Journal ArticleDOI
A new look at DCT-type transforms
TLDR
The proposed transform offers a higher computational efficiency than the traditional even discrete cosine transform and yields a mean-squared error close to that of the DCT.Abstract:
A computationally efficient DCT- (discrete-cosine-transform) type orthogonal transform obtained by using a construction method developed by W. Kou and H. Zu (1986) is proposed. A recursive relation exists between a higher order and a lower order form of the kernel matrix of the transform and includes the DCT matrices as submatrices. The characteristics of the proposed transform and several fast transform algorithms are discussed. The proposed transform offers a higher computational efficiency than the traditional even discrete cosine transform and yields a mean-squared error close to that of the DCT. Since the HDCT has window spectral structures, it can be used in signal filtering and speech and image processing. >read more
Citations
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Journal ArticleDOI
Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Journal ArticleDOI
Unified parallel lattice structures for time-recursive discrete cosine/sine/Hartley transforms
K.J.R. Liu,Ching-Te Chiu +1 more
TL;DR: It is shown that the DCT, DST, DHT and their inverse transforms share an almost identical lattice structure so that they are very suitable for VLSI implementation for high-speed applications.
Journal ArticleDOI
Optimal unified architectures for the real-time computation of time-recursive discrete sinusoidal transforms
TL;DR: The authors provide a theoretical justification by showing that any discrete transform whose basis functions satisfy the fundamental recurrence formula has a second-order autoregressive structure in its filter realization and extend these time-recursive concepts to multi-dimensional transforms.
Journal ArticleDOI
An efficient CORDIC array structure for the implementation of discrete cosine transform
Yu Hen Hu,Zhenyang Wu +1 more
TL;DR: A novel implementation of the discrete cosine transform (DCT) and the inverse DCT (IDCT) algorithms using a CORDIC (coordinate rotation digital computer)-based systolic processor array structure to speed up the DCT and IDCT computation.
References
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Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Journal ArticleDOI
Discrete Cosine Transform
TL;DR: In this article, a discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed, which can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering.
Journal ArticleDOI
A Fast Computational Algorithm for the Discrete Cosine Transform
TL;DR: A Fast Discrete Cosine Transform algorithm has been developed which provides a factor of six improvement in computational complexity when compared to conventional DiscreteCosine Transform algorithms using the Fast Fourier Transform.