrus [131] used a program to generate MATLAB subroutines for DFT s of certain prime sizes. In many cases, these subroutines are the best known in terms of arithmetic complexity. The EXTENT system by Gupta and ....

H. W. JOHNSON AND C. S. BURRUS, The design of optimal DFT algorithms using dynamic programming, IEEE Transactions on Acoustics, Speech and Signal Processing, 31 (1983), pp. 378--387.

....space of formulas. We have implemented the following search methods. Exhaustive Search: Determines the fastest formula, but becomes infeasible even at modest transform sizes since there is a large number of formulas. Dynamic Programming: A common approach has been to use dynamic programming (DP) [15]. DP maintains a list of the fastest formulas it has found for each transform and size. For a particular transform and its applicable rules, DP considers all possible sets of children. For each child, DP substitutes the best ruletree found for that transform. DP makes the assumption that the ....

H. W. Johnson and C. S. Burrus, "The design of optimal DFT algorithms using dynamic programming," IEEE Trans, on Acoustics, Speech, and Signal Processing, vol. ASSP-31, pp. 378--387, 1983.

....(The fractional Fourier transform, announced many years later in [8] is the same as the chirp z transform. An alternative to Bluestein s trick is Winograd s method in [111] Special cases of Winograd s method were published earlier by Rader in [81] and by Singleton in [94] See also [4] 22] [50], 52] 58] and [117] For results on the problem of decomposing non commutative group rings, see, e.g. 26] 8. Good s trick Let R be a ring. Let m;n be coprime positive integers. Good s trick means mapping R[x] x mn 1) to the isomorphic ring (R[y] y m 1) z] z n 1) by x 7 yz. ....

Howard W. Johnson, C. Sidney Burrus, The design of optimal DFT algorithms using dynamic programming, IEEE Transactions on Acoustics, Speech, and Signal Processing 31 (1983), 378-387.

....In addition, a basic dynamic programming strategy for drastically reducing the size of the search space of decompositions is applied to find efficient decompositions. The concept of dynamic programming is introduced in [2] and an explanation of dynamic programming applied to FFTs is provided in [6]. Two more sophisticated versions of dynamic programming are introduced in this chapter and are compared to the basic dynamic programming. Finally, the features of the optimal decompositions for FFTs of size up to 2 20 are investigated. 2.2 Methodology 2.2.1 An Original FFT Program In order to ....

Howard W. Johnson and C. Sidney Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Transactions on Acoustics, Speech, and Signal Processing, 31:378--387, April 1983.

....factor algorithm (PFA) which 4 uses an index map developed by Thomas and Good, 14] Prime factorization is slow when n is large, but the DFT for small cases, such as n = 2; 3; 4; 5; 7; 8; 11; 13; 16, can be made fast using the Winograd algorithm, 8, 16, 17, 18] H. W. Johnson and C. S. Burrus, [15], developed a method to use dynamic programming to design optimal FFT programs by reducing the number of ops as well as data transfers. This approach designs custom algorithms for particular computer architectures. Ecient programs have been developed to implement the split radix FFT algorithm, ....

H. W. Johnson and C. S. Burrus, \The Design of Optimal DFT Algorithms using Dynamic Programming," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 31, pp. 378-387, April 1983.

....numbers without the exponent delimiter E , and this makes them illegal in FORTRAN statements. FFT algorithm. This program is limited to complex transforms of size n, where n must be factorable into mutually prime factors in the set f2; 3; 4; 5; 7; 8; 9; 16g. Johnson 9 and Burrus [86] applied dynamic programming to the automatic design of DFT modules. Selesnick and Burrus [131] used a program to generate MATLAB subroutines for DFT s of certain prime sizes. In many cases, these subroutines are the best known in terms of arithmetic complexity. The EXTENT system by Gupta and ....

H. W. JOHNSON AND C. S. BURRUS, The design of optimal DFT algorithms using dynamic programming, IEEE Transactions on Acoustics, Speech and Signal Processing, 31 (1983), pp. 378--387.

....size 2 k . Perez and Takaoka [PT87] present a generator of Pascal programs implementing a prime factor FFT algorithm. This program is limited to complex transforms of size n, where n must be factorable into mutually prime factors in the set f2; 3; 4; 5; 7; 8; 9; 16g. Johnson 5 and Burrus [JB83] applied dynamic programming to the automatic design of DFT modules. Selesnick and Burrus [SB96] used a program to generate MATLAB subroutines for DFTs of certain prime sizes. In many cases, these subroutines are the best known in terms of arithmetic complexity. The EXTENT system by Gupta and ....

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Transactions on Acoustics, Speech and Signal Processing, 31:378--387, April 1983.

