Type-II/III DCT/DST algorithms with reduced number of arithmetic operations

Authors:
Xuancheng Shao;Steven G. Johnson
Affiliations:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Venue:
Signal Processing
Year:
2008

Citing 22
Cited 4

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

Signal Processing
Discrete cosine transform: algorithms, advantages, applications

Discrete cosine transform: algorithms, advantages, applications
Computational frameworks for the fast Fourier transform

Computational frameworks for the fast Fourier transform
Numerical recipes in C (2nd ed.): the art of scientific computing

Numerical recipes in C (2nd ed.): the art of scientific computing
Accuracy of the Discrete Fourier Transform and the Fast Fourier Transform

SIAM Journal on Scientific Computing
A fast Fourier transform compiler

Proceedings of the ACM SIGPLAN 1999 conference on Programming language design and implementation
JPEG Still Image Data Compression Standard

JPEG Still Image Data Compression Standard
The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

SIAM Journal on Computing
A new matrix approach to real FFTs and convolutions of length 2k

Computing
Discrete Cosine Transfom

IEEE Transactions on Computers
A Storage Efficient Way to Implement the Discrete Cosine Transform

IEEE Transactions on Computers
On Computing the Discrete Cosine Transform

IEEE Transactions on Computers
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

Signal Processing
Fast Fourier Transforms: for fun and profit

AFIPS '66 (Fall) Proceedings of the November 7-10, 1966, fall joint computer conference
An economical method for calculating the discrete Fourier transform

AFIPS '68 (Fall, part I) Proceedings of the December 9-11, 1968, fall joint computer conference, part I
Restructured recursive DCT and DST algorithms

IEEE Transactions on Signal Processing
A Modified Split-Radix FFT With Fewer Arithmetic Operations

IEEE Transactions on Signal Processing
Architecture-oriented regular algorithms for discrete sine andcosine transforms

IEEE Transactions on Signal Processing
Constant geometry algorithm for discrete cosine transform

IEEE Transactions on Signal Processing
A new algorithm to compute the DCT and its inverse

IEEE Transactions on Signal Processing
Fast algorithm for computing discrete cosine transform

IEEE Transactions on Signal Processing
On the multiplicative complexity of discrete cosine transforms

IEEE Transactions on Information Theory

Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

Signal Processing
Real-time fluid simulation using discrete sine/cosine transforms

Proceedings of the 2009 symposium on Interactive 3D graphics and games
Novel VLSI algorithm and architecture with good quantization properties for a high-throughput area efficient systolic array implementation of DCT

EURASIP Journal on Advances in Signal Processing - Special issue on quantization of VLSI digital signal processing systems
Improvement of the Discrete Cosine Transform calculation by means of a recursive method

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.08

Visualization

Abstract

We present algorithms for the discrete cosine transform (DCT) and discrete sine transform (DST), of types II and III, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from 2Nlog"2N+O(N) to 179Nlog"2N+O(N) for a power-of-two transform size N. Furthermore, we show that an additional N multiplications may be saved by a certain rescaling of the inputs or outputs, generalizing a well-known technique for N=8 by Arai et al. These results are derived by considering the DCT to be a special case of a DFT of length 4N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split-radix algorithm). The improved algorithms for the DCT-III, DST-II, and DST-III follow immediately from the improved count for the DCT-II.