Journal ArticleDOI
The discreteW transform
Zhongde Wang,B. R. Hunt +1 more
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TLDR
The relationship among different versions of DWT and their relation with the discrete Fourier transform (DFT) are given and Convolution theorems represented by different version of the DWT are derived.About:
This article is published in Applied Mathematics and Computation.The article was published on 1985-01-01. It has received 120 citations till now. The article focuses on the topics: Discrete sine transform & Discrete Hartley transform.read more
Citations
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Journal ArticleDOI
The Discrete Cosine Transform
TL;DR: A direct proof of orthogonality, by calculating inner products, does not reveal how natural these cosine vectors are, so this work proves orthog onality in a different way.
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Symmetric convolution and the discrete sine and cosine transforms
TL;DR: The author defines symmetric convolution, relates the DSTs and DCTs to symmetric-periodic sequences, and then uses these principles to develop simple but powerful convolution-multiplication properties for the entire family of DST sine and cosine transforms.
A fast Karhunen-Loeve transform for a class of random processes
TL;DR: The Karhunter-Loeve transform for a class of signals is proven to be a set of periodic sine functions and this Karhunen- Loeve series expansion can be obtained via an FFT algorithm, which could be useful in data compression and other mean-square signal processing applications.
Journal ArticleDOI
Spiral: A Generator for Platform-Adapted Libraries of Signal Processing Algorithms
Markus Püschel,Jose M. F. Moura,Bryan Singer,Jianxin Xiong,Jeremy Johnson,David Padua,Manuela Veloso,Robert W. Johnson +7 more
TL;DR: The main components of SPIRAL are described: the mathematical framework that concisely describes signal transforms and their fast algorithms; the formula generator that captures at the algorithmic level the degrees of freedom in expressing a particular signal processing transform; a formula translator that encapsulates the compilation degrees offreedom when translating a specific algorithm into an actual code implementation.
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Algebraic Signal Processing Theory: Foundation and 1-D Time
Markus Püschel,Jose M. F. Moura +1 more
TL;DR: The paper illustrates the general ASP theory with the standard time shift, presenting a unique signal model for infinite time and several signal models for finite time and the latter models illustrate the role played by boundary conditions and recover the discrete Fourier transform and its variants as associated Fourier transforms.
References
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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.
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Hadamard transform image coding
TL;DR: A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed, which provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.
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A Sinusoidal Family of Unitary Transforms
TL;DR: 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.
Journal ArticleDOI
A Fast Karhunen-Loeve Transform for a Class of Random Processes
TL;DR: In this paper, the Karhunen-Loeve transform for a class of signals is proven to be a set of periodic sine functions and this k-means expansion can be obtained via an FFT algorithm.
A fast Karhunen-Loeve transform for a class of random processes
TL;DR: The Karhunter-Loeve transform for a class of signals is proven to be a set of periodic sine functions and this Karhunen- Loeve series expansion can be obtained via an FFT algorithm, which could be useful in data compression and other mean-square signal processing applications.