No context found.

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. Acoust., Speech, Signal Proc., 31(2):378--387, April 1983.

No context found.

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. on Acoustics, Speech, and Signal Processing, ASSP-31:378--387, 1983.

No context found.

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. on Acoustics, Speech, and Signal Processing, ASSP-31:378--387, 1983.

No context found.

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. on Acoustics, Speech, and Signal Processing, ASSP-31:378--387, 1983.

....of a PFA or WFTA algorithm depend upon the availability of prime length FFT modules. As such, prime length Fast Fourier Transforms are a special, important and difficult case. Fast algorithms designed for specific short prime lengths have been developed and have been written as straight line code [7, 9]. These dedicated programs rely upon an observation made in Rader s paper [15] in which he shows that a prime p length DFT can be found by performing a p Gamma 1 length circular convolution. Since the publication of that paper, Winograd had developed a theory of multiplicative complexity for ....

....length and the variety of lengths of a prime factor algorithm or a Winograd Fourier transform algorithm. Furthermore, because the approach taken in this paper gives a bilinear form, it can be incorporated into the dynamic programming technique for designing optimal composite length FFT algorithms [7]. The programs described in this paper can also be adapted to obtain discrete cosine transform (DCT) algorithms by simply permuting the input and output sequences [6] 19 A A 31 Point FFT Program As an example, we list a 31 point FFT program. The matrix D 2 , used in the program, is part of the ....

[Article contains additional citation context not shown here]

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. on Acoust., Speech, Signal Proc., 31(2):378--387, April 1983.

....of a PFA or WFTA algorithm depend upon the availability of prime length FFT modules. As such, prime length Fast Fourier Transforms are a special, important and difficult case. Fast algorithms designed for specific short prime lengths have been developed and have been written as straight line code [7, 9]. These dedicated programs rely upon an observation made in Rader s paper [14] in which he shows that a prime p length DFT can be found by performing a p Gamma 1 length circular convolution. Since the publication of that paper, Winograd had developed a theory of multiplicative complexity for ....

....length and the variety of lengths of a prime factor algorithm or a Winograd Fourier transform algorithm. Furthermore, because the approach taken in this paper gives a bilinear form, it can be incorporated into the dynamic programming technique for designing optimal composite length FFT algorithms [7]. The programs described in this paper can also be adapted to obtain discrete cosine transform (DCT) algorithms by simply permuting the input and output sequences [6] A A 31 POINT FFT PROGRAM 22 A A 31 Point FFT Program As an example, we list a 31 point FFT program. function y = ....

[Article contains additional citation context not shown here]

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. Acoust., Speech, Signal Proc., 31(2):378--387, April 1983.

....algorithm proposed above can also be employed in PFA modules. Moreover, since the approach above gives a bilinear form, it can be used in the Winograd Fourier transform algorithm or incorporated into the dynamic programming technique for designing optimal composite length FFT algorithms [3]. 6 Summary We have given a similarity that makes explicit the equivalence of scalar and matrix cyclotomic convolutions. By employing this similarity we replace long cyclotomic convolutions with shorter matrix convolutions, thereby reducing the overall arithmetic complexity for the circular ....

H. W. Johnson and C. S. Burrus. The design of optimal DFT algorithms using dynamic programming. IEEE Trans. Acoust., Speech, Signal Proc., 31(2):378--387, April 1983.

....the FFT can be found in [9] or in classical textbooks such as [6] Previous work exists on automatic generation of FFT programs: 10] describes the generation of FFT programs for prime sizes, and [11] presents a generator of Pascal programs implementing a Prime Factor algorithm. Johnson and Burrus [12] first applied dynamic programming to the design of optimal DFT modules. Although these papers all deal with the arithmetic complexity of the FFT, we are not aware of previous work where these techniques are used to maximize the actual performance of a program. The behavior of the FFT in the ....

H. W. Johnson and C. S. Burrus, "The design of optimal DFT algorithms using dynamic programming," IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 31, pp. 378--387, Apr. 1983.

No context found.

H. W. Johnson and C. S. Burrus, "The design of optimal DFT algorithms using dynamic programming," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, pp. 169--181, Feb. 1983.

No context found.

H. Johnson and C. Burrus. The Design of Optimal DFT Algorithms Using Dynamic Programming. IEEE Transactions on Acoustics, Speech, and Signal Processing, 31:378--387, April 1983.

No context found.

H. W. Johnson and C. S. Burrus, The Design of Optimal DFT Algorithms Using Dynamic Programming, IEEE Trans. Acoust. Speech Signal Processing, vol. 31, pp. 378-387, 1983.

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