Journal ArticleDOI
A Sinusoidal Family of Unitary Transforms
TLDR
A new family of unitary transforms is introduced and it is shown that the well-known discrete Fourier, cosine, sine, and the Karhunen-Loeve (KL) (for first-order stationary Markov processes) transforms are members of this family.Abstract:
A new family of unitary transforms is introduced. It is shown that the well-known discrete Fourier, cosine, sine, and the Karhunen-Loeve (KL) (for first-order stationary Markov processes) transforms are members of this family. All the member transforms of this family are sinusoidal sequences that are asymptotically equivalent. For finite-length data, these transforms provide different approximations to the KL transform of the said data. From the theory of these transforms some well-known facts about orthogonal transforms are easily explained and some widely misunderstood concepts are brought to light. For example, the near-optimal behavior of the even discrete cosine transform to the KL transform of first-order Markov processes is explained and, at the same time, it is shown that this transform is not always such a good (or near-optimal) approximation to the above-mentioned KL transform. It is also shown that each member of the sinusoidal family is the KL transform of a unique, first-order, non-stationary (in general), Markov process. Asymptotic equivalence and other interesting properties of these transforms can be studied by analyzing the underlying Markov processes.read more
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On discrete cosine transform
TL;DR: In this paper, a generalized discrete cosine transform with three parameters was proposed and its orthogonality was proved for some new cases, and a new type of DCT was also proposed.
Journal ArticleDOI
Fast fourier transforms: a tutorial review and a state of the art
Pierre Duhamel,Martin Vetterli +1 more
TL;DR: Note: V. Madisetti, D. B. Williams, Eds.
Fast Fourier transforms: a tutorial review and a state of the art
Pierre Duhamel,Martin Vetterli +1 more
TL;DR: MadMadisetti, D. B. Williams, Eds. as discussed by the authors, LCAV-2005-009 Record created on 2005-06-27, modified on 2017-05-12
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Image data compression: A review
TL;DR: A large variety of algorithms for image data compression are considered, starting with simple techniques of sampling and pulse code modulation (PCM) and state of the art algorithms for two-dimensional data transmission are reviewed.
References
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TL;DR: The utility and effectiveness of these transforms are evaluated in terms of some standard performance criteria such as computational complexity, variance distribution, mean-square error, correlated rms error, rate distortion, data compression, classification error, and digital hardware realization.