Journal ArticleDOI
Logical convolution and discrete Walsh and Fourier power spectra
TLDR
The Walsh power spectrum of a sequence of random samples is defined as the Walsh transform of the logical autocorrelation function of the random sequence and the Fourier power spectrum can be obtained from the Walsh power Spectrum by a linear transformation.Abstract:
The Walsh power spectrum of a sequence of random samples is defined as the Walsh transform of the logical autocorrelation function of the random sequence. The "logical" autocorrelation function is defined in a similar form as the "arithmetic" autocorrelation function. The Fourier power spectrum, which is defined as the Fourier transform of the arithmetic autocorrelation function, can be obtained from the Walsh power spectrum by a linear transformation. The recursive relations between the logical and arithmetic auto-correlation functions are derived in this paper. For a given process with computed or modeled autocorrelation function the Fourier and Walsh power spectra are computed by using the fast Fourier and Walsh transforms, respectively. Examples are given from the speech and imagery data.read more
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Dissertation
An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing
TL;DR: An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing was proposed in this paper, which is applicable to both single and multi-pixel cameras.
Journal ArticleDOI
Fast one-dimensional digital convolution by multidimensional techniques
R. Agarwal,C. Burrus +1 more
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Journal ArticleDOI
Walsh-Fourier Analysis and its Statistical Applications
TL;DR: The need for Walsh-Fourier analysis is explained, the history and properties of Walsh functions are reviewed, and the existing Walsh-fourier theory for real-time stationary time series is outlined.
Journal ArticleDOI
Natural, Dyadic, and Sequency Order Algorithms and Processors for the Walsh-Hadamard Transform
Geadah,Corinthios +1 more
TL;DR: The Walsh-Hadamard transform has recently received increasing attention in engineering applications due to the simplicity of its implementation and to its properties which are similar to the familiar Fourier transform.
References
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Journal ArticleDOI
A Comparison of Orthogonal Transformations for Digital Speech Processing
S. Campanella,G. Robinson +1 more
TL;DR: Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals and these bit-rate reductions are shown to be somewhat independent of the transmission bit rate.
Journal ArticleDOI
Application of Walsh Functions to Transform Spectroscopy
J. E. Gibbs,H. A. Gebbie +1 more
TL;DR: In this article, Walsh functions are used in transform Spectroscopy to replace the sinusoidal functions appearing in the Fourier transform, and they take only the values + 1 and − 1 and are therefore suitable for the binary digital computer.