Proceedings ArticleDOI
Fast algorithms for the discrete Fourier transform and for other transforms
N. Suehiro,M. Hatori +1 more
- Vol. 11, pp 217-220
TLDR
A new matrix factorization is proposed for DCT-IV, which is the basis of fast algorithms for many sinusoidal transforms and a new fast algorithm for complex-data DFT based on the new factorization requires the same number of multiplications and far fewer additions than the Preuss algorithm.Abstract:
A new matrix factorization is proposed for DCT-IV, which is the basis of fast algorithms for many sinusoidal transforms. A new fast algorithm for complex-data DFT based on the new factorization requires the same number of multiplications and far fewer additions than the Preuss algorithm. A new fast algorithm for real-data DFT based on a new algorithm for the discrete Hartley transform is also proposed.read more
Citations
More filters
Journal ArticleDOI
Short communication: the fast DCT-IV/DST-IV computation via the MDCT
TL;DR: The careful analysis of regular structure of the new fast MDCT algorithm allows to extract a new DCT-IV/DST-IV computational structure and to suggest a new sparse matrix factorization of the D CT-IV matrix.
Book ChapterDOI
CHAPTER 5 – Integer Discrete Cosine/Sine Transforms
TL;DR: The discrete cosine transforms (DCTs) and discrete sine transform (DSTs) are real-valued transforms that map integer-valued signals to floating-point coefficients as discussed by the authors.
Proceedings ArticleDOI
Multiple-transform pipelines for image coding
TL;DR: Pipelined VLSI/WSI architectures supporting image coding transforms support flexible structures characterized by a “basic” pipeline - performing the common kernel of computation - and by transform-dependent input and output stages.
Book ChapterDOI
Chapter 4 - Fast DCT/DST Algorithms
TL;DR: In this paper, fast 1-D and 2-D DCT/DST algorithms for all even types of the discrete cosine transform and discrete sine transform (DST) are discussed.
Dissertation
Sparse Fast Trigonometric Transforms
TL;DR: This thesis develops sublinear algorithms for the fast Fourier transform for frequency sparse periodic functions and presents two different new, deterministic and sub linear algorithms for this problem based on inverse discrete Fourier transforms and complex arithmetic.
References
More filters
Journal ArticleDOI
A new algorithm to compute the discrete cosine Transform
TL;DR: A new algorithm is introduced for the 2m-point discrete cosine transform that reduces the number of multiplications to about half of those required by the existing efficient algorithms, and it makes the system simpler.
Journal ArticleDOI
Fast algorithms for the discrete W transform and for the discrete Fourier transform
TL;DR: A systematic method of sparse matrix factorization is developed for all four versions of the discrete W transform, the discrete cosine transform, and the discrete sine transform as well as for the discrete Fourier transform, which makes new algorithms more efficient than conventional algorithms.
Journal ArticleDOI
The fast Hartley transform
TL;DR: The Fast Hartley Transform (FHT) is as fast as or faster than the Fast Fourier Transform (FFT) and serves for all the uses such as spectral analysis, digital processing, and convolution to which the FFT is at present applied.
Journal ArticleDOI
Very fast computation of the radix-2 discrete Fourier transform
TL;DR: An algorithm that reduces the computational effort to two-thirds of the effort required by most radix-2 algorithms and its structure is particularly appealing when transforming pure real or imaginary sequences and/or symmetric or antisymmetric sequences.