Journal ArticleDOI
Computation of discrete cosine transform using Clenshaw's recurrence formula
TLDR
Clenshaw's recurrence formula provides a unified development for the recursive DCT and IDCT algorithms and applies to arbitrary length algorithms and are appropriate for VLSI implementation.Abstract:
Clenshaw's recurrence formula is used to derive recursive algorithms for the discrete cosine transform (DCT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented requires one fewer delay element per coefficient and one fewer multiply operation per coefficient compared with two other proposed methods. Clenshaw's recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The recursive algorithms apply to arbitrary length algorithms and are appropriate for VLSI implementation. >read more
Citations
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Book ChapterDOI
CHAPTER 1 – Discrete Cosine and Sine Transforms
TL;DR: The book presents the complete set of discrete cosine transforms and discrete sine transforms constituting the entire class of discrete sinusoidal unitary transforms, including their definitions, general mathematical properties, relations to the Karhunen-Loeve transform, with the emphasis on fast algorithms and integer approximations for their efficient implementations in the integer domain.
Journal ArticleDOI
Recursive computation of Tchebichef moment and its inverse transform
Guobao Wang,Shigang Wang +1 more
TL;DR: Both a direct recursive algorithm and a compact algorithm are developed for the computation of Tchebichef moment, suitable for parallel VLSI implementation due to their regular and simple filter structures.
Journal ArticleDOI
Recursive architectures for realizing modified discrete cosine transform and its inverse
TL;DR: The analyzed results show that the proposed recursive infinite-impulse response (IIR) structures possess advantages of high efficiency and high throughput rate.
Journal ArticleDOI
Computation of forward and inverse MDCT using Clenshaw's recurrence formula
V. Nikolajevic,Gerhard Fettweis +1 more
TL;DR: This paper used Clenshaw's recurrence formula to transform kernels of the MDCT and IMDCT of the general length and achieved significant savings for a number of operations compared with existing related systems.
Proceedings ArticleDOI
An efficient unified systolic architecture for the computation of discrete trigonometric transforms
Wen-Hsien Fang,Ming-Lu Wu +1 more
TL;DR: A novel unified systolic architecture which can efficiently implement various discrete trigonometric transforms (DXT) including the discrete Fourier transform (DFT), the discrete Hartley transform, the discrete cosine transform, and the discrete sine transform is described.
References
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Journal ArticleDOI
Recursive algorithm for the discrete cosine transform with general lengths
Lap-Pui Chau,W.-C. Siu +1 more
TL;DR: A novel VLSI algorithm for computing the discrete cosine transform of variable length by using some mathematical techniques, which is particularly suitable for the real-time computation of the DCT and can be implemented using regular and parallel V LSI structures, so that the computational complexity is greatly reduced.
Journal ArticleDOI
Recursive algorithms for the forward and inverse discrete cosine transform with arbitrary length
TL;DR: The authors first demonstrate that the forward and inverse discrete cosine transform (DCT, IDCT) can be represented by Chebyshev polynomials of the third and second kind, respectively, and derive recursive algorithms for the DCT and IDCT with arbitrary length from the recursive formulae for the Chebyshemials.
Journal ArticleDOI
Efficient implementation of discrete cosine transform using recursive filter structure
TL;DR: A formulation for converting a length-2/sup n/ discrete cosine transform into n groups of equations is generalized and converted into recursive filter form, which is particularly simple for practical implementation.
Related Papers (5)
Recursive algorithms for the forward and inverse discrete cosine transform with arbitrary length
Recursive algorithm for the discrete cosine transform with general lengths
Lap-Pui Chau,W.-C. Siu +1 more