Name
Abstract | ||
|---|---|---|
A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record by requiring just 4n log n - 6n + 8 arithmetic operations on real numbers for a size-n DFT, and was widely believed to be the best possible. Recent work by Van Buskirk et al. demonstrated improvements to the split-radix operation count by using multiplier coefficients or "twiddle factors" that are not n-th roots of unity for a size-n DFT. This paper presents a Boolean Satisfiability-based proof of the lowest operation count for certain classes of DFT algorithms. First, we present a novel way to choose new yet valid twiddle factors for the nodes in flowgraphs generated by common power-of-two fast Fourier transform algorithms, FFTs. With this new technique, we can generate a large family of FFTs realizable by a fixed flowgraph. This solution space of FFTs is cast as a Boolean Satisfiability problem, and a modern Satisfiability Modulo Theory solver is applied to search for FFTs requiring the fewest arithmetic operations. Surprisingly, we find that there are FFTs requiring fewer operations than the split-radix even when all twiddle factors are n-th roots of unity. |
Year | Venue | Keywords |
|---|---|---|
2011 | Clinical Orthopaedics and Related Research | discrete fourier transform,boolean satisfiability,symbolic computation,satisfiability modulo theories,information theory,fast fourier transform,roots of unity |
DocType | Volume | Issue |
Journal | 7 | 4 |
ISSN | Citations | PageRank |
Journal on Satisfiability, Boolean Modeling and Computation,
7:145-187, 2011 | 2 | 0.45 |
References | Authors | |
25 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Steve Haynal | 1 | 32 | 3.59 |
| Heidi Haynal | 2 | 2 | 0.45 |