A fast algorithm for the discrete sine transform implemented by the fast cosine transform

1982 ◽  
Vol 30 (5) ◽  
pp. 814-815 ◽  
Author(s):  
Zhong-De Wang
Keyword(s):  
Fast Algorithm ◽  
Cosine Transform ◽  
Sine Transform

scholarly journals Improved Algorithm for ODCT Computation of a Running Data Sequence

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
S. Akhter ◽  
V. Karwal ◽  
R. C. Jain
Keyword(s):  
Real Time ◽  
Discrete Cosine Transform ◽  
Input Data ◽  
Time Sequence ◽  
Data Sequence ◽  
Cosine Transform ◽  
Rectangular Window ◽  
Sine Transform ◽  
Data Points ◽  
Transform Coefficients

Fast windowed update algorithms capable of independently updating the odd discrete cosine transform (ODCT) and odd discrete sine transform (ODST) of a running data sequence are analytically developed. In this algorithm, to compute the ODCT coefficients of a real-time sequence, we do not require the ODST coefficients. Similarly, the ODST coefficients of the shifted sequence can be calculated without using ODCT coefficients. The running input data sequence is sampled using a rectangular window. However, this idea can be easily extended for other windows. The update algorithm derived herein can be used to compute the transform coefficients of the shifted sequence as new data points are available. The complexity of developed algorithm isO(N). The validity of algorithm is tested by MATLAB simulations.

FOURIER SINE AND COSINE TRANSFORMS ON BOEHMIAN SPACES

2013 ◽  
Vol 06 (01) ◽  
pp. 1350005 ◽  
Author(s):  
R. Roopkumar ◽  
E. R. Negrin ◽  
C. Ganesan
Keyword(s):  
Fourier Transform ◽  
Cosine Transform ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Fourier Cosine Transform ◽  
One To One ◽  
The Fourier Transform

We construct suitable Boehmian spaces which are properly larger than [Formula: see text] and we extend the Fourier sine transform and the Fourier cosine transform more than one way. We prove that the extended Fourier sine and cosine transforms have expected properties like linear, continuous, one-to-one and onto from one Boehmian space onto another Boehmian space. We also establish that the well known connection among the Fourier transform, Fourier sine transform and Fourier cosine transform in the context of Boehmians. Finally, we compare the relations among the different Boehmian spaces discussed in this paper.

New fast algorithm of 2-D discrete cosine transform

1995 ◽  
Vol 12 (3) ◽  
pp. 270-275
Author(s):  
Wang Xincheng ◽  
Zhou Xiaoming ◽  
Lu Jie ◽  
Zhu Weile
Keyword(s):  
Discrete Cosine Transform ◽  
Fast Algorithm ◽  
Cosine Transform

A fast algorithm forn-D discrete cosine transform

1998 ◽  
Vol 41 (1) ◽  
pp. 45-54
Author(s):  
Zhishun Wang ◽  
Wenhua Li ◽  
Zhenya He
Keyword(s):  
Discrete Cosine Transform ◽  
Fast Algorithm ◽  
Cosine Transform

Fast Algorithms and Architectures for 8-Point DST-II/DST-VII Approximations

2016 ◽  
Vol 26 (03) ◽  
pp. 1750045
Author(s):  
Renato J. Cintra ◽  
Fábio M. Bayer ◽  
Arjuna Madanayake ◽  
Uma S. Potluri ◽  
Amila Edirisuriya
Keyword(s):  
Video Compression ◽  
Video Processing ◽  
Fast Algorithm ◽  
Circuit Complexity ◽  
Fast Algorithms ◽  
Type Ii ◽  
Search Methods ◽  
Sine Transform ◽  
Image And Video Compression

Multiplier-free fast algorithms are derived and analyzed for realizing the 8-point discrete sine transform of type II and type VII (DST-II and DST-VII) transforms with applications in image and video compression. A new fast algorithm is identified using numerical search methods for approximating DST-VII without employing multipliers. In addition, recently proposed fast algorithms for approximating the 8-point DCT-II are now extended to approximate DST-II. All proposed approximations for DST-II and DST-VII are compared with ideal transforms, and circuit complexity is measured using FPGA-based rapid prototypes on a 90[Formula: see text]nm Xilinx Virtex-4 device. The proposed architectures find applications in emerging video processing standards such as H.265/HEVC.

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